Reference-based sensitivity analysis for repeated count outcomes using negative binomial margins and a Gaussian copula

2026-09-25

AI Summary

This study addresses the lack of effective methods for sensitivity analysis under reference-based multiple imputation for count outcomes in longitudinal clinical trials. To this end, it proposes a Gaussian copula-based negative binomial marginal model that innovatively integrates a covariate-adjusted log-rate model with a copula structure. By employing randomized probability integral transforms to accommodate discreteness, the approach enables flexible reference-based imputation rules, while a Metropolis-within-Gibbs algorithm ensures efficient posterior sampling. Simulation studies demonstrate minimal bias in parameter estimation and accurate recovery of treatment effects. Furthermore, an application to real-world data confirms the consistency of rate ratios across diverse missing-data assumptions. Collectively, this work provides a robust sensitivity analysis framework for longitudinal overdispersed count data subject to informative dropout.

Abstract

Reference-based multiple imputation is used in longitudinal clinical trials to assess sensitivity to assumptions about outcomes unobserved after intercurrent events. Most existing methods target continuous outcomes and use multivariate normal working models. Scheduled count outcomes require a model that preserves integer support, skewness, overdispersion, longitudinal dependence, and an exposure-based rate interpretation. We propose visit-specific negative binomial (NB) margins linked by a Gaussian copula. Covariate-adjusted log rate models define the margins, while the copula captures longitudinal dependence. For missing outcomes in the active arm after a prespecified event, termed the trigger, assigned arm continuation retains the fitted active arm marginal mean, jump to reference uses the corresponding reference arm marginal mean, and the intermediate rule interpolates between these means on the log rate scale. Combined with the copula, the resulting NB margins determine an imputation distribution conditional on the retained history. We account for discreteness through randomized probability integral transform augmentation and fit the model with a custom Metropolis-within-Gibbs sampler. In targeted simulations, the model recovered the generating marginal and dependence parameters with little bias. In simulations with incomplete data, treatment effect estimates were closest to the corresponding complete data estimates when the imputation rule matched the mechanism governing outcomes after the trigger. We illustrate the method using repeated incontinence episode counts from a published trial in overactive bladder. Estimated rate ratios comparing active treatment with placebo remained below 1 under all reference-based assumptions, with modest attenuation toward the null and the greatest separation between rules at the final visit.

Problem

• sensitivity analysis
• reference-based multiple imputation
• repeated count outcomes
• longitudinal clinical trials
• missing data

Innovation

• reference-based multiple imputation
• negative binomial margins
• Gaussian copula
• repeated count outcomes
• Metropolis-within-Gibbs sampler