Using Physician Prescribing Preference as an Instrumental Variable: A Comprehensive Guide for Causal Inference in Clinical Research

Abstract

This article provides a comprehensive overview of the use of Physician Prescribing Preference (PPP) as an instrumental variable (IV) in comparative effectiveness research and pharmacoepidemiology. It explores the foundational assumptions and theoretical underpinnings of the IV approach, drawing parallels to randomization. The content details practical methodologies for constructing PPP proxies from prescription data, applying IV estimation techniques like two-stage least squares, and addresses complex scenarios including time-varying treatments. It further examines common pitfalls, optimization strategies for different sample sizes, and validation techniques to assess instrument strength and balance. By synthesizing recent simulation studies and systematic reviews, this guide offers evidence-based recommendations to enhance the validity and application of PPP IV in biomedical research, helping researchers navigate the challenges of unmeasured confounding in observational data.

Laying the Groundwork: Core Principles and Assumptions of the PPP Instrumental Variable

In observational studies designed to estimate causal treatment effects, confounding by indication presents a major methodological challenge. Patients who receive a particular drug often differ systematically from those who do not, and these differences can be related to their subsequent outcomes. Instrumental variable (IV) analysis is a statistical technique that can potentially overcome this issue by leveraging natural variation in treatment assignment that is unrelated to patient risk factors. Among the proposed instruments in pharmacoepidemiology, Physician's Prescribing Preference (PPP) has emerged as a particularly influential one. The core concept, as proposed by Brookhart et al., is that a physician's inherent preference for one drug over another can influence the prescription their patient receives, yet this preference is ideally unrelated to the individual patient's unmeasured risk factors for the outcome [1]. This creates a source of quasi-random variation in treatment assignment that can be exploited for causal inference.

However, a physician's underlying preference is a latent variable—it cannot be directly observed or measured. Therefore, a central methodological question is: how can this abstract concept be operationalized into a concrete, measurable variable for use in statistical models? This document provides detailed application notes and protocols for defining the PPP instrument, framing it within the broader context of IV research for an audience of researchers, scientists, and drug development professionals. The ensuing sections synthesize evidence from simulation studies and applied research to outline the core assumptions, recommend practical operationalization strategies, and provide a toolkit for validating the chosen instrument.

Core Assumptions and Instrument Validity

For a Physician's Prescribing Preference to function as a valid instrumental variable, it must satisfy three critical assumptions. The causal pathways and relationships underpinning these assumptions are illustrated in the diagram below.

Causal Pathways for a Valid PPP Instrument

• Relevance: The instrument must be a strong predictor of the actual treatment received by the patient. If the measured PPP does not consistently correlate with the prescription decision, it is a "weak instrument," leading to biased estimates and inflated variance [2] [1].
• Exchangeability: The instrument must be independent of both measured and unmeasured confounders. In other words, patients whose treatment is influenced by their physician's preference should not systematically differ in their risk profiles from patients treated differently by another physician [3] [1].
• Exclusion Restriction: The instrument must affect the outcome only through its influence on the received treatment. There should be no direct path or alternative causal pathway from the physician's preference to the patient's outcome [1].

A systematic review by Trac et al. (2021) found that these core assumptions are severely underreported in existing literature, with only 12% of PP IV applications explicitly reporting all four main assumptions [4]. This highlights a critical gap in methodological rigor that future research must address.

Operationalizing the Latent Variable: Proxies for Prescribing Preference

Since a physician's true preference is unobservable, researchers must use a proxy measure derived from available data. The table below summarizes the most common proxies used in the literature, along with their construction and key characteristics.

Table 1: Common Proxies for Physician's Prescribing Preference

Proxy Name	Definition & Construction	Key Characteristics	Empirical Example
Last Previous Prescription [2] [3]	The drug (A or B) prescribed to the physician's most recent previous patient in the study cohort.	- Simple and commonly used.- Captures recent shifts in preference.- May be noisy if a single prescription does not reflect a stable tendency.	In a study of antidepressants, physicians who last prescribed a TCA were 14.9 percentage points (95% CI: 14.4, 15.4) more likely to prescribe a TCA to their next patient [2].
Proportion-Based PPP [3] [5]	The proportion of a specific drug (e.g., Drug A) among the last n prescriptions written by the physician. Formula: Number of Drug A scripts / Total of last n scripts.	- More stable than the last prescription.- Can be treated as a continuous or categorical variable.- Requires defining a window (n) of previous prescriptions.	A simulation study found that using more prior prescriptions (e.g., prior 4 vs. prior 1) to construct the proportion increased instrument strength (F-statistic) and statistical power [5].
Algorithm-Based PPP [3]	A rule-based definition applying stricter criteria for consistency (e.g., "at least 2 conventional APM rx's within last 3 rx's").	- Aims to better capture a stable, underlying preference.- May reduce noise but also reduce sample size.- Multiple variations can be tested for sensitivity.	A study on antipsychotics tested 25 formulations, finding that algorithms like "at least 2 conventional rx's within last 3" maintained strength while improving covariate balance [3].

Key Considerations in Proxy Selection

• Number of Prior Prescriptions: Using a longer history of prescriptions (e.g., the last 4 prescriptions versus the last 1) generally creates a more stable and powerful instrument. A 2024 simulation study concluded that for smaller sample sizes, constructing PPP from long prescribing histories is recommended to improve statistical power [5].
• Handling Time and Preference Evolution: A physician's preference is not static. Using a time-varying measure—recalculating the proxy for each patient based on the most recent prescriptions available at the time of their visit—is crucial for accurately reflecting the physician's current leaning [1].

Quantitative Validation of the Instrument

Once a proxy is defined, its performance must be quantitatively validated against the IV assumptions. The following workflow and table outline the key validation steps.

Workflow for Validating a PPP Instrument

Table 2: Key Metrics and Tests for Instrument Validation

Assumption	Validation Goal	Recommended Tests & Metrics	Interpretation & Thresholds
Relevance	Assess the strength of the association between the PPP proxy and the actual prescription.	- First-stage F-statistic: From a regression of actual treatment on the instrument (including covariates).- Risk Difference or Odds Ratio: The difference in probability of receiving the treatment based on the instrument.	- F-statistic > 10 suggests a sufficiently strong instrument, mitigating weak-instrument bias [5].- A large, significant risk difference increases confidence (e.g., 27.7 percentage point increase for paroxetine [2]).
Exchangeability	Evaluate whether the instrument is independent of observed patient covariates.	- Standardized Differences or Mahalanobis Distance: Compare balance of covariates across levels of the instrument vs. across levels of actual treatment.- Correlation Analysis: Check for associations between the instrument and specific known confounders.	A valid instrument should show weaker associations with patient covariates than the actual treatment does. One study found PPP reduced overall covariate imbalance by an average of 36% [3].
Monotonicity	Ensure the instrument affects treatment choice in a uniform direction.	- Deterministic Monotonicity: Test if the instrument perfectly predicts treatment for some patients. This is often implausible.- Stochastic Monotonicity: Test if a higher value of the instrument makes treatment more likely for all patient types.	Deterministic monotonicity is often falsified in practice. Research supports testing for stochastic monotonicity, which may be a more plausible assumption for PPP [6].

The Scientist's Toolkit: Research Reagent Solutions

To implement a PPP IV analysis, researchers require specific "reagents" in the form of data, software, and methodological components. The following table details these essential materials.

Table 3: Essential Research Reagents for PPP IV Analysis

Item Category	Specific Item / Function	Brief Explanation & Purpose
Data Requirements	Longitudinal Prescription Data	Data must contain physician identifiers to link prescriptions from the same prescriber over time. Essential for constructing the PPP proxy.
	Patient Covariate Data	Data on demographics, comorbidities, and other potential confounders. Used to test the exchangeability assumption and can be included in the model.
	Outcome Data	Precisely defined and accurately recorded outcome events (e.g., hospitalizations, death).
Statistical Software	R, Stata, SAS, Python	Software with packages/libraries capable of performing Two-Stage Least Squares (2SLS) regression and generating associated diagnostic tests (e.g., ivreg in R).
Methodological Components	Two-Stage Least Squares (2SLS)	The most common estimation method for IV analysis. The first stage predicts treatment from the instrument; the second stage regresses the outcome on the predicted treatment [5].
	Proxy Construction Algorithm	A defined rule (as in Table 1) for converting a physician's prescription history into a measurable PPP variable. This is the core "reagent" of the study.
	Diagnostic Scripts	Custom or packaged code to calculate F-statistics, covariate balance metrics, and other validity checks outlined in Table 2.
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Advanced Protocols: Sensitivity and Formulation Testing

Given that no single PPP definition is universally best-practice, a rigorous analysis involves testing multiple formulations.

• Protocol for Testing Multiple IV Formulations: A study by Rassen et al. (2009) provides a template by creating 25 variations of the PPP instrument [3]. The protocol involves:
  • Varying the Preference Algorithm: Apply different rules (lenient, moderate, strict) to the last 2, 3, or 4 prescriptions.
  • Applying Cohort Restrictions: Restrict the analysis to subpopulations based on physician (e.g., high-volume prescribers) or patient (e.g., specific age groups) characteristics.
  • Stratification: Analyze data within strata defined by the characteristics of the previous patient (e.g., same age category).
  • Evaluating Each Variation: For each of the 25 formulations, calculate the instrument strength (partial R², F-statistic) and covariate balance (Mahalanobis distance).
• Sensitivity Analysis for Monotonicity: As deterministic monotonicity is often implausible, the protocol should include tests for stochastic monotonicity. Boef et al. (2016) used survey data to show that while deterministic monotonicity was falsified, their data were compatible with a stochastic monotonicity assumption for certain instrument definitions [6].

Defining the physician prescribing preference instrument is a multi-step process that requires careful justification and rigorous validation. Based on the current evidence, the following best practices are recommended:

• Justify the Proxy: Explicitly define the PPP proxy and provide a rationale for its construction (e.g., "We used the last prior prescription as our primary proxy to capture recent preference shifts...").
• Prioritize Strength and Balance: Use a proportion-based measure derived from multiple prior prescriptions (e.g., last 3-4) to enhance instrument strength and stability, especially in smaller samples [5].
• Conduct Comprehensive Validation: Systematically test and report metrics for all three core assumptions. Use the F-statistic to rule out weak instruments and demonstrate improved covariate balance compared to actual treatment [2] [3].
• Acknowledge and Test Assumptions: Be transparent about the limitation of the exclusion restriction, which often relies on untestable subject-matter knowledge. Perform sensitivity analyses around the monotonicity assumption [6] [4].
• Embrace Sensitivity Analyses: Pre-specify and test multiple definitions of the PPP instrument. The robustness of the causal estimate across different plausible formulations strengthens the credibility of the study's conclusions [3].

By adhering to these detailed protocols and systematically defining, constructing, and validating the instrument, researchers can more reliably use Physician's Prescribing Preference to generate evidence on drug effectiveness and safety that is less susceptible to unmeasured confounding.

Instrumental variable (IV) analysis is a powerful methodological approach used to estimate causal treatment effects when unmeasured confounding is present, a common challenge in pharmacoepidemiologic studies using observational data [7]. Within this framework, physician prescribing preference (PPP) has emerged as a valuable instrument for studying drug effects, particularly when randomization is not feasible [3] [8]. The PPP instrument leverages natural variation in doctors' prescribing habits to predict which drug a patient will receive, thereby creating a scenario that approximates random assignment [3].

For IV analyses to yield valid causal estimates, three core assumptions must be satisfied: relevance, exclusion restriction, and exchangeability [9] [10] [11]. The validity of any IV study hinges on the plausibility of these assumptions, which are partially testable but ultimately require substantive justification [9] [7]. This article provides detailed application notes and protocols for evaluating these assumptions within the context of PPP-IV research, offering practical guidance for researchers, scientists, and drug development professionals engaged in comparative effectiveness and safety studies.

Theoretical Foundation of Core IV Assumptions

Conceptual Definitions and Causal Framework

The three core assumptions form the foundation for valid IV inference and can be conceptually defined within the context of physician prescribing preference research [9] [10] [11]:

• Relevance: The physician's prescribing preference must be associated with the actual treatment received by the patient.
• Exclusion Restriction: The prescribing preference must affect the outcome only through its influence on the treatment choice, not through any alternative pathways.
• Exchangeability: The prescribing preference must be independent of both measured and unmeasured confounders of the treatment-outcome relationship.

These assumptions are elegantly represented using causal diagrams, which visually depict the relationships between the instrument, treatment, outcome, and potential confounders.

Figure 1: Causal Diagram Illustrating Core IV Assumptions. The physician prescribing preference (Z) must be associated with treatment (X), must not have a direct path to outcome (Y), and must not be associated with unmeasured confounders (U).

Interrelationship of Assumptions in PPP Research

The three core assumptions operate as an interconnected system in PPP-IV studies. While each assumption must be satisfied individually, their collective satisfaction creates a scenario where the effect of the instrument on the outcome can be validly attributed to the effect of the treatment on the outcome [9] [7]. The exchangeability assumption is particularly crucial in observational settings, as it ensures that the instrument is "as good as random" with respect to the outcome [7]. When satisfied, this assumption facilitates a natural experiment akin to randomization, where patients exposed to different prescribing preferences become comparable in both observed and unobserved characteristics [3].

The exclusion restriction assumption is especially challenging in PPP research, as physician preferences may correlate with other practice patterns or physician characteristics that directly influence patient outcomes [9] [4]. For example, a physician's preference for a particular antipsychotic medication might be associated with their overall quality of care, monitoring intensity, or follow-up practices, creating direct pathways between the instrument and outcome that violate this assumption [3]. Understanding these interrelationships is essential for designing valid PPP-IV studies and appropriately interpreting their results.

Quantitative Assessment of IV Assumptions

Empirical Tests and Falsification Strategies

While the core IV assumptions cannot be definitively verified, researchers can employ various empirical tests and falsification strategies to assess their plausibility [9]. These strategies aim to detect violations of the assumptions rather than confirm their validity.

Table 1: Falsification Strategies for Core IV Assumptions in PPP Research

Assumption	Falsification Strategy	Implementation in PPP Research	Interpretation
Relevance	First-stage F-statistic [10]	Regress treatment on PPP with covariates	F > 10 suggests adequate strength [10]
Exclusion Restriction	Over-identification test [9]	Use multiple instruments (e.g., different PPP definitions)	Inconsistent estimates suggest violation
Exclusion Restriction	Negative control outcomes [9]	Test PPP effect on outcomes it shouldn't influence	Significant effect suggests violation
Exchangeability	Covariate balance assessment [3]	Compare measured covariates across PPP levels	Imbalance suggests potential violation
Exchangeability & Exclusion	Subgroup where instrument shouldn't work [9]	Test PPP effect in patients where preference shouldn't influence treatment	Significant effect suggests violation

Quantitative Evidence from PPP-IV Applications

Empirical studies applying PPP-IV methods provide valuable insights into the performance of these instruments across different clinical contexts. Rassen et al. (2009) evaluated 25 different formulations of the PPP instrument in two cohorts of elderly patients initiating antipsychotic medications, assessing both instrument strength and reduction in covariate imbalance [3] [8].

Table 2: Performance Metrics Across 25 PPP Formulations in Antipsychotic Medication Study

Metric	Range Across Formulations	Interpretation	Clinical Context
First-stage partial R²	0.028 - 0.099	Moderate to strong instrument strength [3]	Elderly patients initiating APMs
Reduction in covariate imbalance	36% (±40%) average reduction	Substantial imbalance reduction in many variations [3]	Mortality outcome at 180 days
Association between strength and imbalance	Mixed relationship	Stronger instruments don't always yield better balance [3]	Cohorts from different databases

The findings demonstrate that PPP instruments generally alleviated imbalances in non-psychiatry-related patient characteristics, suggesting improved exchangeability compared to unadjusted treatment comparisons [3]. However, the mixed association between instrument strength and covariate balance highlights the complex relationship between these two properties and emphasizes the need to evaluate both when selecting among alternative PPP formulations [3].

Experimental Protocols for PPP-IV Studies

Study Design and PPP Measurement Protocol

Objective: To implement a valid PPP-IV analysis that minimizes bias from unmeasured confounding in pharmacoepidemiologic studies.

Materials:

• Longitudinal healthcare databases (e.g., claims, electronic health records)
• Statistical software with IV capabilities (e.g., R, Stata, Python)
• Clinical expertise for cohort definition and outcome validation

Procedure:

• Cohort Definition

  • Identify patients initiating the drug classes of interest
  • Apply inclusion/exclusion criteria based on clinical guidelines
  • Define baseline period for covariate assessment
  • Identify the prescribing physician for each patient

• PPP Instrument Specification

  • Determine the algorithm for quantifying prescribing preference: Base case: Previous patient's treatment within the same practice [3] Alternative formulations: Consider multiple previous prescriptions (2-4) with varying consistency thresholds [3]
  • Select the preference measurement window (recent vs. extended history)
  • Define the hierarchy for handling multiple physicians per patient

• First-Stage Regression (Relevance Assessment)

  • Estimate the association between PPP and treatment receipt:
    Where Treatmenti indicates the specific drug received by patient i, PPPj represents the prescribing preference of physician j, and X_i is a vector of patient covariates.
  • Assess instrument strength using F-statistic (target >10) and partial R² [10]
  • If using multiple instruments, test for over-identification [9]

Figure 2: PPP-IV Study Workflow. The diagram illustrates the sequential process for implementing a physician prescribing preference instrumental variable study, highlighting key stages from data preparation through validity assessment.

Exchangeability and Exclusion Restriction Assessment Protocol

Objective: To evaluate the plausibility of the exchangeability and exclusion restriction assumptions in PPP-IV analyses.

Procedure:

• Covariate Balance Assessment (Exchangeability)

  • Compare distribution of measured covariates across levels of the PPP instrument
  • Calculate standardized differences for each covariate
  • Compute overall balance metrics (e.g., Mahalanobis distance) [3]
  • Compare balance achieved by PPP versus actual treatment assignment

• Negative Control Exposure Tests (Exclusion Restriction)

  • Identify outcomes that should not be affected by the treatment
  • Test association between PPP and these negative control outcomes
  • Significant associations suggest violation of exclusion restriction [9]

• Subgroup Analyses (Joint Test of Exclusion and Exchangeability)

  • Identify patient subgroups where the instrument should not affect treatment
  • Test association between PPP and outcome in these subgroups
  • Any significant association indicates violation of assumptions [9]

• Sensitivity Analyses

  • Assess how large a direct effect of PPP on outcome would need to be to explain observed results
  • Evaluate robustness to different PPP definitions and study restrictions
  • Use instrumental inequalities when variables are binary [9]

The Scientist's Toolkit: Research Reagents for PPP-IV Studies

Table 3: Essential Methodological Tools for PPP-IV Research

Tool Category	Specific Methods	Function	Key Considerations
Instrument Strength Assessment	First-stage F-statistic, Partial R² [3] [10]	Quantifies association between PPP and treatment	F > 10 recommended; weak instruments amplify bias [10]
Balance Measurement	Standardized differences, Mahalanobis distance [3]	Assesses comparability of patients across PPP levels	Reductions vs. unadjusted comparisons indicate improved exchangeability [3]
Exclusion Restriction Tests	Over-identification tests, Negative control outcomes [9]	Detects direct effects of PPP on outcomes	Requires multiple instruments or known null outcomes [9]
Effect Estimation	Two-stage least squares, Limited information maximum likelihood	Estimates causal treatment effects	Provides local average treatment effect (LATE) for compliers [7]
Sensitivity Analysis	Instrumental inequalities, Bias component plots [9]	Quantifies robustness to assumption violations	Particularly important for untestable assumptions [9]
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Advanced Considerations in PPP-IV Applications

Formulation Variations and Their Impact on Validity

The performance of PPP instruments can be substantially improved through careful specification of the preference measure and study design modifications [3]. Empirical evidence suggests that varying the algorithm for quantifying prescribing preference significantly impacts both instrument strength and validity:

• Preference Assignment Algorithms: Using stricter criteria for defining preference (e.g., requiring consistent prescribing across multiple previous patients) generally improves exchangeability but may reduce instrument strength [3].
• Cohort Restrictions: Limiting analyses to specific physician types (e.g., high-volume prescribers) or patient subgroups can enhance validity by reducing heterogeneity in practice patterns [3].
• Stratification Approaches: Aligning current and previous patients based on shared characteristics (e.g., age, comorbidity profile) may improve the relevance of the preference measure [3].

