Neural Network for Correlated Survival Outcomes Using Frailty Model

Lei Liu

Abstract:

Extensive literature has been proposed for the analysis of correlated survival data. Subjects within a cluster share some common characteristics, e.g., genetic and environmental factors, so their time-to-event outcomes are correlated. The frailty model under proportional hazards assumption has been widely applied for the analysis of clustered survival outcomes. However, the prediction
performance of this method can be less satisfactory when the risk factors have complicated effects, e.g., nonlinear and interactive. To
deal with this issue, we propose a neural network frailty Cox model that replaces the linear risk function with the output of a feed-forward neural network. The estimation is based on quasi-likelihood with the use of Laplace approximation. A simulation study suggests that the proposed method has the best performance compared with five existing methods. The method is applied to the clustered time-to-glaucoma in both eyes from the Ocular Hypertension Treatment Study (OHTS) study.