An improved copula-DNN survival model for clustered survival data

The deep neural networks (DNNs) are useful for modeling nonlinear relationships between inputs and output variables.Copula models have been widely studied for modeling dependence structures in clustered data, including multivariate time-to-event outcomes.Very recently, Kwon et al. (2025) introduced a copula-based DNN survival model for clustered survival data, which accounts for dependence among survival times.However, the model is limited in that the copula dependence parameter is not estimated, but rather treated as known.To overcome this limitation, we propose an improved copula-DNN framework for jointly estimating the copula parameter and the network weights.In particular, we demonstrate how the copula parameter can be estimated using neural network architectures.The predictive performance of the proposed method is evaluated through simulation studies and an analysis of a real dataset.