A Nested Copula Model for Recurrent Gap Times With a Dependent Terminal Event
Yuanjia Duan1, Miao Han1, Liuquan Sun2,3
1School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai, P.R. China.
Statistics in Medicine
|June 8, 2026
Summary
This study introduces a novel nested copula model to analyze recurrent events and terminal events in clinical trials. The model effectively captures complex correlations, offering improved interpretability for covariate effects.
Area of Science:
- Biostatistics
- Clinical Trial Analysis
- Survival Analysis
Background:
- Clinical trials frequently involve recurrent events and terminal events, complicating data analysis.
- Understanding covariate effects on recurrent event gap times and their correlation with terminal events is crucial.
Purpose of the Study:
- To propose a novel nested copula model for analyzing recurrent and terminal events in clinical trials.
- To investigate the effect of covariates on recurrent gap times and their dependence with terminal events.
- To provide a copula-based alternative to frailty models with enhanced interpretability.
Main Methods:
- Development of a two-layer nested copula model: Archimedean copula for internal correlations, bivariate copula for dependence with terminal events.
- Parametric and semiparametric methods for parameter estimation.
- A likelihood-based copula selection procedure for model choice.
Main Results:
- The proposed nested copula model effectively captures correlations among recurrent and terminal events.
- Parametric and semiparametric estimators are consistent and asymptotically normal.
- Simulation studies confirm the finite sample properties of the developed methods.
Conclusions:
- The nested copula model offers a flexible and interpretable framework for analyzing complex event data in clinical trials.
- The methods provide reliable parameter estimation and model selection capabilities.
- The approach is applicable to real-world clinical data, as demonstrated with colorectal cancer data.
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