[Paper Review] Simulating realistically complex comparative effectiveness studies with time-varying covariates and right-censored outcomes

Maria E. Montez‐Rath, Kristopher Kapphahn+4 more|arXiv (Cornell University)|Sep 28, 2017

Statistical Methods and Inference10 references3 citations

TL;DR

This paper presents a flexible, R-based simulation framework for generating realistic comparative effectiveness study data with time-varying covariates, right-censored outcomes, and correlated mixed-type variables (continuous, binary, categorical). It extends prior methods to model within-subject correlations and time-dependent exposures, enabling accurate evaluation of statistical methods and power calculations in complex longitudinal settings.

ABSTRACT

Simulation studies are useful for evaluating and developing statistical methods for the analyses of complex problems. Performance of methods may be affected by multiple complexities present in real scenarios. Generating sufficiently realistic data for this purpose, however, can be challenging. Our study of the comparative effectiveness of HIV protocols on the risk of cardiovascular disease -- involving the longitudinal assessment of HIV patients -- is such an example. The correlation structure across covariates and within subjects over time must be considered as well as right-censoring of the outcome of interest, time to myocardial infarction. A challenge in simulating the covariates is to incorporate a joint distribution for variables of mixed type -- continuous, binary or polytomous. An additional challenge is incorporating within-subject correlation where some variables may vary over time and others may remain static. To address these issues, we extend the work of Demirtas and Doganay (2012). Identifying a model from which to simulate the right-censored outcome as a function of these covariates builds on work developed by Sylvestre and Abrahamowicz (2007). In this paper, we describe a cohesive and user-friendly approach accompanied by R code to simulate comparative effectiveness studies with right-censored outcomes that are functions of time-varying covariates.

Motivation & Objective

• To develop a simulation method that realistically replicates complex longitudinal data structures found in comparative effectiveness research (CER), including time-varying covariates and right-censored outcomes.
• To address the challenge of simulating correlated mixed-type variables (continuous, binary, polytomous) while preserving within-subject and across-subject correlations.
• To enable accurate evaluation of statistical methods—particularly for missing data handling—under realistic data complexities common in CER studies.
• To support power calculations for studies with multiple time-varying exposures, varying exposure prevalence, and clustered subject-level correlations.
• To provide a user-friendly, open-source R tool that supports flexible simulation of complex CER scenarios for methodological research and study design.

Proposed method

• Extends Demirtas and Doganay (2012) to generate multivariate correlated data with mixed variable types (continuous, binary, polytomous) using a copula-based approach.
• Models time-varying covariates (e.g., BMI, viral load) and time-invariant covariates (e.g., age, sex, race) with subject-specific random effects to capture within-subject correlation.
• Uses a proportional hazards model (Cox-type) to generate right-censored time-to-event outcomes (e.g., myocardial infarction) as functions of both time-static and time-varying covariates.
• Implements a variance adjustment mechanism to balance within-subject and across-subject variances when user-specified values are not provided.
• Incorporates flexible parameter input via a spreadsheet interface, allowing users to specify variable types, correlations, exposure patterns, and censoring mechanisms.
• Provides an R package with a Shiny-based interface (under development) to facilitate user access and customization of simulation scenarios.

Experimental results

Research questions

• RQ1 How can we simulate longitudinal comparative effectiveness studies with realistic correlations among mixed-type covariates and time-varying exposures?
• RQ2 What is the impact of within-subject correlation and time-varying covariates on the performance of statistical methods in the presence of right-censored outcomes?
• RQ3 How does exposure prevalence affect statistical power to detect hazard ratios in complex CER settings with multiple time-varying exposures?
• RQ4 Can simulation-based power calculations better capture the probability of detecting multiple relevant exposures compared to standard formulas?
• RQ5 To what extent can simulation-based methods improve the evaluation of missing data handling strategies in longitudinal CER studies?

Key findings

• The simulation framework successfully replicates complex data structures observed in real-world comparative effectiveness studies, including correlated mixed-type variables and time-varying exposures.
• The algorithm achieves high accuracy and precision in reproducing target correlation matrices and marginal distributions across simulated datasets.
• With 10% or higher exposure prevalence, the method achieves 80% power to detect hazard ratios of 1.5 or greater in simulated studies.
• When five exposures were associated with the outcome, the probability of detecting exactly three of them was only 34%, highlighting the challenge of identifying multiple true signals.
• Standard power calculators like stpower cox underestimate power in clustered, time-varying settings and cannot assess probabilities of detecting multiple exposures, unlike the proposed simulation approach.
• The simulation-based method enables comprehensive evaluation of methodological performance, including detection probability of at least one or all relevant features, which is not feasible with traditional formulas.