Copula-based deep neural networks for clustered survival data

Dependence among clustered survival data (i.e.multivariate correlated time-to-event data) can be described through copula survival hazard models or frailty models.Here, the risk prediction is based on the linear predictor which can be a strong assumption.The copula survival models have been relatively less studied as compared to frailty models.The deep neural networks (DNN) is a powerful structured neural network consisting of three layers (input, hidden and output layers) for constructing (or modelling) the functional relationship (mainly nonlinear) between input and output variables.In this paper, we propose a DNN approach for the copula models with clustered survival data.For simplicity, we use Weibull marginal hazard functions under the Clayton copula function.The proposed DNN copula model is trained by using a negative copula likelihood as a loss function.The predictive performance of the proposed method is evaluated by comparing it with existing methods in terms of C-index and integrated Brier score using simulation study and a real data set.