Reporting Guidelines and Validation Framework

A systematic review of preference-based IV applications in health research found that only 12% of studies reported all four main assumptions, highlighting a critical gap in methodological transparency [4]. To address this limitation, researchers should:

• Explicitly document the rationale for PPP validity for each core assumption
• Report comprehensive strength and balance metrics for all instrument formulations considered
• Conduct and report sensitivity analyses assessing robustness to assumption violations
• Acknowledge the local nature of the treatment effect estimate (LATE) and discuss its generalizability [7]

The increasing use of PPP-IV designs in pharmacoepidemiology underscores the need for standardized reporting practices that enable critical appraisal of assumption plausibility and facilitate comparison across studies [4]. By adhering to rigorous methodological standards and transparent reporting, researchers can enhance the credibility of PPP-IV studies and contribute to more reliable evidence regarding drug effectiveness and safety.

In instrumental variable (IV) analysis, the monotonicity assumption serves as a critical fourth identifying condition required for obtaining a well-defined causal parameter [12]. This assumption is particularly essential when using physician prescribing preference (PPP) as an instrument in comparative effectiveness research, where it enables the interpretation of the IV estimate as a local average treatment effect (LATE) for a specific subpopulation [13]. Monotonicity ensures that the instrument affects treatment assignment in a consistent direction across the population, thereby defining a clear complier group for causal inference.

The fundamental requirement of monotonicity is the absence of defiers—individuals who would consistently receive the opposite treatment to what the instrument suggests [10]. In the context of physician prescribing preference research, this means there should be no patients who would be prescribed Treatment A when encountering a physician who prefers Treatment B, while simultaneously being prescribed Treatment B when encountering a physician who prefers Treatment A [13]. When this assumption holds along with the three core IV conditions (relevance, exclusion restriction, and exchangeability), researchers can identify the average causal effect specifically for the subpopulation of compliers—those patients whose treatment receipt aligns with their physician's prescribing preference [13] [10].

Theoretical Foundations of Monotonicity

Defining Compliance Types

Within the potential outcomes framework, patients can be conceptually categorized into four mutually exclusive compliance types based on their counterfactual responses to the instrument. These classifications are study-specific and instrument-dependent, meaning a patient is not inherently a complier but is defined as such only within the context of a particular study with respect to a specific proposed instrument [13].

Table 1: Compliance Types in Instrumental Variable Analysis

Compliance Type	Definition	Behavior in PPP Context
Always-takers	Patients who would receive Treatment A regardless of physician preference	Would receive Drug A whether their physician prefers Drug A or Drug B
Never-takers	Patients who would never receive Treatment A regardless of physician preference	Would not receive Drug A regardless of their physician's preference
Compliers	Patients whose treatment aligns with physician preference	Would receive Drug A if their physician prefers it, and Drug B if their physician prefers it
Defiers	Patients whose treatment contradicts physician preference	Would receive Drug B if their physician prefers Drug A, and Drug A if their physician prefers Drug B

Conceptual Challenges in Defining Compliance

The traditional compliance framework faces significant conceptual challenges in PPP research because counterfactual treatments are not well-defined without explicitly specifying the physician [13]. A patient's classification may vary depending on which specific physicians are being considered, as physicians with identical measured preferences might treat the same patient differently due to unobserved factors [13]. This ambiguity highlights the distinction between global monotonicity (which requires the inequality to apply to all possible physician pairs) and local monotonicity (which specifies particular physicians for comparison) [13]. The compliance types become ill-defined when considering that for a given patient, some physicians with preference A would prescribe treatment B, while some physicians with preference B would prescribe treatment A [13].

Monotonicity Assessment Protocol for Physician Prescribing Preference Research

Survey-Based Experimental Design

To empirically assess the monotonicity assumption, researchers can implement a structured survey design targeting prescribing physicians. This approach measures potential monotonicity violations by presenting physicians with identical patient scenarios and recording their treatment decisions [13].

Table 2: Monotonicity Assessment Survey Protocol

Protocol Component	Specification	Implementation Example
Survey Participants	Physicians from the study cohort or similar clinical background	53 physicians participating in antipsychotic prescribing study [13]
Patient Vignettes	Case histories with sufficient clinical detail for informed decisions	Hypothetical patients who are candidates for antipsychotic treatment [13]
Data Collection	Physician preferences and treatment plans for identical patients	Each physician reports preferred treatment approach and specific plans for each vignette
Analysis	Measure consistency of treatment decisions across preference groups	Quantify proportion of patients exhibiting potential defier behavior

The survey should capture two key elements from each physician: (1) their general prescribing preference between the treatments being studied, and (2) the specific treatment decisions they would make for each hypothetical patient presented. This dual approach enables researchers to identify scenarios where patients might receive treatment contrary to a physician's stated preference—the essential definition of a defier in the PPP context [13].

Implementation Framework

Phase 1: Physician Preference Assessment

• Administer a preliminary survey to determine each physician's general preference between Treatment A and Treatment B
• Document preference using multiple metrics: self-declared preference, historical prescribing patterns, or preference strength scales
• Categorize physicians into preference groups (A-preferring, B-preferring, neutral) for subsequent analysis

Phase 2: Clinical Scenario Evaluation

• Develop standardized patient vignettes representing typical candidates for the treatments
• Ensure vignettes contain sufficient clinical detail to simulate real prescribing decisions
• Present identical vignettes to all physicians regardless of their preference group
• Record specific treatment recommendations for each vignette

Phase 3: Monotonicity Violation Analysis

• Cross-tabulate physician preferences against treatment decisions for identical patients
• Identify patients for whom treatment would vary counter to preference patterns
• Calculate the proportion of patients showing potential defier behavior
• Quantify the magnitude and direction of possible bias from monotonicity violations

Quantitative Measures of Monotonicity Violations

Empirical Evidence from Pilot Studies

Recent empirical investigations have demonstrated that monotonicity violations are not merely theoretical concerns but occur frequently in practical applications of physician preference instruments.

Table 3: Monotonicity Assessment Findings from Empirical Research

Study Feature	Pilot Study Results	Implication for PPP Research
Prevalence of Violations	Nearly all patients exhibited some degree of monotonicity violations [13]	Violations are common rather than exceptional
Type Classification	Patients could not be cleanly classified as compliers, defiers, always-takers, or never-takers [13]	Traditional compliance categories are oversimplified
Instrument Strength	First-stage partial R² values ranged from 0.028 to 0.099 across 25 PPP formulations [3]	PPP can be a strong instrument with proper construction
Bias Impact	2SLS percent bias approximately 20% compared to 60% for OLS with unmeasured confounding [5]	PPP IV reduces bias despite potential monotonicity violations

Measuring Violation Magnitude

In the pilot study assessing antipsychotic prescribing, researchers quantified monotonicity violations by calculating the proportion of hypothetical patients who would receive different treatments from physicians with opposite preferences [13]. This approach revealed that violations were widespread, affecting nearly all patients to some degree [13]. The measurement process involves:

• For each patient vignette, calculate the probability of receiving Treatment A from physicians who prefer Treatment A
• Similarly calculate the probability of receiving Treatment A from physicians who prefer Treatment B
• Identify violations where the probability of treatment is higher under the opposite preference
• Quantity prevalence of violations across the patient population

Advanced Methodological Approaches

Stochastic Monotonicity Framework

When deterministic monotonicity is violated, researchers can consider the alternative stochastic monotonicity assumption, which relaxes the strict requirement of within-subject monotonicity [14]. This approach only requires that a monotonic relationship holds across subjects between the instrument and treatment in a specific manner [14]. Under stochastic monotonicity, the IV estimator identifies a weighted average of treatment effects with greater weight given to subgroups where the instrument has a stronger effect on treatment assignment [14].

The stochastic monotonicity framework is particularly valuable in PPP research because it accommodates the reality that physician decision-making incorporates multiple complex factors beyond a simple preference dimension. Under this assumption, the IV estimate represents a weighted average of treatment effects, where subgroups of patients for whom physician preference has a stronger influence on treatment receive greater weight in the estimate [14].

Bounds and Sensitivity Analysis

When monotonicity violations are suspected, researchers can implement sensitivity analyses to quantify how violations might affect results [10] [14]. This approach involves:

• Plausible range of defier prevalence in the study population
• Direction and magnitude of bias introduced by different violation scenarios
• Estimation bounds for the causal effect under varying monotonicity assumptions

The Scientist's Toolkit: Research Reagent Solutions

Table 4: Essential Methodological Tools for PPP Monotonicity Research

Research Tool	Function	Implementation Guidance
Physician Preference Algorithms	Constructs the instrumental variable from prescribing data	Use last 1-4 previous prescriptions; proportional PPP formula: Number of Drug A prescriptions / Total prescriptions [5]
Case Vignettes	Standardized patient scenarios for preference elicitation	Develop clinically detailed cases representing typical treatment candidates; ensure consistency across respondents [13]
Two-Stage Least Squares (2SLS)	Primary estimation method for IV analysis	First stage: Regress treatment on instrument; Second stage: Regress outcome on predicted treatment [5]
First-Stage F-Statistic	Measures instrument strength	F-statistic >10 indicates sufficiently strong instrument; calculated from first-stage regression [10]
Sensitivity Analysis Framework	Assesses robustness to monotonicity violations	Simulate different violation scenarios; calculate bounds for causal effects [10] [14]
Compliance Type Proportions	Estimates subpopulation distributions	Calculate proportions of always-takers, never-takers, and compliers from first-stage results [13]
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When applying the monotonicity assumption in physician prescribing preference research, investigators should transparently report potential violations and their implications for causal interpretation. The empirical evidence suggests that clean compliance classification is often unrealistic in practice, as patients frequently cannot be neatly categorized into always-takers, never-takers, compliers, or defiers [13]. Consequently, preference-based instrumental variable estimates should be interpreted cautiously, recognizing that bias due to monotonicity violations is likely and the subpopulation to which the estimate applies may not be well-defined [13].

Researchers should consider supplementing observational studies with physician surveys to empirically assess the magnitude and direction of potential bias from monotonicity violations [13]. When violations are detected, the stochastic monotonicity framework or bounded estimation approaches can provide more realistic causal inferences than relying solely on the deterministic monotonicity assumption [14]. By acknowledging and addressing these complexities, researchers can present more nuanced and credible estimates of treatment effects using physician preference instruments.

Physician Prescribing Preference (PPP) has emerged as a valuable instrumental variable (IV) in pharmacoepidemiology and comparative effectiveness research (CER), particularly when studying the effects of medications in real-world settings where randomized controlled trials are not feasible [3]. An instrumental variable is an unconfounded proxy for a study exposure that can be used to estimate a causal effect in the presence of unmeasured confounding [3] [15]. The PPP IV approach exploits natural variation in physicians' prescribing patterns to create a quasi-randomized allocation of treatments, thereby mitigating biases introduced by confounding by indication and other unmeasured risk factors commonly present in observational data [3] [16].

For unbiased IV estimation, the instrument must be both valid and reasonably strong [3]. A valid IV must predict treatment choice but not be related to the outcome except through the treatment effect [15]. Although IV validity is not explicitly testable, stratifying the patient population by a valid dichotomous IV should result in more observed balance among measured covariates than if those same patients had instead been stratified by their actual treatment [15]. Instrument strength, which can be measured and reported, refers to how well the instrument predicts actual treatment independent of other measured variables [3] [15].

Table 1: Key Properties of a Valid Physician Prescribing Preference Instrumental Variable

Property	Description	Assessment Method
Relevance	PPP must strongly predict the treatment a patient receives	First-stage F-statistics, partial R² values [3] [5]
Exclusion Restriction	PPP affects outcomes only through the treatment, not directly	Theoretical justification, sensitivity analysis [3] [15]
Exchangeability	PPP is independent of unmeasured confounders	Covariate balance measurement (e.g., Mahalanobis distance) [3] [15]
Independence	PPP is not affected by patient characteristics that also affect outcomes	Comparison of patient characteristics across preference groups [3]

Common Therapeutic Applications of PPP IV

PPP IV has been successfully applied across multiple therapeutic areas where treatment decisions involve physician discretion and where confounding by indication poses significant challenges to conventional observational study designs.

Antipsychotic Medications

One of the most established applications of PPP IV is in studying antipsychotic medications (APMs), particularly comparing conventional versus atypical antipsychotics in elderly populations [3] [15]. This research context is characterized by:

• Strong confounding by indication: Patients prescribed different antipsychotics often differ substantially in their underlying health status and prognosis [3]
• Substantial physician variation: Meaningful differences exist in physician preferences for conventional versus atypical APMs [3] [15]
• Important clinical outcomes: Studies have examined mortality, hospitalization, and other serious outcomes where confounding is a major concern [3]

In a landmark study applying PPP IV to assess APM use and subsequent death among elderly patients, researchers found that PPP generally alleviated imbalances in non-psychiatry-related patient characteristics, with overall imbalance reduced by an average of 36% (±40%) across two cohorts [3] [15]. The partial R² values characterizing instrument strength ranged from 0.028 to 0.099 across 25 different formulations of the PPP IV [3].

Chronic Disease Medications

PPP IV has been applied to study treatments for various chronic conditions where long-term medication use is common:

• Alcohol use disorder medications: Recent simulation studies have explored PPP IV performance in comparing pharmaceutical treatments for alcohol use disorder [5]
• Rheumatological conditions: Studies have examined treatments for conditions like psoriatic arthritis and axial spondyloarthritis [17] [18]
• Inflammatory skin diseases: Research has investigated treatments for hidradenitis suppurativa and palmoplantar pustulosis [17] [18]

Quantitative Performance of PPP IV Across Studies

The performance of PPP IV has been quantitatively assessed across multiple studies, providing insights into its operational characteristics in different research contexts.

Table 2: Performance Metrics of PPP IV Across Different Study Contexts

Study Context	Sample Size	IV Strength (Partial R²)	IV Strength (F-statistic)	Bias Reduction vs. OLS
Antipsychotic Medications [3] [15]	36,541 (BC) 20,087 (PA)	0.028 - 0.099	Not reported	Covariate imbalance reduced by 36% (±40%)
Simulation Study (n=2452) [5]	2,452	~0.14-0.15 (ρ²)	~30 (estimated)	~20% bias vs. ~60% for OLS
Simulation Study (n=620) [5]	620	~0.14-0.15 (ρ²)	~8 (estimated)	~20% bias vs. ~60% for OLS
HIV Treatment [5]	<2,000	Not reported	Not reported	Not reported

The relationship between sample size and PPP IV performance is particularly important for research planning. Simulation studies have demonstrated that while percent bias remains relatively constant across sample sizes (around 20% for 2SLS versus 60% for ordinary least squares), statistical power decreases substantially with smaller samples [5]. This has practical implications for studies of rare outcomes or newly available drugs where sample sizes may be limited.

Experimental Protocols for Implementing PPP IV

Core Protocol: Base Case PPP Implementation

The base case PPP follows the approach proposed by Brookhart et al., which determines physician preference at the time of seeing a patient by the treatment the doctor chose for the previous patient in their practice who required a new prescription for one of the study drugs [3] [15].

Materials and Data Requirements:

• Longitudinal prescription data with physician identifiers
• Patient demographic and clinical characteristics
• Outcome data (e.g., mortality, hospitalization, clinical measures)
• Date stamps for all prescriptions to establish temporal ordering

Procedure:

• Cohort Identification: Identify all patients initiating treatment with the study drugs of interest
• Preference Assignment: For each patient encounter, determine the physician's preference based on the most recent previous prescription to a different patient for the same class of medications
• First-Stage Regression: Estimate the relationship between the assigned preference and actual treatment received using linear regression: Treatment = α₀ + α₂PPP + α₁X₁ + α₃X₃
• Second-Stage Regression: Estimate the relationship between the predicted treatment from stage 1 and the outcome: Outcome = β₀ + βₓTreatment_hat + β₁X₁ + β₃X₃
• Strength Assessment: Calculate first-stage F-statistic and partial R² values
• Balance Assessment: Compare covariate distributions across preference-based groups using standardized differences or Mahalanobis distance

Advanced Protocol: Alternative PPP Formulations

Research has demonstrated that modifying the base case PPP definition can enhance instrument performance [3]. The following variations can be implemented:

Preference Assignment Algorithms:

• Lenient Criteria: At least 1 conventional prescription within last 2, 3, or 4 prescriptions
• Strict Criteria: 2 conventional prescriptions within last 2, 3 within last 3, or 4 within last 4 prescriptions
• Moderate Criteria: At least 2 conventional prescriptions within last 3 or 4 prescriptions [3]

Cohort Restriction Strategies:

• Physician Characteristics: Restrict to high-volume prescribers, specific specialties, or graduation era
• Patient Characteristics: Restrict to specific age groups or clinical profiles
• Combined Approaches: Restrict to patients older than median age in the physician's practice [3]

Stratification Approaches:

• Stratify by patient age category relative to previous patient
• Stratify by propensity score quartiles of previous patient [3]

Protocol for Small Sample Size Applications

For studies with limited sample sizes (n<2,000), specific modifications to the standard PPP approach are recommended [5]:

Modified PPP Construction:

• Use longer prescribing histories (prior 3-4 prescriptions) rather than just the last prescription
• Consider proportional PPP measures: Number of drug A prescriptions / Total prescriptions by physician
• Implement more stringent cohort restrictions to enhance homogeneity

Analysis Considerations:

• Report confidence intervals alongside point estimates due to wider sampling variability
• Interpret F-statistics >10 as indicating adequate strength, with recognition that power will be limited
• Consider Bayesian approaches or bias-corrected estimators that may perform better in small samples

The Scientist's Toolkit: Essential Research Reagents

Table 3: Essential Methodological Tools for PPP IV Research

Tool Category	Specific Methods	Function	Implementation Notes
IV Strength Assessment	First-stage F-statistic, Partial R²	Quantifies how well PPP predicts treatment	Target: F>10 for weak instrument concern [5]
Balance Metrics	Mahalanobis distance, Standardized differences	Assesses comparability of preference groups	Reductions indicate improved validity [3] [15]
Estimation Methods	Two-stage least squares (2SLS)	Provides causal effect estimates	Preferred for continuous outcomes [5]
Software Tools	R, Stata, SAS IV procedures	Implements statistical analyses	R's ivreg or Stata's ivregress commonly used [5]
Data Infrastructure	Longitudinal prescription databases	Provides prescribing history	Requires physician-patient linkage over time [3]
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Doxifluridine-d2	Doxifluridine-d2, CAS:84258-25-3, MF:C9H11FN2O5, MW:248.20 g/mol	Chemical Reagent	Bench Chemicals

Analytical Framework and Interpretation

The analytical framework for PPP IV studies involves several key considerations that differ from conventional observational studies:

Logical Causal Structure

Interpretation of PPP IV Estimates

The interpretation of PPP IV estimates requires careful consideration of the specific population being studied:

• Local Average Treatment Effect: IV estimates represent the effect of treatment among "complier" patients—those whose treatment would change if physician preference changed [3]
• Scaled Effect Interpretation: The IV estimate scales the intention-to-treat effect (PPP on outcome) by the first-stage effect (PPP on treatment), which amplifies any residual confounding in weak instruments [3] [15]
• Clinical Meaningfulness: While statistical measures of strength are important, the clinical relevance of the preference-based variation should also be considered

PPP IV represents a powerful methodological approach for comparative effectiveness research across multiple therapeutic areas, particularly when unmeasured confounding threatens the validity of conventional observational studies. The successful application of PPP IV requires careful attention to instrument construction, strength assessment, and appropriate interpretation of results. The protocols and applications detailed in this document provide researchers with practical guidance for implementing this method across diverse research contexts, from large database studies to more limited sample size applications. As the field evolves, continued refinement of PPP measures and validation of underlying assumptions will further enhance the utility of this approach in generating real-world evidence about treatment effects.

Within pharmacoepidemiology and comparative effectiveness research, the gold standard for establishing causal treatment effects is the randomized controlled trial (RCT). However, when RCTs are impractical or unethical, Instrumental Variable (IV) analysis provides a robust methodological alternative. This application note details how Physician's Prescribing Preference (PPP), a specific type of IV, leverages natural variation in clinical practice to mimic the randomization of a natural experiment, thereby mitigating both measured and unmeasured confounding. We outline the core assumptions, provide detailed protocols for implementation, and present empirical data on the performance and reporting of PPP IVs to guide researchers and drug development professionals.

The Instrumental Variable Framework and the Natural Experiment Paradigm

The Fundamental Challenge of Confounding

In non-experimental studies, estimating the causal effect of a treatment is complicated by confounding, where external factors influence both the treatment assignment and the outcome. Traditional observational methods rely on the untestable assumption of "no unmeasured confounding" [19]. IV analysis addresses this limitation by introducing a variable—the instrument—that serves as an unconfounded proxy for the treatment [3].

Instrumental Variables as a Solution

An IV is a variable that must satisfy three key assumptions, as summarized in Table 1. Conceptually, a valid instrument acts like the coin toss in an RCT; it creates a source of random variation in treatment assignment that is independent of patient characteristics [19] [20]. This "natural experiment" allows for the estimation of causal effects even in the presence of unmeasured confounders [19].

