Bayesian Neural Network Models for Censored Data

Abstract

AbstractNeural networks are considered by many to be very promising tools for classification and prediction. The flexibility of the neural network models often result in over‐fit. Shrinking the parameters using a penalized likelihood is often used in order to overcome such over‐fit. In this paper we extend the approach proposed by FARAGGI and SIMON (1995a) to modeling censored survival data using the input‐output relationship associated with a single hidden layer feed‐forward neural network. Instead of estimating the neural network parameters using the method of maximum likelihood, we place normal prior distributions on the parameters and make inferences based on derived posterior distributions of the parameters. This Bayesian formulation will result in shrinking the parameters of the neural network model and will reduce the over‐fit compared with the maximum likelihood estimators. We illustrate our proposed method on a simulated and a real example.