Analysis of survival data having time-dependent covariates.

Cox's proportional hazards model has been widely used for the analysis of treatment and prognostic effects with censored survival data. In this paper, we propose a neural network model based on bootstrapping to estimate the survival function and predict the short-term survival at any time during the course of the disease. The bootstrapping for the neural network is introduced when selecting the optimum number of hidden units and testing the goodness-of-fit. The proposed methods are illustrated using data from a long-term study of patients with primary biliary cirrhosis (PBC).