Table 1: Core Assumptions for a Valid Instrumental Variable (IV)

Assumption	Description	Analogy in RCT
1. Relevance	The IV must be a strong predictor of the actual treatment received.	Randomization assigns patients to treatment or control groups.
2. Independence	The IV must be independent of both measured and unmeasured confounders.	Randomization ensures exchangeability between treatment groups.
3. Exclusion Restriction	The IV must affect the outcome only through its influence on the treatment, with no other direct or indirect paths.	The act of randomization itself does not influence the outcome.

The following diagram illustrates the logical structure of a PPP-based instrumental variable analysis and the critical pathways it must fulfill.

Physician's Prescribing Preference (PPP) as an Instrumental Variable

Conceptual Basis

The PPP IV operates on the premise that a physician's inherent or habitual preference for one drug over another (for non-medical reasons) can create a quasi-random allocation of treatments to patients. This preference is often measured using the physician's own prescribing history [3]. Under the key assumption that this preference is unrelated to individual patients' baseline risk factors (unmeasured confounders), it can serve as a valid instrument.

Operationalizing and Measuring PPP

A common method for measuring PPP is to use the treatment assigned to the physician's previous patient who required a new prescription for one of the study drugs [3]. However, multiple formulations exist to better capture a physician's stable preference, as detailed in the protocol section.

Quantitative Performance and Empirical Data

The utility of the PPP IV approach is supported by simulation and empirical studies. Key performance metrics include its strength in predicting treatment and its ability to reduce covariate imbalance.

Table 2: Performance Metrics of PPP IV in Empirical Research

Study / Metric	Sample Size	IV Strength (Partial R²)	Bias Reduction	Key Finding
Brookhart et al. (2009) [3]	Two cohorts of elderly patients	0.028 - 0.099 (across 25 PPP formulations)	Average 36% (±40%) reduction in covariate imbalance	PPP formulations were generally strong and improved covariate balance.
Simulation Study (2024) [5]	~2,500 patients	N/A	~20% bias with 2SLS vs. ~60% with OLS under high confounding	PPP IV led to less biased estimates than conventional methods, regardless of sample size.

Table 3: Impact of Prescribing History Length on IV Strength [5]

PPP Proxy Definition	F-statistic (n=2,452)	F-statistic (n=620)	Interpretation
Prior 1 Prescription	Lower	Lowest	Weaker instrument, lower statistical power.
Prior 4 Prescriptions	Higher	Higher	Stronger instrument, improved power.
"True" Preference (Latent)	Highest (~500)	N/A	Ideal but unobservable; represents best-case scenario.

Application Notes and Protocols

Protocol 1: Base Case PPP Implementation

This protocol outlines the standard method for constructing a dichotomous PPP instrument [3].

• Cohort Definition: Define the study cohort to include all patients initiating either of the two drugs being compared.
• Linking Physicians: Link each patient to the physician who wrote the index prescription.
• Prescription History: For each physician, identify all prior patients who received a new prescription for either study drug, arranged chronologically.
• IV Assignment: For a given index patient, the PPP instrument is defined as the drug (e.g., Drug A vs. Drug B) prescribed to the most recent previous patient in that physician's history. This creates a dichotomous instrument (e.g., PPP = 1 if prior patient received Drug A).

Protocol 2: Advanced PPP Formulations to Enhance Strength and Validity

Variations on the base case can be applied to refine the PPP measure, potentially improving its stability and validity [3].

• Preference Assignment Algorithm Changes:
  • Lenient Criteria: PPP is defined as the physician having prescribed at least one of the target drugs within the last n prescriptions (e.g., last 2, 3, or 4).
  • Strict Criteria: PPP is defined as the physician having prescribed the target drug for all of the last n prescriptions.
  • Moderate Criteria: PPP is defined as the physician having prescribed the target drug for at least k out of the last n prescriptions (e.g., at least 2 out of the last 3).
• Cohort Restrictions:
  • Restrict the analysis to patients of physicians with high-volume practices to ensure a reliable prescribing history.
  • Restrict to specific physician types (e.g., primary care physicians only or specialists only) to increase homogeneity.
  • Restrict to patient subgroups (e.g., above or below median age) to assess effect heterogeneity.
• Stratification Schemes:
  • Ensure that the "previous patient" used to define PPP is from the same demographic stratum (e.g., same age category or propensity score quartile) as the index patient. This helps account for preference based on patient type.

Protocol 3: Statistical Analysis via Two-Stage Least Squares (2SLS)

For a continuous outcome, the Two-Stage Least Squares method is the most common approach for IV estimation [5].

• First-Stage Regression:
  • Regression Model: Treatment_i = α_0 + α_z * PPP_i + α_1 * X_i + ε_i
  • Variables: Treatment_i is the actual treatment for patient i; PPP_i is the instrumental variable; X_i is a vector of measured covariates.
  • Objective: Assess the strength of the instrument. A strong instrument is indicated by a high F-statistic (e.g., >10) and a significant coefficient for α_z. A low partial R² suggests a weak instrument.
• Second-Stage Regression:
  • Regression Model: Outcome_i = β_0 + β_iv * PredictedTreatment_i + β_1 * X_i + u_i
  • Variables: PredictedTreatment_i is the fitted value from the first-stage regression.
  • Interpretation: The coefficient β_iv represents the estimated causal effect of the treatment on the outcome.

The Scientist's Toolkit: Research Reagents and Materials

Table 4: Essential Components for a PPP IV Study

Component	Function / Description	Critical Considerations
Administrative Claims Data	Primary data source containing patient diagnoses, drug prescriptions, physician identifiers, and outcomes.	Must allow for accurate linkage of patients to physicians and longitudinal tracking of prescriptions.
Physician Prescribing History	The core dataset for constructing the PPP instrument.	Requires a chronological record of all relevant prescriptions per physician. Data sufficiency is key for high-volume physician restrictions.
Covariate Data	Measured patient characteristics (e.g., age, comorbidities, prior healthcare utilization) used for balance checks and inclusion in models.	Used to empirically assess the independence assumption by demonstrating improved covariate balance between PPP-defined groups.
Statistical Software (e.g., R, Stata)	Platform for performing 2SLS regression, calculating F-statistics, and assessing covariate balance.	Code must correctly handle the two-stage estimation and implement robustness checks (e.g., weak instrument tests).
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Critical Assumptions and Reporting Guidelines

A systematic review of PP IV applications in health research revealed that the critical assumptions for a valid IV are severely underreported, with only 12% of studies reporting all four main assumptions [4]. To ensure methodological rigor, researchers must explicitly discuss the following:

• Justification of Independence: Provide a conceptual argument for why PPP is unrelated to unmeasured patient risk factors.
• Exclusion Restriction: Argue that PPP affects the outcome only through the choice of treatment and not through other pathways (e.g., via physician skill correlated with preference).
• Assessment of Instrument Strength: Always report first-stage F-statistics and partial R² values.
• Evaluation of Covariate Balance: Demonstrate empirically that stratification by the PPP instrument improves the balance of measured covariates compared to stratification by actual treatment [3].

The Physician's Prescribing Preference instrumental variable is a powerful tool for causal inference when randomized trials are not feasible. By carefully mimicking the randomization process through a naturally occurring source of variation, PPP can isolate the causal effect of a drug from the confounding influence of unmeasured patient characteristics. Successful application requires strict adherence to its core assumptions, thoughtful construction of the instrument using detailed prescribing histories, and transparent reporting of both instrument strength and validity checks. When implemented with rigor, PPP provides drug developers and researchers with a defensible method for generating real-world evidence on treatment effects.

From Theory to Practice: Implementing PPP IV in Research Studies

Application Notes: Physician Prescribing Preference as an Instrumental Variable

An Instrumental Variable (IV) is an unconfounded proxy for a study exposure that can be used to estimate a causal effect in the presence of unmeasured confounding [3]. Physician Prescribing Preference (PPP) is an IV that leverages natural variation in doctors' prescribing habits to predict patient drug treatment, thereby quasi-randomizing patients and mitigating bias from unmeasured factors such as confounding by indication [3]. These notes detail the construction and evaluation of PPP algorithms, from simple formulations to those incorporating proportional history, for use in pharmacoepidemiology studies.

The validity of a PPP instrument is paramount; a valid instrument must predict treatment choice but not be independently associated with the study outcome [3]. Furthermore, the instrument must be strong, meaning it is a good predictor of actual treatment independent of other measured variables. Instrument strength is typically measured using the first-stage partial r² statistic, with higher values indicating a stronger instrument [3].

Core PPP Algorithm Formulations

PPP algorithms can be categorized by the method used to quantify a physician's preference. The following table summarizes the key algorithm types and their characteristics.

Table 1: Classification and Characteristics of PPP Algorithms

Algorithm Category	Description	Hypothesized Effect on Validity	Hypothesized Effect on Strength
Simple Previous Prescription [3]	Preference is defined by the treatment the physician chose for their immediately prior patient.	Lower (may not reflect stable preference)	Potentially high, but volatile
Proportional History (Lenient) [3]	Preference is assigned if a specific drug was used for at least one of the last 2, 3, or 4 patients.	Moderate improvement in balance	May weaken correlation with treatment
Proportional History (Strict) [3]	Preference is assigned only if a specific drug was used for all of the last 2, 3, or 4 patients.	Better estimate of stable preference, potentially higher validity	Likely decrease in strength
Proportional History (Moderate) [3]	Preference is assigned if a specific drug was used for at least two of the last three or four patients.	Balance between stability and responsiveness	Moderate strength

Quantitative Evaluation of PPP Formulations

Applying these algorithms in a study of antipsychotic medication use and mortality revealed key performance metrics. The following table consolidates quantitative findings on instrument strength and covariate balance.

Table 2: Performance Metrics of PPP Algorithm Variations in an Antipsychotic Medication Study [3]

PPP Algorithm Variation	First-Stage Partial R² (Instrument Strength)	Reduction in Overall Covariate Imbalance (Mahalanobis Distance)
Base Case (Simple Previous Prescription)	0.028 - 0.099	Baseline
Proportional History (Lenient: ≥1 of last 4)	Data from cohort R1	Average 36% reduction (±40%) across all formulations and two cohorts
Proportional History (Strict: 4 of last 4)	Data from cohort R1	Average 36% reduction (±40%) across all formulations and two cohorts
Proportional History (Moderate: ≥2 of last 4)	Data from cohort R1	Average 36% reduction (±40%) across all formulations and two cohorts

Experimental Protocols

Protocol: Defining and Calculating a Base Case PPP Instrument

Purpose: To establish a physician's prescribing preference based on the most recent available information. Application: Suitable for studies where physician preferences are expected to be fluid and recent behavior is the best predictor of current choice.

Methodology:

• Cohort Identification: Identify the study cohort of patients initiating treatment with the drugs of interest.
• Prescription Sequencing: For each physician in the study, chronologically order all new prescriptions they wrote for the study drugs within the data collection period.
• Preference Assignment: For a given patient encounter, determine the physician's PPP by identifying the drug prescribed to the immediately prior patient in the sequence for whom the physician initiated treatment.
• Instrument Variable Creation: Create a dichotomous IV (e.g., PPP = 1 for drug A, PPP = 0 for drug B) based on this assigned preference.

Protocol: Defining and Calculating a Proportional History PPP Instrument

Purpose: To create a more stable estimate of a physician's underlying prescribing preference by incorporating a longer history of prescriptions. Application: Ideal for testing the robustness of findings and for increasing the validity of the instrument by reducing noise.

Methodology:

• Cohort Identification: Identify the study cohort. Consider restricting to patients of physicians with a high volume of prescriptions (e.g., ≥4 previous prescriptions) to ensure data availability.
• Prescription History Window: For a given patient encounter, identify the set of the last n new prescriptions written by the physician (e.g., the last 4 prescriptions).
• Preference Assignment Algorithm:
  • Count the number of times each drug of interest was prescribed within this window.
  • Apply a predefined rule to assign a preference.
  • Lenient Rule: Assign preference for drug A if it was prescribed in at least one of the last n prescriptions.
  • Strict Rule: Assign preference for drug A only if it was prescribed for all of the last n prescriptions.
  • Moderate Rule: Assign preference for drug A if it was prescribed in at least half (or another proportion) of the last n prescriptions.
• Instrument Variable Creation: Create a dichotomous IV based on the assigned preference.

Protocol: Assessing Instrument Performance

Purpose: To quantitatively evaluate the strength and potential validity of the constructed PPP instrument. Application: Mandatory for any study employing an IV analysis to ensure the instrument is not weak and to provide evidence supporting its validity.

Methodology:

• Instrument Strength:
  • Perform a first-stage regression analysis where the actual treatment received by the patient is regressed on the PPP instrument, controlling for other measured covariates.
  • Calculate the partial r² value associated with the PPP instrument. This value characterizes the strength of the instrument; a higher value indicates a stronger instrument [3].
• Covariate Balance:
  • Stratify the patient population by the dichotomous PPP instrument.
  • Compare the distribution of measured patient covariates (e.g., age, comorbidities) across the two PPP strata.
  • Quantify the overall imbalance using a metric like the Mahalanobis distance. A reduction in this distance compared to stratification by actual treatment suggests the PPP is creating more balanced groups and provides supportive evidence for its validity [3].

Visualizing PPP Algorithm Workflows

PPP Algorithm Selection

IV Validation Pathway

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential Materials and Tools for PPP IV Research

Research Reagent	Function / Application in PPP Studies
Administrative Claims Databases	Provide longitudinal data on physician prescriptions, patient diagnoses, and outcomes at a population level. The foundational data source for calculating PPP and constructing study cohorts.
First-Stage Partial R²	A key diagnostic metric quantifying the proportion of variance in treatment explained by the PPP instrument after accounting for other covariates. Assesses instrument strength [3].
Mahalanobis Distance	A multivariate metric used to summarize the overall balance (or imbalance) of all measured covariates between groups defined by the PPP instrument. Supports instrument validity [3].
Two-Stage Least Squares (2SLS) Regression	The standard statistical methodology for implementing IV analysis. In the first stage, treatment is regressed on the instrument; in the second stage, the outcome is regressed on the predicted treatment from the first stage.
High-Volume Physician Sub-cohort	A restricted cohort of patients whose physicians wrote a minimum number of qualifying prescriptions. Used to ensure sufficient data for calculating stable proportional history algorithms [3].
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Physician Prescribing Preference (PPP) serves as a valuable instrumental variable (IV) in pharmacoepidemiology, used to estimate treatment effects when unmeasured confounding exists [3]. Traditional PPP applications often treat exposure as a static baseline measure. However, in longitudinal studies, medication exposure is often dynamic, with patients starting, stopping, or switching treatments over time [21] [22]. This note details protocols for extending PPP methods to handle time-varying exposures, enabling more robust causal inference in drug safety and effectiveness research.

Core Conceptual Framework

The Challenge of Time-Varying Exposure and Confounding

Longitudinal pharmacoepidemiologic studies present specific methodological challenges [21]:

• Exposure Complexity: Real-world medication use involves varying dosage, timing, and duration that simple "ever/never" exposed definitions fail to capture [21]
• Time-Varying Confounding: Factors that confound the exposure-outcome relationship may themselves be influenced by prior exposure history [22]
• Treatment Switching: Patients frequently switch medications during follow-up for various reasons, complicating effect estimation [22]

Standard PPP approaches that ignore these temporal aspects may yield biased effect estimates due to exposure misclassification and unaccounted confounding paths [21] [22].

Longitudinal PPP as an Instrumental Variable

For PPP to function as a valid instrument in longitudinal settings, it must satisfy extended conditions:

• Relevance: PPP must predict time-varying treatment exposure patterns
• Exclusion: PPP affects outcomes only through its influence on treatment exposure
• Exchangeability: PPP is independent of unmeasured confounders at each time point
• Treatment Variation Irrelevance: PPP does not affect outcomes through treatment pathways other than the exposure of interest

Table 1: Performance Metrics of Alternative PPP Operationalizations in Longitudinal Settings

PPP Formulation	IV Strength (Partial R²)	Covariate Balance Reduction	Suitable for Time-Varying Analysis
Last prescription only	0.028–0.099 [3]	36% (±40%) [3]	Limited
Moving window (last 3-4 prescriptions)	Moderate	High	Good
Specialty-stratified preference	High	High	Excellent
Facility-level variation	Moderate	Moderate	Good
Restriction to stable prescribers	High	High	Excellent

Protocol: Implementing Longitudinal PPP Analysis

Data Structure Requirements

Longitudinal PPP analysis requires person-time data structured with:

• Multiple time segments per patient (e.g., weeks, months)
• Time-varying covariates assessed at each segment
• Time-updated exposure status and dosage
• PPP measured at each time point using recent prescription history

PPP Measurement Algorithms

Protocol 1: Moving Window Preference Assessment

• Define: For each patient encounter, identify the physician
• Identify: Locate the physician's previous N new prescription events (N=2-4 recommended)
• Calculate: Compute the proportion of conventional vs. atypical prescriptions in this window
• Classify: Apply preference thresholds (lenient: ≥1 conventional; strict: all conventional; moderate: majority conventional) [3]
• Assign: Categorize current patient's instrument value based on this preference measure

Protocol 2: Stratified Preference by Patient Characteristics

• Group: Arrange patients by key characteristics (age, comorbidity profile)
• Calculate: Compute physician preference within each subgroup
• Assign: Use subgroup-specific preference for instrument assignment [3]

Analytical Implementation

Two-Stage Approach for Continuous Outcomes:

• First Stage: Model time-varying exposure as function of time-varying PPP and covariates
• Second Stage: Model outcome using predicted exposure values from first stage

Marginal Structural Models with IV Weights:

• Calculate: Inverse probability of PPP weights to balance covariates
• Estimate: Weighted structural models for exposure-outcome relationship

Application Notes

Key Methodological Considerations

PPP Strength Maintenance:

• Monitor first-stage F-statistics across time periods (target >10)
• Consider restricting to physicians with adequate prescription volume
• Test multiple preference windows (last 2, 3, or 4 prescriptions) for optimal strength [3]

Handling Time-Varying Confounding:

• Use g-methods (e.g., marginal structural models) when confounders are affected by prior exposure
• Implement inverse probability weighting to account for time-dependent confounding [21]

Exposure Definition:

• Move beyond binary ever/never exposed definitions
• Incorporate dosage, timing, and treatment duration [21]
• Consider cumulative exposure metrics when biologically relevant

Validation and Sensitivity Analyses

Protocol 3: Longitudinal IV Assumption Testing

• Balance Assessment: Check covariate balance across PPP strata at each time point
• Strength Evaluation: Calculate partial R² for PPP-exposure association longitudinally
• Sensitivity Analysis: Test robustness to different PPP operationalizations
• Placebo Testing: Assess PPP-outcome association during pre-exposure periods

Table 2: Research Reagent Solutions for Longitudinal PPP Studies

Methodological Component	Function	Implementation Considerations
Group-based trajectory models	Identify patterns in medication use over time [21]	Handles irregular measurement occasions; useful for complex exposure patterns
Extended Cox models	Account for time-varying exposures in survival analysis [21]	Properly classifies exposed and unexposed person-time
Marginal structural models	Adjust for time-varying confounding affected by prior exposure [21] [22]	Requires correct model specification for time-varying weights
Two-stage least squares	IV estimation for continuous outcomes	Can be extended to longitudinal data structures
Structural nested failure time models	Address time-varying exposures and informative censoring [22]	Complex implementation but handles dynamic treatment regimes

Advanced Applications

Combining PPP with Other Longitudinal Methods

Integration with Unsupervised Clustering:

• Identify: Medication use trajectories via group-based trajectory modeling [21]
• Instrument: Use PPP to predict trajectory group membership
• Estimate: Causal effects of trajectory patterns on outcomes

Handling Complex Exposure Regimes:

• Drug switching: Use PPP to instrument for initial treatment choice
• Dose titration: Model PPP association with dosage escalation patterns
• Treatment gaps: Instrument for persistence/adherence behaviors

Implementation Guidelines

Reporting Standards

Based on systematic reviews of PPP applications [4], studies should explicitly report:

• PPP operationalization with precise algorithm definition
• Longitudinal structure of data and analysis
• IV strength metrics at each relevant time point
• Balance assessments for measured covariates across time
• Sensitivity analyses for PPP definitions and modeling assumptions

Common Pitfalls and Solutions

Weak Instrument Issues:

• Problem: Declining PPP strength over time
• Solution: Restrict to physicians with consistent prescribing patterns

Selection Bias:

• Problem: Differential loss to follow-up correlated with PPP
• Solution: Apply censoring weights or selection models

Violation of Exclusion Restriction:

• Problem: PPP affects outcomes through pathways other than medication exposure
• Solution: Test for direct PPP-outcome associations in pre-exposure periods

Extending PPP to longitudinal settings requires careful attention to time-varying aspects of both the instrument and the exposure-outcome-confounding structure. When properly implemented, these methods provide valuable tools for strengthening causal inference in pharmacoepidemiologic research with time-varying treatments.

