H‐Likelihood Approach on the Joint Frailty Model for Clustered Bivariate Survival Data

Recently, clustered bivariate survival data have been extensively studied using different modeling approaches, such as frailty models and copula models. These data can take several forms, including bivariate censored data, semicompeting risks data, and competing risks data. Traditionally, each type has been analyzed using a separate model. In this paper, we propose a unified joint frailty modeling approach that is capable of handling the three different types of clustered bivariate survival data within a single model-based likelihood framework. Here, the unknown baseline hazards in the joint frailty models are modeled based on a cubic M-spline basis function that does not require a specific parametric form. Inference for the model parameters is performed via the hierarchical likelihood (h-likelihood) method, which avoids the intractable integration over frailty required in marginal likelihood approaches and effectively captures heterogeneity across clusters. The performance of the proposed approach is evaluated through simulation studies, which demonstrate that the estimated regression coefficients appear reasonable for the three types of clustered bivariate survival data. The proposed method is further illustrated using three real-world data sets.