Journal of Data Science

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 these issues, 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 using Laplace approximation. A simulation study suggests that the proposed method has the best performance compared with existing methods. The method is applied to the clustered time-to-failure prediction within the kidney transplantation facility using the national kidney transplant registry data from the U.S. Organ Procurement and Transplantation Network. All computer programs are available at https://github.com/rivenzhou/deep_learning_clustered.

Abstract: Existing methods on sample size calculations for right-censored data largely assume the failure times follow exponential distribution or the Cox proportional hazards model. Methods under the additive hazards model are scarce. Motivated by a well known example of right-censored failure time data which the additive hazards model fits better than the Cox model, we proposed a method for power and sample size calculation for a two-group comparison assuming the additive hazards model. This model allows the investigator to specify a group difference in terms of a hazard difference and choose increasing, constant or decreasing baseline hazards. The power computation is based on the Wald test. Extensive simulation studies are performed to demonstrate the performance of the proposed approach. Our simulation also shows substantially decreased power if the additive hazards models is misspecified as the Cox proportional hazards model.