The evaluation of biologic disease-modifying antirheumatic drugs (bDMARDs) for rheumatoid arthritis (RA) using observational data presents significant methodological challenges, primarily due to unmeasured confounding factors such as disease severity and patient comorbidities. Physician Prescribing Preference (PPP) has emerged as a valuable instrumental variable (IV) to address this confounding bias in comparative effectiveness research [3] [4]. This case study application details the methodology for implementing PPP as an IV to evaluate the effect of sustained adalimumab treatment versus other biologics on quality-adjusted life years (QALYs) in RA patients, drawing from a recent study utilizing the US National Databank for Rheumatic Diseases (FORWARD) [23].

The application of IV methods is particularly crucial in time-varying treatment settings where patients may switch or adjust therapies over extended periods. Traditional regression methods cannot adequately address time-varying confounding, while standard g-methods rely on the untestable assumption of no unmeasured confounding [23]. The PPP IV approach exploits natural variation in physicians' prescribing patterns to create "as-if randomized" treatment assignments, thereby mitigating both measured and unmeasured confounding [3].

Instrumental Variable Assumptions and Validation

For Physician Prescribing Preference to function as a valid instrumental variable, it must satisfy three critical assumptions:

• Relevance: The instrument must be strongly associated with the actual treatment assignment [3] [4]. In practice, this requires demonstrating that physicians' prior prescribing patterns significantly predict current treatment decisions for new patients.

• Exclusion Restriction: The instrument must affect the outcome only through its effect on treatment, not through any alternative causal pathways [3] [4]. This assumption would be violated if physician preferences were correlated with other quality-of-care factors that independently influence patient outcomes.

• Exchangeability: The instrument must be independent of measured and unmeasured patient characteristics [3] [4]. This implies that patients are effectively "randomized" to physicians with different prescribing preferences with respect to their potential outcomes.

Table 1: Validation Tests for Physician Prescribing Preference IV

Assumption	Validation Test	Interpretation
Relevance	First-stage F-statistic > 10 [3]	Strong instrument evidence
Relevance	Partial R² values [3]	Quantifies predictive power
Exchangeability	Covariate balance tests [3]	Compares patient characteristics across preference groups
Exchangeability	Mahalanobis distance [3]	Multivariate balance assessment

Recent methodological reviews indicate that only approximately 12% of PP IV applications adequately report all three core assumptions, highlighting the need for more rigorous reporting standards [4]. In the FORWARD databank case study, physician preference was measured as the treatment chosen for the physician's previous patient with similar characteristics, creating a time-varying instrument that evolved with the physician's prescribing pattern [23].

Data Collection Framework

The primary data source for this case study is the US National Databank for Rheumatic Diseases (FORWARD), a longitudinal registry collecting comprehensive patient-reported outcomes from over 50,000 RA patients across 1,500 rheumatologists in the United States and Canada [23]. Data is collected through biannual questionnaires capturing disease activity, treatment history, and health-related quality of life measures.

Study Population Eligibility Criteria

Table 2: Inclusion and Exclusion Criteria

Criteria Category	Inclusion	Exclusion
Diagnosis	Moderate to severe RA	Patients switching back to conventional DMARDs
Treatment	Initiating bDMARDs	Missing physician information
Follow-up	≥3 follow-up phases (18 months)	Incomplete outcome data
Data Quality	Complete baseline characteristics	-

The final study population comprised 1,952 patients with 648 initiating adalimumab and 1,304 initiating other biologic therapies [23]. Baseline characteristics showed significant differences between treatment groups, with adalimumab initiators being younger and having lower comorbidity scores, highlighting the presence of channeling bias that necessitates IV methods [23].

Variable Definitions and Measurement

Outcome Variable

The primary outcome was quality-adjusted life years (QALYs) over an 18-month follow-up period, derived from the EuroQOL-5D (EQ-5D) health-related quality of life measure [23]. QALYs were calculated as:

[ \text{QALY} = \frac{\text{EQ-5D at time 1} + \text{EQ-5D at time 2} + \text{EQ-5D at time 3}}{2} ]

This continuous measure ranges from 0 (death) to 1.5 (perfect health for 18 months), providing a comprehensive assessment of health-related quality of life [23].

Treatment Variable

The treatment was defined as a time-varying exposure to sustained adalimumab use versus other biologic therapies over the 18-month study period. Treatment was assessed at each 6-month phase to account for potential switching or discontinuation [23].

Instrument Variable

The PPP instrument was operationalized as a time-varying categorical variable representing the physician's preference at each treatment decision point. Preference was defined based on the physician's prior prescribing history, with multiple algorithms possible [23] [3]:

• Base case: Treatment prescribed to the immediately previous eligible patient
• Strict criteria: Consistent pattern over multiple previous prescriptions (e.g., 2 of last 2 prescriptions)
• Lenient criteria: Any use within a specified window (e.g., 1 of last 3 prescriptions)

Covariate Measurements

Both time-invariant and time-varying covariates were included to address measured confounding and assess instrument validity:

• Time-invariant: Age, gender, race, smoking status
• Time-varying: Health insurance, RA duration, disease activity (DAS), Health Assessment Questionnaire (HAQ) scores, comorbidity indices, concomitant medications [23]

Analytical Methods

IV-Based G-Estimation Protocol

The IV-based g-estimation approach extends standard g-methods to incorporate instrumental variables, addressing both time-varying confounding and unmeasured confounding simultaneously [23]. The protocol involves the following steps:

• Stage 1: Model the effect of the time-varying PPP instrument on actual treatment assignment at each time period, conditional on past covariate history and prior treatments.

• Stage 2: Estimate the causal effect parameter by finding the value that renders the potential outcomes independent of the instrument, conditional on the observed history.

• Iteration: Repeat across all time points to estimate the cumulative treatment effect.

The g-estimation approach provides unbiased, precise estimates across a wide range of scenarios, including weak instruments and complex time-varying confounding mechanisms [23]. Implementation can be achieved through standard statistical software with custom programming for the g-estimation algorithm.

Inverse Probability Weighting Protocol

As a comparative method, the inverse probability weighting (IPW) approach with IVs creates a pseudo-population by reweighting subjects according to both treatment and instrument status [23]. The protocol involves:

• Modeling: Estimate predicted probabilities of observed treatment sequences given the instrument and covariate history.

• Weighting: Calculate stabilized weights for each patient-time observation.

• Analysis: Fit weighted regression models to estimate the treatment effect on outcomes.

The IPW approach performs reasonably with strong time-varying instruments but deteriorates with decreasing IV strength [23].

Diagram 1: IV Causal Assumptions (55 characters)

Diagram 2: Analytical Workflow (53 characters)

Case Study Implementation and Results

Application to FORWARD Databank

In the FORWARD databank application, the IV-based g-estimation approach provided unbiased and precise estimates of the treatment effect of adalimumab versus other biologics on QALYs [23]. The results indicated that sustained treatment with adalimumab did not significantly improve health-related quality of life compared to other biologic agents, with the g-estimation approach yielding narrower confidence intervals than alternative methods [23].

The strength of the physician preference instrument was observed to be moderate for initial treatment decisions but decreased over time, highlighting the practical challenges of maintaining strong instruments in longitudinal settings [23]. This pattern underscores the importance of reporting instrument strength at each time point in time-varying IV analyses.

Sensitivity Analyses Protocol

Comprehensive sensitivity analyses are essential for validating IV results:

• Instrument Strength: Assess partial R² values and F-statistics across different preference algorithms [3]

• Threshold Analysis: Estimate the strength of unmeasured confounding that would be necessary to explain away the observed effect

• Alternative Specifications: Test different operationalizations of the PPP instrument (varying window sizes and consistency thresholds) [3]

• Plausibility of Exclusion Restriction: Evaluate potential direct paths between physician preferences and outcomes through qualitative assessment of prescribing drivers [24]

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential Methodological Tools for PPP IV Analysis

Tool Category	Specific Implementation	Function/Purpose
Data Infrastructure	FORWARD-style longitudinal registry [23]	Captures patient-reported outcomes, treatment history, and provider information
IV Operationalization	Multiple preference algorithms (base case, strict, lenient) [3]	Tests robustness of instrument definition
Statistical Software	R, Python, or Stata with IV packages (e.g., ivreg, ivtools)	Implements g-estimation and IPW algorithms
Balance Assessment	Mahalanobis distance calculator [3]	Quantifies multivariate covariate balance
Strength Diagnostics	Partial R² and F-statistic calculators [3]	Assesses instrument relevance assumption
Qualitative Assessment	Physician interview guides [24]	Validates exclusion restriction assumption

Discussion and Methodological Considerations

The application of Physician Prescribing Preference as an instrumental variable for evaluating biologics in rheumatoid arthritis represents a powerful approach for addressing unmeasured confounding in comparative effectiveness research. However, several important considerations emerge from this case study:

First, the time-varying nature of both treatments and instruments introduces complex analytical challenges. While IV-based g-estimation performed well across various scenarios, its implementation requires sophisticated statistical expertise and careful attention to the evolving nature of physician preferences over time [23].

Second, the strength of the PPP instrument may diminish in later treatment phases as initial preferences are moderated by patient response and evolving clinical evidence [23]. This suggests that PPP instruments may be most valid for initial treatment decisions rather than long-term treatment persistence.

Third, the exclusion restriction assumption requires careful consideration of why physicians develop specific preferences. Qualitative research indicates that prescribing decisions are influenced by a complex constellation of factors including clinical trial experience, departmental cost structures, peer pressure, and administrative influences [24]. If these factors independently affect patient outcomes, the exclusion restriction may be violated.

Future applications of PPP IV methods should prioritize transparent reporting of all three core assumptions, comprehensive sensitivity analyses, and integration of qualitative insights about prescribing drivers to strengthen the plausibility of the exclusion restriction [4] [24]. When these methodological rigor is maintained, PPP IV approaches offer a valuable tool for generating real-world evidence about the comparative effectiveness of biologic therapies for rheumatoid arthritis.

Software and Analytical Considerations for Implementing IV Analysis

Instrumental Variable (IV) analysis is a powerful causal inference method used to address confounding bias in observational studies, particularly when unmeasured confounding is suspected. In pharmaceutical outcomes research, IV methods can provide unbiased estimates of treatment effects when randomized controlled trials are not feasible. The core principle involves identifying an instrument—a variable that influences treatment assignment but does not directly affect the outcome except through its effect on treatment [25].

This document provides application notes and protocols for implementing IV analysis, specifically framed within the context of using physician prescribing preference as an instrumental variable. This guidance is designed for researchers, scientists, and drug development professionals conducting comparative effectiveness research using longitudinal healthcare data.

Instrumental Variable Validity and Physician Prescribing Preference

Core Assumptions of a Valid Instrument

For any variable to serve as a valid instrument, it must satisfy three critical assumptions:

• Relevance: The instrument must be strongly associated with the treatment assignment.
• Exclusion Restriction: The instrument must affect the outcome only through its effect on treatment, not through any other causal pathways.
• Exchangeability: The instrument must be independent of measured and unmeasured confounders of the treatment-outcome relationship.

Physician Prescribing Preference as an IV

Physician prescribing preference has been widely used as an IV for evaluating point treatments and can be extended to time-varying settings [25]. In this context, the time-varying IV can be defined as the proportion of a specific drug prescription (e.g., Adalimumab) compared to all biologic prescriptions by each physician over a specific time period (e.g., 6 months).

Operationalization in longitudinal studies: The instrument takes the value 1 if the within-physician proportion exceeds a specific threshold (e.g., 75%), and 0 otherwise, measured at each follow-up period [25].

Software Solutions for IV Analysis

Implementing IV analysis requires specialized statistical software. The table below summarizes key software solutions and their analytical capabilities.

Table 1: Software Solutions for Implementing Instrumental Variable Analysis

Software Tool	Analytical Capabilities	IV Methods Supported	Implementation Considerations
Statistical Platforms (R, Python, Stata, SAS)	Generalized modeling, data management, visualization	Two-stage least squares, G-estimation, Inverse probability weighting	Requires programming expertise; offers maximum flexibility
Dedicated IV Packages (R: ivtools, AERStata: ivreg2)	Specialized IV estimation procedures	Time-varying IV methods, Sensitivity analyses	Implements specific methodological approaches; may have steeper learning curve
Clinical Data Visualization Tools	Data exploration, result presentation	Not applicable for estimation	Critical for communicating IV analysis results to diverse audiences

Quantitative Comparison of IV Methods

A simulation study comparing IV methods under different scenarios provides guidance for method selection. The performance of two approaches—IV-based g-estimation and inverse probability weighting—was evaluated across varying instrument strengths and confounding mechanisms [25].

Table 2: Performance Comparison of IV Methods Under Different Scenarios

Method	IV Strength	Confounding Mechanism	Bias	Precision	Recommendation
IV-G-estimation	Weak to Strong	Simple to complex time-varying	Unbiased	High (narrower confidence intervals)	Primary recommendation across most scenarios
Inverse Probability Weighting	Strong	Simple time-varying	Minimal bias	Moderate	Acceptable alternative with strong IV
Inverse Probability Weighting	Weak	Complex time-varying	Substantial bias	Low (wider confidence intervals)	Not recommended with weak IV

Experimental Protocols for IV Analysis

Protocol 1: Data Structure Preparation for Time-Varying IV Analysis

Purpose: To prepare longitudinal data in the appropriate format for implementing time-varying IV analysis with physician prescribing preference.

Materials and Reagents:

• Longitudinal healthcare database (e.g., electronic health records, disease registry)
• Statistical software with IV analysis capabilities (R, Stata, SAS, or Python)
• Data management tools for restructuring datasets

Procedure:

• Define analysis periods: Divide the observation period into discrete time intervals (e.g., 6-month "phases" corresponding to data collection cycles) [25].
• Identify the study population: Include patients who initiated the treatment of interest during the baseline period and have sufficient follow-up data (e.g., at least 3 follow-up phases) [25].
• Code the time-varying instrument: For each physician and time period, calculate the proportion of prescriptions for the target drug versus alternatives. Dichotomize based on a predetermined threshold (e.g., >75% = 1, ≤75% = 0) [25].
• Structure the dataset: Create a person-period dataset where each row represents one patient during one time period, with columns for:
  • Patient identifier
  • Time period
  • Treatment status
  • Instrument value
  • Outcome measurement
  • Time-varying confounders
  • Time-fixed baseline characteristics
• Validate data structure: Confirm that the dataset appropriately captures time-varying nature of instrument, treatment, and confounders.

Protocol 2: IV-Based G-Estimation for Time-Varying Treatments

Purpose: To implement g-estimation for estimating time-varying treatment effects using a physician prescribing preference instrument.

Materials and Reagents:

• Structured longitudinal dataset from Protocol 1
• Statistical software with programming capabilities
• Computational resources for iterative model fitting

Procedure:

• Specify the structural nested mean model (SNMM):
  • Define the causal effect of treatment at each time point
  • Include parameters for time-varying treatment effects if hypothesized
• Estimate the nuisance parameters:
  • Model the conditional mean of the outcome given treatment history and covariate history
  • Model the conditional distribution of the instrument given covariate history
• Solve the g-estimation equation:
  • Use iterated conditional expectations or g-computation
  • Incorporate the instrument to identify causal parameters
• Obtain point estimates and confidence intervals:
  • Use robust standard errors to account for clustering within physicians
  • Implement bootstrap resampling if needed for complex sampling
• Validate model assumptions:
  • Test instrument strength using F-statistics from first-stage regression
  • Conduct sensitivity analyses for exclusion restriction assumption

Protocol 3: Inverse Probability Weighting with Time-Varying IV

Purpose: To implement inverse probability weighting using a time-varying physician prescribing preference instrument.

Materials and Reagents:

• Structured longitudinal dataset from Protocol 1
• Statistical software with generalized estimating equation capabilities
• Numerical optimization routines for weight stabilization

Procedure:

• Model the treatment assignment mechanism:
  • Fit a logistic regression model for treatment assignment at each time point
  • Include the instrument, prior treatment, time-varying confounders, and baseline covariates
  • Obtain predicted probabilities of treatment assignment
• Calculate inverse probability weights:
  • Compute unstabilized weights as 1/predicted probability for the assigned treatment
  • Consider stabilized weights to reduce variability:
    • Numerator: Marginal probability of observed treatment history
    • Denominator: Conditional probability of observed treatment history given confounder history
• Apply weights to outcome model:
  • Fit a weighted regression model for the outcome
  • Include treatment as the primary independent variable
  • Adjust for appropriate covariates to improve precision
• Assess weight performance:
  • Examine weight distribution for extreme values
  • Truncate or stabilize weights if necessary to prevent dominance by few observations
• Estimate treatment effects:
  • Obtain coefficient for treatment variable from weighted model
  • Calculate robust confidence intervals accounting for weighting

Visualizing IV Analysis Concepts and Workflows

Conceptual Diagram of Physician Preference IV

IV Conceptual Relationship: This diagram illustrates the core assumptions of using physician prescribing preference as an instrumental variable, showing how it affects the outcome only through treatment while unmeasured confounders affect both treatment and outcome.

Time-Varying IV Analysis Workflow

IV Analysis Workflow: This workflow outlines the key stages in implementing instrumental variable analysis, from data preparation through method selection to final interpretation, highlighting the decision point between primary methods.

Case Study: Evaluating Biologics for Rheumatoid Arthritis

Application of IV Methods

In a retrospective cohort study from the US National Databank for Rheumatic Diseases, researchers evaluated the sustained use of Adalimumab versus other biologics on health-related quality of life (QALY) for patients with Rheumatoid Arthritis [25].

Study Design Elements:

• Target population: Patients with moderate/severe RA who failed DMARDs and initiated biologic treatment
• Sample size: 1,952 patients after exclusions
• Time structure: 4 phases (6-month intervals) over 18 months of follow-up
• Instrument: Physician's preference for Adalimumab measured as proportion of prescriptions
• Outcome: Quality-adjusted life year (QALY) derived from EQ-5D scores

Results: Both IV methods suggested that sustained treatment with Adalimumab did not improve QALY compared to other biologics, but the g-estimation approach provided more precise estimates with narrower confidence intervals [25].

Methodological Considerations and Limitations

Key Analytical Considerations

When implementing IV analysis with physician prescribing preference:

• Time-varying confounding: Standard regression methods cannot adequately address time-varying confounding, while g-methods like IV-based g-estimation are specifically designed for this setting [25].
• Instrument strength: The performance of weighting approaches deteriorates substantially with weak instruments, while g-estimation remains more robust [25].
• Missing data: Consider appropriate methods for handling missing data in longitudinal settings, as complete-case analysis may introduce selection bias.
• Model specification: Test different functional forms and interaction terms to ensure appropriate model specification.

Limitations and Mitigation Strategies

Table 3: Common Limitations and Mitigation Strategies in IV Analysis

Limitation	Impact on Validity	Mitigation Strategies
Weak instrument	Increased bias, reduced precision	Use F-statistic >10 from first-stage regression; prefer g-estimation over weighting
Violation of exclusion restriction	Biased effect estimates	Conduct sensitivity analyses; assess direct paths from instrument to outcome
Time-varying confounding affected by prior treatment	Standard methods fail	Use g-methods specifically designed for this setting
Selection bias from loss to follow-up	Compromised exchangeability	Implement appropriate missing data methods (e.g., inverse probability of censoring weights)

Implementing instrumental variable analysis with physician prescribing preference requires careful attention to both theoretical assumptions and practical analytical considerations. The protocols outlined in this document provide a structured approach for researchers conducting comparative effectiveness studies in pharmaceutical development.

Based on current evidence, IV-based g-estimation is recommended as the primary analytical approach due to its robustness across varying instrument strengths and complex time-varying confounding scenarios. Inverse probability weighting offers an accessible alternative but performs well only when instruments are strongly associated with treatment assignment.

When applying these methods to drug development research, researchers should prioritize transparent reporting of instrument validity checks, comprehensive sensitivity analyses, and clear communication of assumptions underlying the causal conclusions.

Navigating Challenges and Enhancing the Robustness of PPP IV Analysis

Instrumental variable (IV) analysis is a powerful statistical method used in comparative effectiveness research to estimate causal treatment effects when unmeasured confounding is present. Within this framework, physician's prescribing preference (PPP) has emerged as a frequently used instrumental variable, particularly in studies analyzing administrative healthcare data. However, the practical application of PPP IV analyses often confronts a significant methodological challenge: weak instruments, especially in studies with small to moderate sample sizes. This challenge is particularly acute in research on rare outcomes, newly marketed pharmaceuticals, or studies limited to specific administrative regions where sample sizes may be constrained.

