Multivariate generalized linear frailty models for clustered competing risk data

Clustered competing risk data occur when individuals within clusters are subject to multiple mutually exclusive event types, inducing dependence both across events and within clusters. We propose a joint modeling framework for such data based on a multivariate generalized linear frailty model. Cause-specific hazards are specified in a piecewise exponential form with shared cluster-level random effects to account for unobserved heterogeneity and between-event correlation. Using the equivalence between the piecewise exponential and Poisson regression likelihoods, estimation is performed under the generalized linear mixed model (GLMM) framework, allowing implementation with standard mixed-model software. Simulation studies show that the proposed method yields nearly unbiased and efficient estimation across a wide range of correlation structures, whereas conventional univariate and Cox-type frailty models exhibit bias or instability under moderate dependence. Application to multicenter clinical trial data illustrates the practical utility and interpretability of the proposed model. The approach offers a flexible and extensible framework for modeling clustered survival data with competing risks.