A copula-based mixed Poisson model for bivariate recurrent events under event-dependent censoring

Area of Science:

• Biostatistics
• Epidemiology
• Clinical Trials

Background:

• Chronic diseases often involve multiple types of adverse events occurring simultaneously or sequentially.
• Accurate modeling of event associations and censoring is crucial for reliable clinical trial analysis.
• Traditional marginal analyses may yield biased estimates in the presence of dependent censoring.

Purpose of the Study:

• To develop and evaluate a bivariate mixed Poisson model using copula functions to capture the association between two types of events.
• To address event-dependent censoring, where the occurrence of one event influences patient withdrawal from a study.
• To provide consistent parameter estimation for rate and mean functions, and associated treatment effects.

Main Methods:

• A bivariate negative binomial process is derived from a bivariate mixed Poisson model with gamma-distributed random effects and a copula function.
• Parametric and semiparametric models are estimated using an Expectation-Maximization (EM) algorithm.
• The model's performance is assessed through simulation studies under independent and event-dependent censoring scenarios.

Main Results:

• The proposed joint model yields consistent estimates, unlike naive marginal analyses, especially under event-dependent censoring.
• Simulation studies demonstrate the empirical performance of the estimators.
• The approach is illustrated with applications in breast cancer and chronic obstructive pulmonary disease (COPD) trials.

Conclusions:

• The bivariate negative binomial process offers a robust framework for analyzing multiple correlated events in chronic disease research.
• The model effectively handles event-dependent censoring, providing more reliable results for clinical trial evaluations.
• This methodology enhances the analysis of complex event data, leading to better insights into disease progression and treatment efficacy.