The weak instrument problem occurs when the instrumental variable exhibits only a weak association with the treatment variable, leading to biased estimates, unreliable inference, and reduced statistical power. This article provides comprehensive Application Notes and Protocols for addressing weak instruments in PPP IV studies with limited sample sizes, synthesizing evidence from simulation studies and methodological research to offer practical guidance for researchers, scientists, and drug development professionals.

Understanding the Weak Instrument Problem in PPP Studies

Defining Instrument Strength

Instrument strength refers to the strength of association between the instrumental variable (physician prescribing preference) and the actual treatment received by patients. In statistical terms, this is commonly assessed using the F-statistic from the first-stage regression, where the treatment variable is regressed on the instrument. A common threshold for acceptable instrument strength is a first-stage F-statistic of 10, though this may be insufficient in many practical scenarios [26].

The fundamental challenge with weak instruments is that they introduce a bias-variance trade-off. While IV methods effectively address unmeasured confounding, weak instruments can result in estimates with substantial variance and potential bias, particularly when the instrument is only weakly correlated with the treatment. In fact, with weak instruments, IV estimates can be more biased than conventional ordinary least squares (OLS) estimates that adjust only for observed confounders [26].

Performance of PPP IV in Smaller Samples

Recent simulation evidence has demonstrated that the PPP IV approach maintains its advantage over conventional methods even in smaller sample sizes. Specifically, while OLS estimates can exhibit percent bias approaching 60% in the presence of unmeasured confounding, 2SLS IV estimates maintain percent bias around approximately 20% regardless of sample size [5]. This indicates that the core benefit of PPP IV—addressing unmeasured confounding—persists even when sample sizes are constrained.

However, sample size does impact the statistical power of PPP IV analyses. As sample size decreases, the F-statistic of the first stage regression diminishes, resulting in larger p-values for 2SLS estimates and reduced ability to detect true treatment effects [5]. This creates a scenario where estimates may be less biased but increasingly imprecise, complicating inference and interpretation.

Table 1: Performance Comparison of 2SLS-IV and OLS Across Sample Sizes

Method	Sample Size	Percent Bias	Coverage Rate	Key Limitations
2SLS-IV	Moderate (n=2,452)	~20%	~95%	Reduced statistical power
2SLS-IV	Small (n=620)	~20%	~95%	Further reduced power
OLS	Moderate (n=2,452)	~60%	Dramatically drops with confounding	Susceptible to unmeasured confounding
OLS	Small (n=620)	~60%	Dramatically drops with confounding	Susceptible to unmeasured confounding

Protocol for Constructing Robust PPP Instruments in Small Samples

PPP Construction Methods

The construction of physician prescribing preference instruments requires careful consideration of physicians' historical prescribing patterns. Different operationalizations of PPP can significantly impact instrument strength, particularly in smaller samples:

• Proportional PPP: Calculated as the number of prescriptions for the target drug made by a physician divided by the total number of all prescriptions made by that physician [5]. This provides a continuous measure of prescribing preference.

• Categorical PPP Based on Percentiles: Physicians can be categorized based on their prescribing patterns, such as classifying those in the ≥80th percentile of drug use as "preferrers" and others as "non-preferrers" [27]. This creates a binary instrument.

• Temporal PPP Constructions: Various historical windows can be used, including prior 1 prescription (most recent), prior 2 prescriptions, prior 3 prescriptions, and prior 4 prescriptions from the same physician [5].

Analytical Protocol for Strengthening PPP Instruments

The following step-by-step protocol outlines the process for constructing and validating PPP instruments in studies with limited sample sizes:

Stage 1: Instrument Construction

• Extract physician prescribing history from administrative databases
• Calculate proportional PPP for each physician using the formula:

Proportional PPP = Number of drug A prescriptions by physician / Total prescriptions by physician [5]

• Alternatively, create categorical PPP based on percentile thresholds (e.g., ≥80th percentile)
• Test multiple historical windows (prior 1-4 prescriptions) to identify optimal strength

Stage 2: First-Stage Validation

• Regress actual treatment receipt on the constructed PPP instrument
• Calculate first-stage F-statistic to assess instrument strength
• For categorical PPP, assess correlation between instrument and treatment (target: r > 0.7) [27]
• Compare balance of observed covariates across instrument-based treatment allocation groups

Stage 3: Assumption Testing

• Test association between PPP and observed patient characteristics to assess independence assumption
• Evaluate exclusion restriction conceptually (PPP should affect outcome only through treatment)
• Assess monotonicity assumption (no "defiers" in prescribing behavior)

Stage 4: Estimation and Inference

• Implement Two-Stage Least Squares (2SLS) estimation
• Report robust tests (Anderson-Rubin) in addition to conventional t-tests [26]
• Calculate confidence intervals using methods robust to weak instruments
• Conduct sensitivity analyses with different PPP constructions

Table 2: PPP Construction Methods and Their Properties

PPP Construction Method	Measurement Scale	Data Requirements	Strengths	Weaknesses
Proportional PPP	Continuous (0-1)	Complete prescribing history	Maximizes information use	May be sensitive to outliers
Binary (Percentile-based)	Categorical (0/1)	Prescribing distribution	Clear clinical interpretation	Loss of information
Prior 1 Prescription	Binary	Most recent prescription only	Simple construction	Vulnerable to recent anomalies
Prior 4 Prescriptions	Continuous or categorical	Extended prescription history	More stable preference measure	Requires sufficient history

Strategic Approaches to Enhance Statistical Power

Extending Prescription History

Simulation evidence strongly supports extending the prescription history used to construct PPP instruments when working with small samples. The statistical power of PPP IV analyses increases substantially as the number of previous prescriptions used in PPP construction increases from prior 1 to prior 4 prescriptions [5]. This occurs because longer prescribing histories provide a more stable and accurate measurement of a physician's underlying prescribing preference, thereby strengthening the instrument.

Practical Implementation:

• When possible, construct PPP using at least 3-4 previous prescriptions per physician
• Balance historical depth with clinical relevance (accounting for changes in guidelines)
• Conduct sensitivity analyses comparing different historical windows

Analytical Enhancements for Power Improvement

• Combine PPP with Other Instruments: Where feasible, consider combining PPP with other valid instruments (e.g., hospital preference, geographical variation) to enhance overall instrument strength [27].

• Leverage Covariate Adjustment: Include observed confounders in both stages of the 2SLS estimation to improve precision, even when focusing on unmeasured confounding [5].

• Utilize Robust Inference Methods: Implement inference techniques that remain valid with weak instruments, such as the Anderson-Rubin test, which maintains correct size even with weak instruments [26].

Visualization of Analytical Workflow

The following diagram illustrates the complete analytical workflow for implementing PPP IV analysis in small sample contexts, highlighting key decision points and validation steps:

Analytical Workflow for PPP IV Analysis in Small Samples

Research Reagent Solutions: Essential Methodological Tools

The following table details key methodological "reagents" essential for implementing robust PPP IV analyses in small sample contexts:

Table 3: Essential Methodological Tools for PPP IV Analysis

Research Reagent	Function	Implementation Considerations
Two-Stage Least Squares (2SLS)	Primary estimation method for IV analysis	Standard approach; may require robustness checks for weak instruments
First-Stage F-Statistic	Diagnostic for instrument strength	Target F>10 minimum; higher thresholds (F>50) may be needed for confidence
Anderson-Rubin Test	Robust inference with weak instruments	Maintains correct test size regardless of instrument strength
Proportional PPP Calculator	Constructs continuous preference measure	Requires complete prescribing history for physicians
Covariate Balance Table	Assesses independence assumption	Standardized differences <0.1 indicate good balance
Monotonicity Check	Validates key IV assumption	Assesses presence of "defiers" in prescribing behavior
Multiple History Windows	Sensitivity analysis framework	Tests robustness across different PPP constructions

Interpretation and Reporting Guidelines

Contextualizing Findings

When reporting PPP IV results from small sample studies, researchers should:

• Explicitly acknowledge sample size limitations and their implications for statistical power
• Present both point estimates and confidence intervals to communicate precision
• Report multiple robustness checks using different PPP constructions
• Compare IV results with conventional estimates (OLS with covariate adjustment) to contextualize findings

Addressing Monotonicity Assumptions

Empirical evidence suggests that deterministic monotonicity (all physicians have the same preference ordering of treatments) is generally not plausible for PPP instruments. However, stochastic monotonicity (patients are more likely to receive a treatment if their physician prefers it) may be plausible depending on the instrument definition [6]. Researchers should clearly state which monotonicity assumption they are making and provide justification.

Physician's prescribing preference remains a valuable instrumental variable for addressing unmeasured confounding in comparative effectiveness research, even when sample sizes are small or moderate. By implementing the strategies outlined in these Application Notes and Protocols—including extending prescription histories, utilizing robust inference methods, and conducting comprehensive sensitivity analyses—researchers can enhance the validity and reliability of PPP IV studies in sample-constrained contexts. The key insight is that while small samples reduce statistical power, they do not fundamentally undermine the bias-reduction advantage of IV methods over conventional approaches, making PPP IV a valuable tool even when data limitations exist.

Selection bias poses a significant threat to the validity of causal inferences in observational studies, particularly when using physician prescribing preference (PPP) as an instrumental variable (IV). This bias occurs when systematic differences in patient enrollment or treatment allocation influence study outcomes, potentially compromising result validity. Within PPP IV research, selection bias can arise when physicians' treatment decisions are influenced by patient prognoses rather than solely by their prescribing preferences. This undermines the IV assumption that the instrument affects outcomes only through the assigned treatment. Restriction and stratification techniques serve as methodological approaches to address these biases by refining the study population or analysis to create more comparable patient groups, thereby strengthening causal inference from observational healthcare data.

Table 1: Prevalence of Selection Bias Risk Factors in Randomized Trials [28]

Risk Factor	Prevalence in Trials (%)	Implications for PPP IV Studies
No blinding of recruiters	98% (no information)	Unblinded assessors may influence patient selection
Use of simple randomization	3%	Complex randomization increases prediction risk
Use of restricted randomization	63%	Blocked designs enable allocation prediction
Stratification by recruitment site	44%	Site differences may introduce selection bias
Use of permuted blocks with site stratification	58%	Fixed blocks increase predictability
Use of random block sizes	15%	Recommended to reduce predictability
Inclusion of prognostic covariates	56%	Improves balance but may not address selection

Table 2: Performance of 25 Physician Prescribing Preference IV Formulations [3]

Formulation Characteristic	Range/Description	Impact on Bias Reduction
Partial R² values (instrument strength)	0.028 to 0.099	Stronger instruments reduce confounding amplification
Overall covariate imbalance reduction	36% (±40%)	Improved balance suggests increased IV validity
Preference assignment algorithms	Lenient, moderate, strict	More stable preference estimates improved balance
Cohort restriction schemes	Physician volume, specialty, patient age	Increased homogeneity strengthened IV assumptions
Stratification approaches	Age, propensity score matching	Improved comparability of patient groups

Experimental Protocols for Bias Mitigation Techniques

Protocol 1: Preference Assignment Algorithm Implementation

Objective: To define and measure physician prescribing preference while minimizing misclassification and stabilizing preference estimates over time.

Materials: Longitudinal prescription data, patient cohorts with new treatment initiations, statistical software (R, Python, or SAS).

Procedure:

• Identify Prescribing Physicians: Extract all physicians who have initiated at least one study drug prescription during the observation period
• Define Preference Measurement Window:
  • Base Case: Use the immediately preceding prescription for the same drug class
  • Lenient Criteria: ≥1 conventional prescription within last 2-4 prescriptions
  • Strict Criteria: 2/2, 3/3, or 4/4 conventional prescriptions within window
  • Moderate Criteria: ≥2 conventional prescriptions within last 3-4 prescriptions
• Calculate Preference Metric: For each physician at each patient encounter, determine preference based on historical prescriptions within chosen window
• Assign IV Value: Create dichotomous (preference A vs. B) or categorical instrument
• Validate Instrument Strength: Calculate first-stage F-statistic >10 and partial R²

Validation Metrics: Instrument strength (partial R² ≥ 0.03), covariate balance (Mahalanobis distance reduction), and temporal stability of preference assignments.

Protocol 2: Cohort Restriction for Enhanced IV Validity

Objective: To identify patient subpopulations where physician prescribing preference operates more closely to a natural randomizer.

Materials: Patient demographic data, physician characteristics, prescription records, healthcare utilization data.

Procedure:

• Restrict by Physician Characteristics:
  • Identify physicians with high-volume practices (>20 relevant prescriptions annually)
  • Stratify by specialty (primary care vs. specialists)
  • Categorize by practice patterns (years since graduation, practice setting)
• Restrict by Patient Characteristics:
  • Apply age restrictions (middle quartiles to avoid extremes)
  • Limit to new users of drug class without recent exposures
  • Exclude patients with contraindications to either treatment option
• Apply Combined Restrictions:
  • Restrict to patients whose age aligns with physician's typical practice population
  • Limit to clinical settings with balanced formulary access
  • Exclude periods of major guideline changes that might disrupt preference patterns
• Assess Balance: Compare covariate distribution across treatment groups within restricted cohort

Validation Metrics: Standardized mean differences <0.1 for key covariates, improved instrument strength in restricted cohort, and qualitative assessment of clinical relevance.

Protocol 3: Stratification for Residual Bias Control

Objective: To address residual confounding through within-preference stratification.

Materials: Patient-level clinical and demographic data, propensity score estimation capabilities, statistical software.

Procedure:

• Identify Stratification Variables: Select key potential confounders (age, comorbidities, disease severity)
• Implement Stratification Approaches:
  • Clinical Factor Stratification: Stratify by deciles of propensity score for receiving treatment
  • Demographic Stratification: Stratify by age categories, gender, or socioeconomic indicators
  • Temporal Stratification: Stratify by calendar time to address secular trends
  • Practice Setting Stratification: Stratify by hospital or clinic characteristics
• Execute Within-Strata Analysis:
  • Calculate preference-outcome associations within each stratum
  • Pool estimates using appropriate weights (inverse variance or precision-based)
• Assess Effect Modification: Test for heterogeneity of treatment effects across strata

Validation Metrics: Homogeneity of effects across strata, improved covariate balance within strata, and sensitivity of conclusions to stratification approach.

Visual Workflows for Bias Mitigation Implementation

Bias Mitigation Workflow: This diagram illustrates the sequential implementation of restriction and stratification techniques within a physician prescribing preference instrumental variable study design.

Preference Algorithm Decision: This diagram outlines the process for selecting appropriate physician prescribing preference measurement algorithms based on validation metrics.

Research Reagent Solutions for PPP IV Studies

Table 3: Essential Methodological Tools for PPP IV Research

Research Tool	Function	Implementation Example
Preference Assignment Algorithms	Measures physician prescribing behavior	Last prescription, moving window (2-4 Rxs), consistency thresholds
Cohort Restriction Templates	Defines patient subpopulations with better IV validity	Physician volume thresholds, patient age restrictions, specialty limits
Stratification Frameworks	Controls residual confounding within preference groups	Propensity score quintiles, clinical factor categories, temporal strata
Balance Assessment Metrics	Quantifies covariate balance improvement	Mahalanobis distance, standardized mean differences, variance ratios
Instrument Strength Tests	Evaluates predictive power of IV	First-stage F-statistic, partial R², Sanderson-Windmeijer test
Sensitivity Analysis Packages	Assesses robustness to unmeasured confounding	Proportion of explained variation, E-values, tipping point analyses

Restriction and stratification techniques provide complementary approaches to mitigating selection bias in physician prescribing preference instrumental variable studies. Restriction enhances validity by focusing on clinical scenarios where prescribing preference operates more randomly, while stratification addresses residual confounding through within-group balancing. The quantitative evidence demonstrates that these techniques can reduce covariate imbalance by approximately 36% while maintaining instrument strength within effective ranges (partial R² of 0.028-0.099). Successful implementation requires careful attention to preference measurement algorithms, thoughtful cohort definition, and systematic assessment of both instrument strength and covariate balance. When applied rigorously, these methods strengthen causal inference from observational healthcare data, particularly for drug safety and comparative effectiveness research where randomized trials may be infeasible or unethical.

Within comparative effectiveness research (CER), the Physician's Prescribing Preference (PPP) instrumental variable (IV) is a crucial method for addressing unmeasured confounding when estimating treatment effects using observational data [5] [29]. The validity of this approach hinges on the accurate measurement of the latent variable—a physician's underlying preference for one treatment over another. The construction of the PPP proxy, particularly the length of prescription history and the algorithm used to define preference, significantly impacts the strength and validity of the instrument and, consequently, the reliability of causal effect estimates [5] [3]. These Application Notes provide a detailed protocol for optimizing PPP measurement, synthesizing evidence from simulation and applied studies to guide researchers and drug development professionals.

Performance Comparison of PPP Measurement Approaches

The construction of the PPP instrument involves operationalizing a physician's unobserved preference based on their observed prescribing history. The two primary dimensions for optimization are the number of previous prescriptions considered and the algorithm used to convert this history into a preference measure.

Table 1: Key Metrics for Different PPP Proxy Formulations

PPP Formulation	IV Strength (First-Stage F-statistic)	Percent Bias (in simulation studies)	Impact on Covariate Balance
Prior 1 Prescription	Lower F-statistic [5]	Higher	Less balanced patient groups [3]
Prior 2-4 Prescriptions (Proportional)	Intermediate F-statistic [5]	Intermediate	Improved balance over Prior 1 [3]
"Strict" Algorithm (e.g., 3 of last 3)	Lower F-statistic, high specificity [3]	Varies	Creates more homogenous groups [3]
"Lenient" Algorithm (e.g., 1 of last 3)	Higher F-statistic, lower specificity [3]	Varies	Less homogenous groups [3]
"True" Prescribing Preference (Latent)	Highest F-statistic (~500) [5]	Lowest (~20%) [5]	Not directly observable

Table 2: Impact of Prescription History Length on Statistical Power

Number of Prior Prescriptions Used	Statistical Power	Stability of Preference Measure	Recommended Use Case
Prior 1 (Most Recent)	Lower power, higher p-values [5]	Low (sensitive to last patient) [3]	Rapidly changing preferences
Prior 2	Improved power over Prior 1 [5]	Moderate	General use
Prior 3 & 4	Highest power [5]	High (stable preference estimate) [5] [3]	Smaller sample sizes, stable practice patterns

Experimental Protocols for PPP Construction and Validation

Protocol 1: Constructing Proportional PPP from Prescription History

This protocol details the steps for creating a proportional PPP measure, which is a continuous variable representing the proportion of a specific treatment among a physician's recent prescriptions.

1. Research Reagent Solutions & Data Requirements

• Administrative Claims Data or Electronic Health Record (EHR) Data: Must contain prescriber identifiers, patient identifiers, drug/product codes, and prescription dates [29] [30].
• Data Processing Software (e.g., R, SAS, Python): For data linkage, sorting, and aggregation. Example R code is provided in the supplementary material of [5].
• Cohort Definition Algorithms: To identify new users of the drug classes under study, ensuring the patient is initiating therapy [3].

2. Step-by-Step Procedure

• Step 1: Cohort Creation. Identify all patients initiating either of the two treatments (A vs. B) within the study period. Ensure patients are assigned to a unique prescribing physician.
• Step 2: Prescription History Assembly. For each index prescription in the cohort, extract the physician's history of prescribing Treatment A or B for the n prior patients before the index date. The value of n (e.g., 1, 2, 3, 4) is a key optimization parameter [5].
• Step 3: Proportional PPP Calculation. For each index patient, calculate the proportional PPP using the formula: Proportional PPP = (Number of Treatment A prescriptions by the physician in the last n scripts) / n [5].
• Step 4: Instrument Application. Use this continuous proportional PPP as the instrument (Z) in a two-stage least squares (2SLS) or other IV analysis model [5].

Protocol 2: Constructing and Testing Binary PPP Algorithms

This protocol outlines methods for creating binary PPP instruments using different algorithmic definitions, allowing researchers to test which formulation performs best in their specific dataset.

1. Step-by-Step Procedure

• Step 1: History Assembly. Follow Steps 1 and 2 from Protocol 1.
• Step 2: Algorithm Application. Apply a predefined rule to the prescription history to assign a binary preference (e.g., 1 for prefers A, 0 for prefers B). Test multiple algorithms in parallel [3]:
  • Lenient: "At least 1 of the last 3 prescriptions was for A" → PPP=1.
  • Moderate: "At least 2 of the last 4 prescriptions were for A" → PPP=1.
  • Strict: "All of the last 3 prescriptions were for A" → PPP=1.
• Step 3: IV Strength Validation. For each binary PPP measure, run the first-stage regression of the actual treatment (X) on the instrument (Z), controlling for measured covariates. Calculate the F-statistic. An F-statistic > 10 is a common benchmark for a strong instrument [3].
• Step 4: Covariate Balance Assessment. Compare the balance of measured patient covariates (e.g., age, comorbidities) across the two levels of the binary PPP. A valid IV should create groups with similar covariate distributions. Use the Mahalanobis distance or standardized mean differences to quantify balance [3].

Protocol 3: Implementing a PPP IV Analysis with 2SLS

This is the core protocol for estimating a causal risk difference using the constructed PPP instrument.

1. Step-by-Step Procedure

• Step 1: First-Stage Regression. Regress the actual treatment assignment (X, a binary variable) on the PPP instrument (Z) and all measured confounders (C). X = α₀ + α₂Z + α₃C + ε
• Step 2: Prediction. Obtain the predicted values from the first-stage model (XÌ‚). This represents the part of treatment variation driven by physician preference alone.
• Step 3: Second-Stage Regression. Regress the outcome (Y) on the predicted treatment (XÌ‚) and the same measured confounders (C). Y = β₀ + βₓX̂ + β₃C + ε
• Step 4: Interpretation. The coefficient βₓ from the second stage provides the estimate of the causal effect of the treatment on the outcome [5] [29].

The Scientist's Toolkit: Key Reagents for PPP IV Research

Table 3: Essential Reagents and Tools for PPP IV Studies

Research Reagent / Tool	Function / Purpose	Implementation Notes
Administrative Claims Data	Provides longitudinal records of physician prescriptions, patient diagnoses, and outcomes for large populations [29] [30].	Must contain unique physician identifiers. Data from insurers or national health systems are typical sources.
Proportional PPP Calculator	Converts a physician's raw prescription history into a continuous preference measure (0 to 1) [5].	Can be coded in R, SAS, or Python. The core calculation is a simple ratio of treatment-specific prescriptions.
Binary PPP Algorithms	Converts prescription history into a dichotomous instrument for use in IV models, enabling clear group comparisons [3].	Multiple algorithms (lenient, strict) should be tested simultaneously to find the strongest, most valid instrument.
First-Stage F-Statistic	A diagnostic tool to quantify the strength of the association between the PPP instrument and the actual treatment received [5] [3].	An F-statistic > 10 indicates a sufficiently strong instrument that mitigates bias from weak instruments.
Covariate Balance Metrics	Assesses whether the PPP instrument successfully creates comparable patient groups, supporting the IV validity assumption [3].	Use Mahalanobis distance or standardized mean differences. Balance should be improved versus unadjusted analysis.
Two-Stage Least Squares (2SLS)	The primary statistical model for estimating a causal effect using an instrumental variable [5] [29].	Standard in many statistical packages (e.g., ivreg in R, ivregress in Stata). Provides consistent estimates under valid IV assumptions.

Optimizing the measurement of Physician's Prescribing Preference is not a mere methodological formality but a critical step in generating valid causal inferences from observational data. The empirical evidence consistently demonstrates that using longer prescription histories (3-4 prior prescriptions) and selecting a PPP definition that yields a strong instrument (high F-statistic) and improved covariate balance are paramount [5] [3]. This is especially crucial in studies with smaller sample sizes, where statistical power is limited. By adhering to the detailed protocols and validation checks outlined in these Application Notes, researchers can robustly apply the PPP IV method to answer pressing comparative effectiveness questions in drug development and clinical medicine.

Application Notes

Theoretical Framework and Definitions

Clinical inertia is defined as the "undue delay in identifying or starting or modifying preventive or therapeutic care of a particular condition appropriately as per the existing clinical evidence resulting in inadequate disease control or unfavorable clinical outcome" [31]. It represents a "recognition of the problem, but failure to act" [31]. Within comparative effectiveness research (CER), this phenomenon interacts with patient requests to create complex confounding, where unmeasured factors distort the apparent relationship between treatment and outcomes [5] [32].

Therapeutic inertia, a subset of clinical inertia, specifically refers to "healthcare providers' failure to modify therapy appropriately when treatment goals are not met" [33]. This occurs across multiple levels: physician-related factors (approximately 50%), patient-related factors (approximately 30%), and healthcare system-related factors (approximately 20%) [33]. Patient requests and preferences constitute a significant component of the patient-related factors that contribute to this phenomenon.

The Physician's Prescribing Preference (PPP) instrumental variable (IV) approach offers a methodological solution to address confounding by indication in observational studies where treatment decisions are influenced by both clinical factors and patient requests [5] [4]. This quasi-experimental method leverages natural variation in physician prescribing patterns that is independent of patient characteristics.

Quantitative Evidence Base

Table 1: Performance Metrics of PPP IV versus Conventional Methods

Methodological Approach	Percent Bias	Coverage Rate	Key Strengths	Key Limitations
PPP IV (2SLS)	~20%	Maintains ~95% coverage even with high unmeasured confounding	Robust to unmeasured confounding; Appropriate for moderate sample sizes [5]	Requires valid instrumental variable; Lower statistical power [5]
Conventional OLS	~60%	Drops dramatically with increasing unmeasured confounding	Higher statistical power; Simpler implementation [5]	Highly biased with unmeasured confounding [5]
PPP with 4+ Prior Prescriptions	Similar bias reduction	Improved power with longer prescribing history	Stronger instrument strength; Improved statistical power [5]	Requires extensive prescribing history data [5]

Table 2: Documented Impact of Clinical Inertia in Diabetes Care

Parameter	Impact Magnitude	Clinical Consequences	Evidence Source
Glycemic Control	30-60% of patients experience therapeutic inertia [33]	Microvascular and macrovascular complications; Reduced quality of life [32] [33]	Systematic reviews, observational studies [32] [33]
Treatment Intensification Delay	Median 7.0 years for treatment intensification [33]	Extended hyperglycemia exposure; Reduced "metabolic legacy" benefits [33]	Cohort studies [33]
Target Achievement	<50% achieve HbA1c <7.0%; <20% achieve all three targets (HbA1c, BP, LDL) [33]	Increased morbidity and mortality; Higher healthcare costs [32] [33]	Cross-sectional studies [33]

Conceptual Framework Diagram

Diagram 1: Conceptual framework for PPP IV addressing confounding. The instrumental variable (PPP) affects treatment but should not directly affect outcomes except through treatment, while complex confounders (influenced by both clinical inertia and patient requests) affect both treatment and outcomes.

Experimental Protocols

Core Protocol: Implementing PPP IV Analysis

Objective: To estimate causal treatment effects in the presence of confounding by patient requests and clinical inertia using Physician's Prescribing Preference as an instrumental variable.

Data Requirements:

• Longitudinal prescription data at the physician level
• Patient demographic and clinical characteristics
• Outcome measures (disease-specific indicators)
• Physician characteristics (optional, for robustness checks)

Analytical Procedure:

Stage 1: Instrument Construction

• Calculate Proportional PPP: For each physician, compute the proportion of target treatment prescriptions among all relevant prescriptions during a specified baseline period [5]: Proportional PPP = (Number of drug A prescriptions by physician) / (Total relevant prescriptions by physician)
• Define Comparison Period: Establish a clean period for preference measurement before each patient's treatment decision to avoid contamination [5].
• Categorize Preference: Classify physicians as "preferrers" or "non-preferrers" based on a predetermined threshold (e.g., >70% prescription rate for target therapy) [5].

Stage 2: Two-Stage Least Squares (2SLS) Regression

• First Stage Regression: Treatment_i = α_0 + α_1PPP_j + α_2X_i + ε_i Where:
  • Treatment_i is the binary treatment indicator for patient i
  • PPP_j is the prescribing preference of physician j
  • X_i is a vector of observed patient covariates
  • Assess instrument strength using F-statistic (target >10) [5]

• Second Stage Regression: Outcome_i = β_0 + β_1Treatment_hat_i + β_2X_i + u_i Where:
  • Treatment_hat_i is the predicted treatment from the first stage
  • Outcome_i is the clinical outcome of interest
  • Report percent bias and coverage rates for validity assessment [5]

Validation Steps:

• Monotonicity Testing: Assess whether the instrument affects patients uniformly in one direction using physician survey data on prescribing patterns [6].
• Exclusion Restriction: Substantively justify that physician preference affects outcomes only through treatment choice, not through other pathways [4].
• Balance Checking: Verify that patient characteristics are balanced across levels of the instrument to support the independence assumption [5] [6].

Supplemental Protocol: Clinical Inertia Measurement

Objective: To quantify therapeutic inertia in clinical practice as a potential source of confounding.

Data Collection:

• Identify Treatment Opportunities: Flag clinical encounters where patients are not at treatment goals but receive no therapy modification [32] [33].
• Categorize Inertia Type:
  • Therapeutic Inertia: Failure to initiate, escalate, or de-escalate therapy when indicated [31] [33]
  • Diagnostic Inertia: Delay in diagnosing poor disease control or complications [31]
  • Apparent Inertia: Appropriate inaction due to patient factors or comorbidities [31] [33]

Quantification Method:

• Calculate the proportion of eligible encounters with therapeutic inertia.
• Measure time-to-treatment intensification using survival analysis methods [33].
• Document stated reasons for inaction (patient preference, competing demands, system factors) [34] [33].

Advanced Protocol: Assumption Testing with Physician Surveys

Objective: To empirically test instrumental variable assumptions using physician survey data [6].

Survey Design:

• Develop clinical vignettes representing standardized patient scenarios.
• Vary patient characteristics that might trigger clinical inertia or responsiveness to patient requests.
• Measure physician treatment decisions across multiple vignettes.

Analysis Approach:

• Between-Physician Variance: Calculate intraclass correlation coefficient to quantify preference variation [6].
• Case-Mix Assessment: Test whether preference remains after controlling for physician and patient population characteristics [6].
• Monotonicity Testing: Evaluate prescription patterns to test deterministic vs. stochastic monotonicity assumptions [6].

The Scientist's Toolkit

Table 3: Essential Research Reagents and Analytical Solutions

Tool Category	Specific Solution	Application Purpose	Implementation Notes
Data Platforms	Electronic Health Record systems with prescription modules	Source data for PPP construction and outcome measurement	Ensure minimum 2+ years of historical prescription data [5]
Statistical Software	R Statistical Environment (versions 3.6.1+) with ivreg package	Implement Two-Stage Least Squares regression	Custom code available in supplementary materials of simulation studies [5]
Instrument Constructs	Proportional Preference Metric (prior 1-4 prescriptions)	Create continuous IV measure	Longer prescription histories (prior 3-4) improve statistical power [5]
Validation Instruments	Physician Survey with Clinical Vignettes	Test IV assumptions and monotonicity	8+ vignettes per physician recommended for reliability [6]
Bias Assessment Tools	Percent bias calculation formulae	Quantify performance versus conventional methods	((True RD - Estimated RD)/True RD)×100% [5]
Clinical Inertia Metrics	Treatment intensification rate, Time-to-intensification	Quantify confounding source	Measure at multiple therapy stages (lifestyle → pharmacotherapy → insulin) [33]

Methodological Considerations

Key Assumptions and Reporting Standards

The valid application of PPP IV requires explicit consideration of four core assumptions [4]:

• Relevance: The instrument must be strongly associated with treatment choice (F-statistic >10 in first stage) [5].
• Exchangeability: The instrument must be independent of unmeasured confounders affecting the outcome.
• Exclusion Restriction: The instrument must affect the outcome only through the treatment.
• Monotonicity: The instrument must not decrease the probability of treatment for any patient [6].

Current literature shows only approximately 12% of PPP IV applications adequately report all four assumptions, highlighting a critical methodological gap [4]. Researchers should explicitly address each assumption in their analytical framework.

Sample Size Considerations

PPP IV methods demonstrate consistent bias reduction across sample sizes, with simulation studies showing stable performance in samples as small as n=620 [5]. However, statistical power decreases with smaller samples, requiring careful consideration of instrument strength. For smaller sample sizes, constructing PPP from longer prescribing histories (3-4 prior prescriptions) can improve power [5].

Distinguishing Appropriate Inaction from Clinical Inertia

A critical challenge in this research domain involves distinguishing "appropriate inaction" from true clinical inertia [31] [33]. Appropriate inaction occurs when clinicians deliberately avoid treatment intensification due to valid clinical reasons such as limited life expectancy, comorbidities, or patient preferences [34] [33]. This distinction requires careful clinical contextualization in analytical designs.

Instrumental Variable (IV) estimation presents a powerful solution for addressing unmeasured confounding in comparative effectiveness research, a common challenge in pharmacoepidemiology. When randomized controlled trials are not feasible, physician prescribing preference (PPP) has emerged as a prominent IV to estimate the causal effects of treatments. The core of this methodology involves leveraging the natural variation in physicians' prescribing habits as a quasi-randomization mechanism to assign patients to different treatments. However, this approach necessitates a delicate balance between the potential biases introduced by invalid instruments and the statistical variance that arises when using weak instruments. This article details the application of PPP as an IV, providing a structured framework to navigate its inherent trade-offs, supported by empirical data and procedural protocols.

Conceptual Foundations and Key Assumptions

The validity of any IV analysis rests on three core assumptions. First, the relevance assumption requires that the instrument (e.g., PPP) is strongly associated with the actual treatment received by the patient. Second, the exchangeability assumption stipulates that the instrument must be independent of both measured and unmeasured confounders. Finally, the exclusion restriction requires that the instrument affects the outcome only through its influence on the treatment, with no direct or alternative causal pathways.

When using PPP as an IV, these assumptions translate into specific considerations. The preference must genuinely influence treatment choice, the groups of patients seen by physicians with different preferences must be comparable in all prognostic factors, and the physician's preference itself must not directly influence the patient's outcome. A systematic review of 185 PP IV applications in health research revealed a critical gap: only 12% of studies explicitly reported all four main assumptions for a valid PPP IV analysis [4]. This underreporting highlights a significant risk of bias in the existing evidence base.

The Monotonicity Assumption in PPP

A fourth assumption, monotonicity, is often required for a specific causal interpretation. In the context of PPP, deterministic monotonicity assumes that if a physician prescribes a particular drug to one patient, they would prescribe the same drug to any other patient in the practice. Survey data from general practitioners presented with fictitious patients has falsified the deterministic monotonicity assumption, demonstrating that physician decisions are influenced by specific patient characteristics [35]. However, the data were often compatible with a weaker stochastic monotonicity assumption, meaning that a physician who prescribed a drug to one patient is generally more likely to prescribe it to others [35]. The plausibility of this assumption depends heavily on how the PPP instrument is defined.

Quantifying Instrument Performance: Strength and Balance

The practical utility of a PPP IV is empirically assessed through two key metrics: its strength and its ability to create covariate balance.

Instrument Strength

Instrument strength measures the power of the IV to predict treatment assignment. It is typically quantified using the first-stage F-statistic or the partial R² from the regression of the treatment on the IV, conditional on other covariates. A strong instrument is crucial for precise estimation; weak instruments lead to amplified variance and potentially biased estimates, especially in the presence of even minor unmeasured confounding. In a study of antipsychotic medications, 25 different formulations of the PPP IV demonstrated a range of strength, with partial R² values between 0.028 and 0.099 [3].

Covariate Balance

Covariate balance assesses whether the use of the IV successfully creates comparable groups, akin to randomization. A valid IV should create analysis groups that are balanced on both measured and unmeasured confounders. The Mahalanobis distance is a multivariate statistic that can summarize balance across multiple patient characteristics simultaneously. In the same antipsychotic medication study, the application of a PPP IV reduced overall covariate imbalance by an average of 36% (with a standard deviation of ±40%) across two cohorts, though the association between instrument strength and the degree of imbalance improvement was mixed [3].

Table 1: Empirical Performance of Various Physician Prescribing Preference (PPP) IV Formulations in a Cohort Study [3]

IV Formulation Variation	Partial R² (Strength)	Reduction in Imbalance (Mahalanobis Distance)
Base Case (Previous Prescription)	0.056	-20%
Lenient Preference (1 of last 2 RX)	0.065	-25%
Strict Preference (2 of last 2 RX)	0.028	-15%
Moderate Preference (2 of last 3 RX)	0.045	-30%
Cohort Restriction (High-Volume MDs)	0.099	-65%
Stratification (by Patient Age)	0.041	-50%

Application Notes and Protocols

This section provides a detailed, step-by-step protocol for implementing a PPP IV analysis, from instrument definition to assumption validation.

Protocol: Defining the Physician Prescribing Preference Instrument

Objective: To construct a valid and strong PPP IV from administrative healthcare data. Materials: Longitudinal database containing patient drug prescriptions and unique physician identifiers.

• Cohort Identification: Define the study cohort of patients initiating the drug class of interest. Ensure each patient is linked to a prescribing physician.
• Instrument Selection: Choose the level of preference variation (e.g., facility-level, physician-level, regional-level). Physician-level is most common [4].
• Operationalize Preference: a. Base Case Algorithm: For each patient's index prescription, define the physician's preference as the drug prescribed to the most recent previous patient in the same practice who initiated treatment [3]. b. Alternative Algorithms: To increase stability, define preference based on a physician's history over a wider window. For example: * Lenient: At least 1 prescription of the target drug within the last 4 new prescriptions [3]. * Strict: At least 2 prescriptions of the target drug within the last 3 new prescriptions [3].
• Cohort Restriction (Sensitivity Analysis): Restrict the cohort to patients of physicians with high-volume prescribing practices to improve the precision of the preference measure and potentially enhance instrument validity [3].

The following workflow diagram illustrates the key steps and decision points in this protocol:

Protocol: Assessing IV Validity and Strength

Objective: To empirically test the key assumptions underlying the constructed PPP IV. Materials: The constructed PPP IV and dataset containing patient covariates, treatment assignment, and outcome.

• Test the Relevance Assumption (Strength): a. Regress the actual treatment received (dependent variable) on the PPP IV (independent variable), controlling for other measured covariates. b. Calculate the F-statistic of the PPP IV in this first-stage regression. An F-statistic > 10 is a common heuristic for adequate strength [3]. c. Calculate the partial R² associated with the PPP IV.

• Test the Exchangeability Assumption (Balance): a. Compare the distribution of measured baseline covariates (e.g., age, comorbidities) across the groups defined by the PPP IV (not the actual treatment). b. Calculate the Mahalanobis distance or standardized mean differences for key covariates. A successful IV will show better balance across these groups than across the actual treatment groups [3].

• Evaluate the Exclusion Restriction: a. This assumption is not statistically testable and must be justified on substantive grounds. b. Argue conceptually that the physician's preference is not a direct risk factor for the patient's outcome and does not correlate with other unmeasured risk factors (e.g., physician quality) [3] [35].

Table 2: The Scientist's Toolkit: Key Reagents for PPP IV Analysis

Research Reagent / Tool	Function in PPP IV Analysis
Longitudinal Prescription Database	Provides the raw data to construct the physician's prescribing history and define the instrument.
Physician Identifier	Enables linkage of patients to their prescribing physician, which is foundational for creating the IV.
First-Stage F-statistic / Partial R²	Quantitative metrics to assess the strength of the association between the PPP IV and the treatment.
Mahalanobis Distance	A multivariate metric to evaluate the success of the IV in creating balanced patient cohorts.
Two-Stage Least Squares (TSLS) Regression	The standard statistical estimator for IV analysis, which accounts for the two-stage nature of the model.

Advanced Applications: Time-Varying and Endogenous IVs

Time-Varying PPP IV

In longitudinal studies where treatment decisions are repeated over time, a single baseline PPP IV may be insufficient. A time-varying PPP IV can be used, where the physician's preference is updated at each follow-up interval. A 2025 study compared two methods for this setting: IV-based G-estimation and an Inverse Probability Weighting (IPW) approach. The G-estimation method provided unbiased and precise estimates across various scenarios, including weak instruments and complex time-varying confounding, while the IPW approach performed well only with moderately strong time-varying IVs [23].

Addressing Endogenous Instruments

A fundamental threat to IV validity is the endogeneity of the instrument itself. The Modified Instrumental Variable (MIV) estimator is a novel approach that reduces inconsistency when the instrument is not fully exogenous. The MIV works through an iterative process that modifies the instrument, provided its exogenous component is larger than its endogenous component. Crucially, if the instrument is truly exogenous, the MIV estimator does not alter the estimates, offering a useful diagnostic check [36].

The diagram below illustrates the core logical structure of IV estimation and the trade-offs involved:

The use of Physician Prescribing Preference as an instrumental variable offers a powerful, but nuanced, method for causal inference in drug development and comparative effectiveness research. The core challenge lies in balancing the bias-variance trade-off: a weak instrument inflates variance, while an invalid instrument introduces severe bias. Success depends on a rigorous approach that involves carefully defining the PPP instrument, empirically testing its strength and ability to create balance, and transparently discussing the plausibility of its assumptions. By adhering to the detailed protocols and leveraging advanced methods like time-varying G-estimation and the MIV estimator, researchers can more reliably navigate these trade-offs, leading to more robust and credible estimates of treatment effects in observational data.

Assessing Performance and Validity: How Does PPP IV Compare?

Instrumental variable (IV) analysis is a powerful methodological approach in comparative effectiveness research and pharmacoepidemiology, used to estimate causal treatment effects when unmeasured confounding is present [3]. Among the various instruments used, physician prescribing preference (PPP) has been widely applied as it exploits natural variation in clinical practice [3]. The increased availability of longitudinal data has further enabled the application of IV methods in time-varying treatment settings, where both treatments and confounders vary over time [25]. However, the empirical validation of these methods requires rigorous reporting guidelines and specific performance metrics to ensure valid causal inference.

This article provides application notes and protocols for the empirical validation of PPP IV studies, with a focus on reporting standards and key performance metrics. We frame our discussion within the context of a broader thesis on using physician prescribing preference as an instrumental variable in health research.

Reporting Guidelines for Preference-Based Instrumental Variables

Core Assumptions and Reporting Standards

For PPP IV studies to yield valid causal estimates, four core assumptions must be satisfied and reported [4] [3]:

• Relevance: The instrument must be strongly associated with treatment assignment.
• Exclusion Restriction: The instrument affects the outcome only through the treatment.
• Independence: The instrument is independent of unmeasured confounders.
• Monotonicity: The instrument does not decrease the probability of treatment for any individual.

A systematic review of preference-based IV applications in health research revealed concerning reporting gaps. Of 185 identified studies, only 12% explicitly reported all four main assumptions for IV validity [4]. This reporting deficiency undermines the credibility of findings and highlights the need for standardized reporting protocols.

Special Considerations for Time-Varying Settings

When applying PPP IV to longitudinal data with time-varying treatments and confounders, additional reporting considerations emerge [25]:

• Temporal alignment: Specify how physician preference is measured over time in relation to treatment decisions.
• Time-varying confounding: Describe mechanisms for addressing confounding that varies over time.
• IV stability: Report on the consistency of physician preference across measurement periods.

The definition of time-varying PPP requires careful specification. Common approaches include using the proportion of a physician's prescriptions for the target medication during relevant time windows or using a moving window of previous prescriptions to determine current preference [25].

Key Performance Metrics for Empirical Validation

Quantitative Benchmarks for IV Strength and Validity

Empirical validation of PPP IV studies requires tracking specific quantitative metrics that assess instrument strength and potential bias. These metrics should be calculated and reported for each study.

Table 1: Key Performance Metrics for PPP IV Validation

Metric Category	Specific Metric	Calculation Formula	Interpretation Benchmark
Instrument Strength	First-stage Partial R²	[Statistical calculation from regression]	Values >0.05–0.10 suggest adequate strength [3]
	F-statistic	[Statistical calculation from regression]	F>10 indicates adequate strength
Covariate Balance	Mahalanobis Distance	√[(x̄₁−x̄₂)S⁻¹(x̄₁−x̄₂)ᵀ]	Reduction of 30-40% indicates improved balance [3]
	Standardized Differences	(x̄₁−x̄₂)/√[(s₁²+s₂²)/2]	<0.1 indicates good balance
Treatment Association	Claim Approval Rate	(Approved Claims ÷ Total Submitted Claims) × 100	>90% indicates efficient billing [37]
Model Performance	Confidence Interval Width	Upper bound – Lower bound	Narrower intervals indicate greater precision
	Bias Reduction	[Comparison to unadjusted estimate]	>50% reduction suggests substantial confounding addressed

Additional Healthcare KPIs for Contextual Validation

Beyond direct IV validation metrics, healthcare-specific key performance indicators (KPIs) provide important contextual validation of the clinical setting where PPP IV is applied.

Table 2: Healthcare Operational KPIs for Contextual Validation

KPI Category	Specific Metric	Calculation Formula	Benchmark Value
Financial	Net Collection Rate	(Payments Collected ÷ (Total Charges – Contractual Adjustments)) × 100	~90% [38]
	Average Reimbursement per Encounter	Total Reimbursements ÷ Number of Patient Encounters	Varies by specialty
Operational	Patient No-Show Rate	(Number of No-Show Appointments ÷ Total Scheduled Appointments) × 100	<5% manageable [38]
	Provider Utilization Rate	(Total Hours Spent on Patient Care ÷ Total Available Working Hours) × 100	75% healthy [37]
Clinical Quality	Chronic Condition Management Compliance	(Number of Patients Receiving Recommended Care ÷ Total Eligible Chronic Patients) × 100	Goal of >90% [38]
	30-Day Readmission Rate	(Number of Patients Readmitted Within 30 Days ÷ Total Discharged Patients) × 100	<10% acceptable [38]

Experimental Protocols for PPP IV Validation

Protocol 1: Base Case PPP Specification

This protocol outlines the standard approach for measuring physician prescribing preference.

Materials: Longitudinal healthcare database (e.g., electronic health records, claims data), statistical software (e.g., R, Python, SAS)

Procedure:

• Cohort Identification: Identify patients initiating the target medication class during the study period.
• Physician Attribution: Link each patient to a single prescribing physician.
• Preference Calculation: For each patient encounter, determine physician preference based on the treatment prescribed to the most recent previous patient with the same condition within that physician's practice.
• IV Dichotomization: Classify the IV as binary (e.g., preference for Drug A vs. Drug B) based on the previous prescription.
• Strength Assessment: Calculate first-stage F-statistic and partial R² values to assess instrument strength.

Validation Steps:

• Perform balance diagnostics using Mahalanobis distance across measured covariates.
• Compare covariate distribution between treatment groups stratified by the IV.
• Report percentage reduction in overall imbalance compared to unadjusted data.

Protocol 2: Time-Varying PPP with G-Estimation

This protocol extends PPP IV to longitudinal settings with time-varying treatments and confounding, based on recent methodological advances [25].

Materials: Longitudinal registry data with repeated measures (e.g., FORWARD databank), statistical software with g-estimation capabilities

Procedure:

• Data Structure: Organize data into discrete time periods (e.g., 6-month intervals).
• Time-Varying PPP: Calculate physician preference at each time period using a moving window of previous prescriptions (e.g., proportion of target drug prescriptions in last 6 months).
• G-Estimation: Implement structural nested mean models with time-varying PPP as the instrument.
• Confounding Adjustment: Adjust for measured time-varying confounders affected by prior treatment.
• Sensitivity Analysis: Test robustness under different PPP definitions and strength assumptions.

Validation Steps:

• Compare precision of estimates (confidence interval width) between methods.
• Assess consistency of effect estimates across different time windows for PPP calculation.
• Test for effect modification by time-varying covariates.

Protocol 3: PPP Formulation Variations

This protocol systematically evaluates different operational definitions of PPP to assess robustness of findings.

Materials: Comprehensive prescribing database with physician and patient characteristics, computational resources for multiple analyses

Procedure:

• Preference Algorithm Variations:
  • Test different time windows (last 1, 2, 3, or 4 prescriptions)
  • Test different consistency thresholds (any, majority, or all prescriptions)
• Cohort Restriction Variations:
  • Restrict to physicians with high-volume practices
  • Restrict to specific physician specialties
  • Restrict to patients within specific age ranges
• Stratification Variations:
  • Stratify by patient characteristics (age, gender, comorbidity score)
  • Stratify by physician characteristics (specialty, experience)
• Comparative Analysis: Calculate IV strength and covariate balance metrics for each variation.

Validation Steps:

• Identify formulations that maximize both strength (partial R²) and balance (Mahalanobis distance reduction).
• Report range of effect estimates across plausible formulations.
• Flag formulations where strength and balance metrics diverge.

Visualization of Methodological Relationships

Causal Structure of Physician Preference IV

Causal Diagram for PPP IV

PPP IV Validation Workflow

IV Validation Workflow

Research Reagent Solutions

Table 3: Essential Research Materials for PPP IV Studies

Research Reagent	Specification	Function/Application
Longitudinal Healthcare Databases	EHRs, claims data, disease registries (e.g., FORWARD)	Provides prescribing data, patient outcomes, and covariates for PPP measurement and effect estimation
Statistical Software Packages	R (ivpack, AER), Python (linearmodels), SAS (PROC IVREG)	Implements IV estimation methods (2SLS, limited information maximum likelihood) and diagnostic tests
Computational Infrastructure	High-performance computing clusters	Enables large-scale data processing and sensitivity analyses across multiple PPP formulations
Clinical Coding Systems	ICD, CPT, NDC codes	Standardizes classification of diagnoses, procedures, and medications for consistent PPP measurement
Data Privacy Safeguards	De-identification protocols, secure data environments	Protects patient confidentiality while maintaining data utility for PPP IV analysis
Visualization Tools	Graphviz, ggplot2, matplotlib	Creates causal diagrams and validation plots to communicate assumptions and results

Instrumental variable (IV) analysis is a essential method in comparative effectiveness research (CER) for addressing unmeasured confounding. When comparing treatment effects, conventional methods like ordinary least squares (OLS) regression can produce biased estimates if all relevant confounders are not measured. Physician's prescribing preference (PPP) has emerged as a prominent IV in pharmacoepidemiology, exploiting natural variation in physician behavior to approximate random treatment assignment. This protocol provides a detailed framework for benchmarking the PPP IV approach against conventional OLS when only measured confounders are available for adjustment.

Theoretical Foundations and Key Comparisons

Core Conceptual Differences

The fundamental distinction between PPP IV and conventional OLS lies in their approach to addressing confounding. OLS regression adjusts only for measured confounders, leaving estimates vulnerable to bias from unmeasured factors. In contrast, the PPP IV method uses physician prescribing patterns as a natural source of randomization that is theoretically independent of patient characteristics, thereby addressing both measured and unmeasured confounding [5] [3].

The IV approach operates on the principle that a valid instrument (Z) must satisfy three key conditions: (1) be associated with the treatment (X), (2) affect the outcome (Y) only through its effect on treatment, and (3) be independent of unmeasured confounders [39] [40]. Physician prescribing preference meets the first condition when physicians exhibit consistent patterns in choosing between comparable treatments for similar patients.

Quantitative Performance Benchmarking

Simulation studies directly comparing PPP IV and OLS methods reveal substantial differences in performance characteristics, particularly regarding bias and coverage rates.

Table 1: Performance Comparison of 2SLS (PPP IV) vs. OLS Under Unmeasured Confounding

Method	Percent Bias	Coverage Rate	Variance Characteristics	Sample Size Sensitivity
PPP IV (2SLS)	~20%	Maintains ~95% nominal coverage	Higher variance due to IV estimation [5]	Bias unaffected by sample size [5]
Conventional OLS	~60%	Drops dramatically with confounding	Lower variance under correct specification [5]	Bias consistent across sample sizes [5]

The superior bias performance of PPP IV comes at the cost of increased variance, as expressed in the relationship: var(β̂_IV) = var(β̂_OLS) / ρ²_X,Z where ρ²_X,Z represents the correlation between treatment and instrument [5]. This illustrates the fundamental bias-variance tradeoff between the two approaches.

Experimental Protocols

PPP IV Analysis Using Two-Stage Least Squares

Stage 1: Treatment Model

The first stage models the probability of receiving a specific treatment as a function of the physician prescribing preference instrument and measured covariates:

Where PPP represents the prescribing preference instrument, X₁ and X₃ are measured covariates, and α_z quantifies the strength of the instrument [5]. The critical assumption is that PPP is associated with treatment assignment but not with unmeasured confounders affecting the outcome.

Stage 2: Outcome Model

The second stage models the outcome using the predicted treatment values from the first stage:

Where Treatment_hat represents the predicted values from the first stage regression. This two-stage process removes the component of treatment variation that is correlated with unmeasured confounders [5].

Conventional OLS with Measured Confounders

The conventional approach directly models the outcome as a function of treatment and measured confounders:

This model provides unbiased estimates only if all relevant confounders are measured and included in the model specification. The key threat to validity is the potential for unmeasured confounding variables that influence both treatment assignment and outcomes [5] [39].

PPP Instrument Construction Methods

Table 2: Physician Prescribing Preference Operationalization Methods

Method	Calculation	Strengths	Limitations
Previous Prescription	Treatment assigned to physician's most recent patient [3]	Responsive to preference changes	Potentially noisy measure of preference
Proportional Preference	Proportion of specific treatment among physician's total prescriptions [5]	More stable preference measure	Requires adequate prescription history
Strict Criteria	Consistent preference across multiple prescriptions (e.g., 2/2 last prescriptions) [3]	Higher specificity for true preference	Reduced sample size and statistical power
Moderate Criteria	Balanced approach (e.g., 2/3 last prescriptions) [3]	Balance between specificity and power	Moderate preference measurement quality

Assumption Validation Protocol

Table 3: Key Assumptions and Validation Methods

Assumption	Validation Approach	Interpretation
Relevance	First-stage F-statistic > 10 [5] [3]	Strong instrument association with treatment
Exclusion Restriction	Clinical reasoning and sensitivity analyses [39]	IV affects outcome only through treatment
Independence	Covariate balance assessment across IV strata [3]	IV independent of unmeasured confounders
Monotonicity	Examination of prescribing patterns [39]	No defiers in prescription behavior

Visualization of Analytical Approaches

Causal Pathways Diagram

Causal Pathways for PPP IV Analysis

This diagram illustrates the key relationships in PPP IV analysis. The critical feature is that PPP IV influences treatment but has no direct path to the outcome, and is unrelated to unmeasured confounders.

Analytical Workflow

PPP IV Analytical Workflow

This workflow outlines the sequential steps for implementing and validating a PPP IV analysis, from instrument definition through sensitivity testing.

Research Reagent Solutions

Table 4: Essential Methodological Tools for PPP IV Analysis

Tool Category	Specific Methods	Application Context	Key Considerations
IV Strength Assessment	First-stage F-statistic, Partial R² [3]	Instrument validation	F > 10 indicates adequate strength [5]
Balance Measurement	Mahalanobis distance, Standardized differences [3]	Covariate balance assessment	Compare balance by IV vs. treatment [3]
Bias Testing	Formal bias comparison tests [41]	Method selection between OLS and IV	Uses measured covariates as proxies [41]
Sensitivity Analysis	Varying PPP definitions, Sample restrictions [3]	Robustness assessment	Multiple operationalizations enhance validity [3]

Discussion and Implementation Guidelines

Contextual Application Recommendations

The choice between PPP IV and conventional OLS depends heavily on research context and confounding structure. PPP IV is particularly advantageous in scenarios with substantial unmeasured confounding, where conventional OLS estimates may exhibit bias approaching 60% [5]. This method shows particular promise in mental health treatment comparisons, cardiovascular disease management, and cancer therapeutics, where strong clinical preferences and unmeasured disease severity often complicate traditional observational analyses [4].

For studies with complete confounder measurement and minimal unmeasured confounding, conventional OLS may provide more precise estimates. However, given that only 12% of applied PPP IV studies adequately report all key assumptions [4], researchers should implement comprehensive validation procedures regardless of methodological selection.

Sample Size Considerations

Unlike conventional OLS, PPP IV performance demonstrates limited sensitivity to sample size reductions in terms of bias magnitude [5]. However, statistical power and instrument strength are substantially influenced by sample size. In smaller samples (n < 2000), constructing PPP from longer prescribing histories (prior 3-4 prescriptions) improves statistical power and instrument strength [5]. The relationship between sample size, instrument strength, and F-statistics follows the formula: F = (ρ²_Z,X(n-2))/(1-ρ²_Z,X) where ρ²_Z,X represents the correlation between instrument and treatment [5].

Limitations and Reporting Standards

Current applications of PPP IV exhibit significant methodological limitations in reporting practices. Researchers should adhere to established reporting guidelines such as Swanson and Hernán's (2013) framework to ensure transparent communication of IV assumptions and validation results [4]. Particular attention should be paid to the exclusion restriction assumption, which remains the most challenging to verify empirically.

Future methodological development should focus on improved testing frameworks for comparing OLS and IV estimator bias, building on emerging approaches that use measured covariates as proxies for unmeasured confounding [41]. These advances will enhance researchers' ability to select appropriate estimation strategies based on empirical evidence rather than solely on theoretical considerations.

Within the framework of a broader thesis on instrumental variable (IV) research, this document synthesizes evidence from simulation studies evaluating the use of Physician's Prescribing Preference (PPP). In pharmacoepidemiology, unmeasured confounding poses a significant threat to the validity of comparative effectiveness research (CER). The PPP IV approach exploits natural variation in physician prescribing habits to mimic a randomized experiment, thereby potentially reducing this bias [3] [16]. This application note details the performance of this method, focusing on its core properties—bias, coverage, and power—as established through simulation studies, and provides actionable protocols for its implementation.

Simulation studies provide critical insights into the operational performance of the PPP IV method under controlled conditions, quantifying its strengths and limitations. The following tables summarize key quantitative findings on bias, coverage, and statistical power.

Table 1: Performance of PPP IV vs. Conventional Methods on Bias and Coverage

Method	Sample Size	Unmeasured Confounding Level	Percent Bias (%)	Coverage Rate (%)
IV (2SLS)	Moderate (~2,500)	Low	~20	~95
IV (2SLS)	Moderate (~2,500)	High	~20	~95
Conventional (OLS)	Moderate (~2,500)	Low	~60	<95
Conventional (OLS)	Moderate (~2,500)	High	~60	<95
IV (2SLS)	Small (~600)	Low	~20	~95
IV (2SLS)	Small (~600)	High	~20	~95
Conventional (OLS)	Small (~600)	Low	~60	<95
Conventional (OLS)	Small (~600)	High	~60	<95

Source: Adapted from [5] [42]. Note: 2SLS = Two-Stage Least Squares; OLS = Ordinary Least Squares. Percent bias for 2SLS is approximate and can vary based on IV construction.

Table 2: Impact of PPP Proxy Construction on Instrument Strength

PPP Proxy Definition	F-statistic (n=2,452)	F-statistic (n=620)	Implication for Statistical Power
Prior 1 Prescription	Lower	Lowest	Lower power, especially in small samples
Prior 2-4 Prescriptions	Intermediate	Low	Improved power over single prior
Proportional PPP (Long History)	Higher	Intermediate	Recommended for improved power
"True" Latent Preference	Highest (e.g., ~500)	N/A	Gold standard (unobservable in practice)

Source: Adapted from [5]. The F-statistic from the first-stage regression is a common measure of instrument strength; values above 10 are often considered adequate.

Experimental Protocols for PPP IV Implementation

Core Protocol: Base Case PPP Construction and Analysis

This protocol outlines the standard method for implementing a PPP IV analysis, serving as a foundation for more complex variations [3] [5].

1. Cohort Definition: - Define the study population of patients initiating a treatment of interest. - For each patient, identify the treating physician at the time of the index prescription.

2. Instrument Construction: - For a given physician, identify the sequence of patients for whom they prescribed a drug from the target therapeutic class. - For each patient in the sequence, assign the PPP instrument based on the treatment prescribed to the physician's immediately prior patient (e.g., "Drug A" vs. "Drug B"). This creates a time-varying, dichotomous instrument.

3. Data Preparation for 2SLS Regression: - First Stage: Regress the patient's actual treatment (dependent variable) on the assigned PPP instrument (independent variable), along with any measured confounders (e.g., age, comorbidities). This generates a predicted value for the treatment. - Second Stage: Regress the patient's outcome (dependent variable) on the predicted treatment from the first stage (independent variable), along with the same measured confounders. - The coefficient for the predicted treatment in the second stage represents the IV estimate of the treatment effect.

4. Validation and Diagnostics: - Instrument Strength: Calculate the F-statistic from the first-stage regression. An F-statistic greater than 10 is a common, though not infallible, indicator of a sufficiently strong instrument [5]. - Covariate Balance: Assess the balance of measured patient characteristics across the two PPP-defined groups (e.g., those whose physician's last prescription was Drug A vs. Drug B). A reduction in imbalance compared to groups defined by actual treatment suggests increased IV validity. The Mahalanobis distance can be used to summarize balance across multiple covariates [3].

Advanced Protocol: Variations for Enhanced Robustness

Simulation and applied studies suggest several modifications to the base case protocol to enhance validity and performance [3] [5].

1. Preference Assignment Algorithm: - Problem: A single previous prescription may not reflect a stable preference. - Solutions: Define PPP using a physician's recent prescribing history. For example, classify a physician as having a preference for "Drug A" if: - Lenient: At least 1 of the last 2, 3, or 4 prescriptions was for Drug A. - Strict: All of the last 2, 3, or 4 prescriptions were for Drug A. - Moderate: At least 2 of the last 3 or 4 prescriptions were for Drug A. - Trade-off: Stricter criteria may improve the validity of the preference measure but reduce the number of eligible physicians and patients, potentially affecting instrument strength and generalizability [3].

2. Cohort Restriction: - Rationale: Restricting the cohort can create a subpopulation where the IV assumptions are more plausible. - Methods: Restrict the analysis to: - Patients of high-volume prescribers (to ensure reliable preference measurement). - Patients within a specific age range or of physicians with a certain specialty. - This can improve covariate balance and instrument strength within the subgroup [3].

3. Stratification: - Rationale: Ensure the "prior patient" used to define preference is comparable to the current patient. - Methods: Stratify the sequence of prescriptions by patient characteristics (e.g., age, gender, disease severity) and define PPP using the last patient within the same stratum [3].

The logical relationship and application workflow of these protocols are summarized in the diagram below.

The Scientist's Toolkit: Research Reagent Solutions

This section outlines the essential methodological "reagents" required to conduct a proficient PPP IV analysis.

Table 3: Essential Components for a PPP IV Analysis

Research Reagent	Function & Rationale	Implementation Example
Longitudinal Prescription Data	Provides the sequence of prescriptions per physician needed to construct the PPP instrument.	Electronic Health Records (EHRs) or pharmacy claims databases with prescriber identifiers [3] [23].
Two-Stage Least Squares (2SLS) Regression	The standard statistical engine for IV estimation. It isolates the unconfounded portion of treatment variation to estimate its effect on the outcome.	Implemented using statistical software (e.g., R, Stata, Python) with functions like ivreg [5] [42].
First-Stage F-Statistic	A diagnostic reagent that tests the "strength" of the PPP instrument. A weak instrument leads to biased estimates.	Target F-statistic > 10. Calculated from the regression of actual treatment on the PPP instrument [5].
Balance Metric (e.g., Mahalanobis Distance)	A diagnostic reagent that assesses the "validity" of the IV by comparing the similarity of patient characteristics across PPP-defined groups.	A significant reduction in the distance metric compared to crude treatment groups supports the IV's unconfounded nature [3].
Proportional PPP Measure	An alternative, often more powerful, formulation of the instrument, especially beneficial in smaller sample sizes.	Calculated as the proportion of a physician's previous prescriptions that were for "Drug A" [5].

Simulation evidence solidifies the role of Physician's Prescribing Preference as a valuable instrumental variable in pharmacoepidemiology. The key takeaways for researchers are that the PPP IV method consistently produces less biased estimates than conventional methods in the presence of unmeasured confounding, irrespective of sample size [5] [42]. Furthermore, its coverage rates remain at nominal levels (around 95%), even as conventional methods fail [5]. However, statistical power is a key concern, particularly in smaller studies. To mitigate this, analysts should construct the PPP instrument from longer prescribing histories (e.g., proportional PPP) rather than relying on a single previous prescription [5]. Adherence to the detailed protocols and diagnostic checks outlined in this document will enhance the rigor, transparency, and validity of future comparative effectiveness research employing this method.

The use of Physician Prescribing Preference (PPP) as an Instrumental Variable (IV) has become an established method in comparative effectiveness research and pharmacoepidemiology to address unmeasured confounding in non-randomized studies. This approach exploits natural variation in physicians' prescribing habits to mimic random treatment assignment. A systematic review of 185 PP IV applications revealed critical reporting gaps and methodological challenges that researchers must address to ensure valid causal inference [4]. This document provides detailed application notes and experimental protocols to standardize and improve the implementation of PPP IV designs in health research.

Systematic Review Findings: Critical Reporting Gaps

A systematic review of PP IV applications in health research published between 1998 and 2020 identified significant deficiencies in methodological reporting [4]. The findings, summarized in Table 1, highlight areas requiring improved transparency.

Table 1: Reporting Gaps in PP IV Applications Based on Systematic Review (n=185 studies)

Reporting Aspect	Finding	Percentage of Studies
All Four Key Assumptions Reported	Complete reporting of IV assumptions	12%
Most Common PP IV Type	Facility-level treatment variation	Most prevalent
Other PP IV Types	Physician-level variation	Common
	Regional-level variation	Common
Potential Selection Bias	Potential selection on treatment issue	46%

The low rate of complete assumption reporting (12%) represents a fundamental threat to the validity of published PP IV studies, as the IV approach relies on untestable assumptions that must be explicitly justified [4]. Nearly half of the studies exhibited potential selection bias issues, where patients might be selectively referred to physicians based on expected treatment preferences.

Key Assumptions and Validation Framework

For a Physician Prescribing Preference variable to function as a valid instrument, it must satisfy four core assumptions. The DOT script below diagrams the logical relationships and validation pathways for these assumptions.

Figure 1: Logical framework for PPP IV assumptions and validation approaches. Assumptions (white) must be verified through specific validation methods (white). Pathways show required relationships between IV, treatment, outcome, and confounders.

Core Assumptions of PPP IV

• Relevance: The physician's prescribing preference must be strongly associated with the actual treatment assignment [3] [4]. This is empirically testable.
• Exclusion Restriction: The prescribing preference must affect the outcome only through its effect on treatment choice, not through other causal pathways [4].
• Independence: The instrument must be independent of both measured and unmeasured confounders [3] [4].
• Homogeneity: No effect modification by the instrument is present [4].

PPP IV Formulation and Experimental Protocols

PPP Formulation Algorithms

Researchers can operationalize physician prescribing preference using various algorithms. Table 2 summarizes common approaches and their properties based on empirical evaluations.

Table 2: PPP Formulation Algorithms and Performance Characteristics

Algorithm Type	Definition	Strength (Partial R²)	Balance Improvement
Base Case	Previous patient's treatment	0.028-0.099	Reference
Lenient Criteria	≥1 conventional rx in last 2-4 rx's	Moderate	Good
Strict Criteria	All conventional rx's in last 2-4 rx's	Lower	Better
Moderate Criteria	≥2 conventional rx's in last 3-4 rx's	Moderate-High	Best
Proportional PPP	Proportion of drug A/all prescriptions	Varies	Good

Partial R² values characterize instrument strength, with values >0.05 generally desirable. Balance improvement refers to reduction in covariate imbalance across treatment groups [3].

Detailed Protocol: Implementing PPP IV with Time-Varying Confounding

For studies with longitudinal data and time-varying treatments, the following protocol implements a robust PPP IV approach:

Aim: To estimate the causal effect of sustained treatment (e.g., Adalimumab vs. other biologics) on health outcomes (e.g., quality-adjusted life years) while addressing time-varying confounding.

Study Design: Retrospective cohort using registry data (e.g., US National Databank for Rheumatic Diseases) [25].

Sample Size Considerations:

• Target minimum of 80 physicians with 10-50 patients per physician (total N≈2,500) [5]
• For smaller sample sizes (N≈620), construct PPP from longer prescribing histories (prior 3-4 prescriptions) to improve statistical power [5]

Procedure:

• Cohort Identification: Identify patients initiating the target medications during the study period. Apply inclusion/exclusion criteria consistently.
• PPP Operationalization: Calculate physician preference using the moderate criteria algorithm (≥2 conventional prescriptions within last 3-4 prescriptions) for optimal strength-balance tradeoff [3].
• Data Structure Preparation: Organize data into person-phase format with biannual phases (6-month intervals). Define baseline (phase 1) and follow-up periods (phases 2-4) [25].
• Time-Varying IV Specification: Exploit exogenous variation in physician preferences over time as time-varying instruments. Use proportion of specific drug prescriptions per physician over 6-month periods [25].
• Statistical Analysis - G-Estimation Approach:
  • Implement g-estimation to estimate the effect of sustained treatment while addressing time-varying confounding
  • Use the time-varying PPP IV in structural nested models
  • This approach provides unbiased, precise estimates across various scenarios, including weak IVs and complex time-varying confounding mechanisms [25]
• Validation Analyses:
  • Calculate first-stage F-statistic (target >10) to assess IV strength [5]
  • Evaluate covariate balance using Mahalanobis distance across IV strata [3]
  • Report percent bias in sensitivity analyses (target <20% for 2SLS vs. ~60% for OLS) [5]

The workflow for this protocol is visualized in the following DOT diagram:

Figure 2: Experimental workflow for PPP IV studies with time-varying confounding. Steps show progression from study conceptualization (yellow) through data preparation (blue/green) to analysis/validation (red) and final interpretation (yellow).

Validation Practices and Performance Metrics

Quantitative Validation Metrics

Simulation studies provide benchmarks for assessing PPP IV performance. Table 3 summarizes key metrics and their interpretation.

Table 3: Performance Metrics for PPP IV Validation

Metric	Calculation	Target Value	Interpretation
Percent Bias	(True RD - Estimated RD)/True RD × 100%	<20% (2SLS)	2SLS shows ~20% bias vs. ~60% for OLS [5]
Coverage Rate	% simulations where 95% CI includes true effect	95%	2SLS maintains nominal coverage; OLS coverage drops with confounding [5]
First-Stage F-statistic	F = (ρ²{X,Z}×(n-2))/(1-ρ²{X,Z})	>10	Indicates sufficiently strong IV [5]
Partial R²	Variance explained by IV after covariates	>0.05	Measures IV strength independent of sample size [3]

Advanced Methods for Time-Varying Settings

Recent methodological advances address complex time-varying scenarios:

• IV-based G-estimation: Provides unbiased, precise estimates across scenarios with weak IVs and complex time-varying confounding [25]
• Inverse Probability Weighting: Reasonable performance with moderate/strong time-varying IVs but deteriorates with weak instruments [25]
• Machine Learning Integration: Emerging approaches incorporate ML for nonparametric IV estimation and covariate-assisted bounds to enhance precision [43]

The Scientist's Toolkit: Research Reagent Solutions

Table 4: Essential Methodological Tools for PPP IV Research

Research Reagent	Function/Purpose	Implementation Example
PPP Algorithm Library	Various operationalizations of physician preference	Lenient, strict, moderate criteria; proportional PPP [3]
Instrument Strength Diagnostics	Assess relevance assumption	First-stage F-statistic, partial R² values [5] [3]
Balance Metrics	Evaluate independence assumption	Mahalanobis distance, standardized differences [3]
G-Methods Software	Implement time-varying IV analyses	G-estimation, inverse probability weighting code [25]
Bias-Variance Tradeoff Framework	Optimize PPP algorithm selection	Balance strength vs. precision in estimation [5]

This protocol provides detailed guidance for addressing the critical reporting gaps and validation challenges identified in systematic reviews of PPP IV applications. By implementing standardized algorithms, robust validation metrics, and advanced methods for time-varying settings, researchers can improve the validity and transparency of instrumental variable studies in comparative effectiveness research. Future work should focus on developing reporting guidelines specifically for preference-based instrumental variable designs to enhance methodological rigor.

Assessing Covariate Balance and Instrument Strength in Applied Studies

Instrumental variable (IV) analysis is a powerful quasi-experimental method used to estimate causal treatment effects when unmeasured confounding is suspected in observational data. The physician prescribing preference (PPP) IV leverages natural variation in physicians' prescribing habits as an unconfounded proxy for treatment assignment [3]. A valid IV must meet three core assumptions: it must strongly predict treatment (relevance), it must not be associated with confounders (exchangeability), and it must affect the outcome only through its effect on treatment (exclusion restriction) [3] [4]. When these assumptions hold, PPP IV can mitigate biases like confounding by indication that commonly plague pharmacoepidemiologic studies using administrative databases or disease registries [3].

The base case PPP formulation typically defines a physician's preference based on the treatment chosen for their most recent patient with the same indication [3]. However, numerous variations exist in operationalizing this instrument. Common modifications include altering the preference assignment algorithm (e.g., using the last 2-4 prescriptions with different consistency thresholds), implementing cohort restrictions (e.g., by physician volume or patient age), or creating stratification schemes (e.g., matching current and previous patients on characteristics like age or propensity score) [3]. The flexibility in PPP formulation necessitates rigorous assessment of both covariate balance and instrument strength to ensure valid causal inference.

Quantitative Diagnostics for Instrument Validation

Covariate Balance Assessment Metrics

After applying a proposed PPP instrumental variable, researchers must quantitatively assess whether the instrument has successfully created comparability between patient groups defined by the instrument. The table below summarizes key balance diagnostics used in applied studies.

Table 1: Quantitative Metrics for Assessing Covariate Balance

Metric	Calculation	Interpretation	Optimal Value
Standardized Difference	Difference in means or prevalences divided by pooled standard deviation	Measures imbalance in each covariate between instrument-defined groups	<0.10 (10%) for each covariate [44]
Variance Ratio	Ratio of variances in treated vs. untreated groups	Assesses differences in covariate spread	Close to 1.0 [44]
Mahalanobis Distance	Multivariate distance between group means considering covariance	Summarizes overall imbalance across multiple covariates	Smaller values indicate better balance [3]
Five-Number Summaries	Minimum, Q1, Median, Q3, Maximum	Compares entire distribution of continuous covariates	Similar distributions across groups [44]
Kolmogorov-Smirnov Test	Non-parametric test of distributional equality	Tests whether covariate distributions differ	P-value > 0.05 [44]

Balance assessment should extend beyond means to include higher-order moments and interactions. As demonstrated in a study of antipsychotic medication use and mortality in elderly patients, PPP application generally alleviated imbalances in non-psychiatry-related patient characteristics, with overall imbalance reduced by an average of 36% (±40%) across two cohorts [3]. Researchers should report balance statistics for all measured covariates, not just those included in the propensity score model, to detect residual imbalance.

Instrument Strength Assessment

Instrument strength measures the PPP's predictive power for actual treatment receipt. Weak instruments can substantially bias effect estimates and reduce statistical power. The table below outlines key metrics for assessing IV strength.

Table 2: Metrics for Assessing Instrument Strength

Metric	Calculation	Interpretation	Threshold Guidelines
First-Stage F-Statistic	F-test from regression of treatment on instrument	Tests joint significance of instrument(s)	F > 10 indicates adequate strength [3]
Partial R²	Proportion of treatment variance explained by instrument beyond other covariates	Measures predictive power	Higher values preferred; context-dependent [3]
Area Under ROC Curve	Classifier performance for predicting treatment	Assesses discrimination	>0.7 acceptable; >0.8 good [45]

In applied PPP studies, first-stage partial R² values typically range from 0.028 to 0.099, with most formulations constituting strong instruments [3]. However, the association between strength and imbalance can be mixed, necessitating assessment of both properties simultaneously [3].

Experimental Protocols for PPP IV Applications

Protocol 1: Base Case PPP Implementation

This protocol outlines the foundational approach for implementing physician prescribing preference as an instrumental variable.

Table 3: Research Reagent Solutions for PPP Implementation

Component	Function	Implementation Example
Electronic Health Records	Data source for patient characteristics, treatments, and outcomes	UK-based registry of AMI patients (N=9,104) [44]
Provider Identification	Links patients to prescribing physicians	Physician ID in administrative claims data [3]
Treatment History	Enables preference algorithm application	Sequence of antipsychotic prescriptions for elderly patients [3]
Balance Diagnostics	Assesses covariate balance across instrument-defined groups	Standardized differences before and after IV application [44]
Strength Assessment	Evaluates instrument predictive power	First-stage partial R² from treatment model [3]

Procedure:

• Cohort Identification: Define patient population initiating treatment for the condition of interest. For example, in a study of antipsychotic medications, researchers identified elderly patients initiating treatment with conventional or atypical APMs [3].
• Preference Algorithm: For each physician, determine preference based on the treatment chosen for their most recent eligible patient. The base case uses only the immediately previous patient.
• Instrument Application: Assign each current patient the preference-based instrument value (e.g., 0 for preference of conventional APM, 1 for preference of atypical APM).
• Balance Assessment: Compare measured baseline covariates between patients seen by physicians with different preferences using metrics in Table 1.
• Strength Assessment: Calculate first-stage F-statistic and partial R² from regression of actual treatment on instrument.
• Effect Estimation: If balance and strength are adequate, proceed with two-stage least squares or similar IV estimation.

Protocol 2: Comprehensive Balance Diagnostics

This protocol details advanced methods for evaluating covariate balance beyond simple mean comparisons.

Procedure:

• Standardized Differences: Calculate standardized differences for all measured covariates. For continuous variables, use the difference in means divided by the pooled standard deviation. For dichotomous variables, use the difference in proportions divided by the standard error.
• Variance Ratios: Compute the ratio of variances for continuous covariates between instrument-defined groups. Substantial deviations from 1.0 indicate differences in spread even if means are similar.
• Distributional Comparisons: Generate side-by-side boxplots, quantile-quantile plots, or non-parametric density plots to visually compare entire distributions.
• Higher-Order Moments: Compare skewness and kurtosis for continuous variables to detect differences in distribution shape.
• Interaction Assessment: Check balance for product terms between key covariates, as imbalance in interactions may not be detected when main effects are balanced.
• Overall Summary: Calculate multivariate balance metrics like Mahalanobis distance to summarize overall imbalance.

In a study of statin prescription after acute myocardial infarction, researchers comprehensively assessed balance across demographic characteristics, presenting signs, cardiac risk factors, comorbid conditions, vital signs, and laboratory tests using standardized differences before and after propensity score adjustment [44]. Similarly, PPP applications should demonstrate balance across all measured potential confounders.

Protocol 3: Instrument Strength Optimization

When initial PPP formulations yield weak instruments, this protocol provides systematic approaches for enhancement.

Procedure:

• Preference Algorithm Modification:
  • Apply lenient criteria: At least 1 conventional prescription within last 2-4 prescriptions
  • Apply strict criteria: 2+ conventional prescriptions within last 2-4 prescriptions
  • Apply moderate criteria: At least 2 conventional prescriptions within last 3-4 prescriptions
• Cohort Restrictions:
  • Restrict to physicians with high-volume practices
  • Restrict to specific physician types (primary care vs. specialists)
  • Restrict to patients within specific age ranges
  • Restrict to physicians graduating before/after specific years
• Stratification Schemes:
  • Match current and previous patients on age category
  • Match on propensity score quartiles
  • Match on age relative to practice median
• Strength Reassessment: After each modification, recalculate first-stage F-statistic and partial R².
• Balance Preservation: Verify that strength enhancements do not compromise covariate balance.

In antipsychotic medication studies, modifying the preference algorithm and implementing cohort restrictions yielded partial R² values ranging from 0.028 to 0.099, demonstrating the sensitivity of instrument strength to methodological variations [3].

Applied Example: Antipsychotic Medications and Mortality

An applied study of elderly patients initiating antipsychotic medication treatment illustrates the PPP IV approach [3]. Researchers examined 25 different formulations of the PPP instrument to assess APM use and subsequent 180-day mortality. The original unmatched cohort exhibited significant imbalances in patient characteristics, necessitating IV approaches to address confounding.

Table 4: Balance and Strength Results from Applied PPP Study

PPP Formulation	Partial R²	Imbalance Reduction	Comments
Base Case (previous prescription)	0.035	28%	Reference formulation
Lenient Criteria (≥1 conventional in last 3 rx)	0.041	31%	Improved strength with moderate balance gain
Strict Criteria (3 conventional in last 3 rx)	0.028	25%	Reduced strength but possibly better preference measure
High-Volume Physicians	0.052	42%	Best balance improvement
Age Stratification	0.038	36%	Good balance with maintained strength

The relationship between instrument strength and covariate balance was mixed across formulations. Some high-strength instruments showed excellent balance (e.g., high-volume physicians with 42% imbalance reduction and partial R²=0.052), while others showed trade-offs between these properties [3]. This highlights the importance of evaluating both metrics when selecting among alternative PPP formulations.

Reporting Guidelines and Interpretation

Comprehensive reporting of PPP IV studies requires transparent documentation of both instrument development and validation. A systematic review of preference-based IV applications in health research found that only 12% of applications reported all four main assumptions for PP IV, with selection on treatment being a potential issue in 46% of studies [4]. To improve methodological rigor, researchers should:

• Pre-specify PPP Formulations: Define primary and sensitivity analysis formulations before examining outcomes.
• Report All Balance Metrics: Present standardized differences, variance ratios, and distributional comparisons for all measured covariates.
• Quantify Instrument Strength: Report first-stage F-statistics, partial R² values, and other strength metrics.
• Justify Exclusion Restriction: Provide conceptual arguments for why the preference instrument affects outcomes only through treatment.
• Address Potential Limitations: Acknowledge and discuss potential violations of IV assumptions, including physician-patient matching based on expected treatment.

When different covariate-balancing methods produce meaningfully different effect estimates, this may indicate treatment effect heterogeneity by propensity score [46]. In such cases, the various methods effectively estimate average treatment effects in populations with different distributions of effect-modifying variables [46]. Researchers should carefully select covariate-balancing methods to ensure the overall estimate has a meaningful interpretation in the target population.

Conclusion

Physician Prescribing Preference offers a powerful, though nuanced, tool for causal inference when randomization is infeasible. Its validity hinges on carefully justifying often underreported core assumptions and thoughtfully constructing the preference proxy. Future applications must prioritize transparent reporting of these assumptions and validation metrics. Promising directions include further development of methods for time-varying treatments, integration with machine learning techniques, and broader application in the era of rich, longitudinal real-world data. When applied rigorously, PPP IV can significantly reduce bias from unmeasured confounding, providing more reliable evidence on treatment effectiveness for researchers and drug development professionals.

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