Comparison of the performance of neural network methods and Cox regression for censored survival data

Abstract

Strategies that have been developed to extend NN prediction methods to accommodate right-censored data include methods due to Faraggi–Simon, Liestol–Andersen–Andersen, and a modification of the Buckley–James method. In a Monte Carlo simulation study, we evaluated the performance of all three NN methods with that of Cox regression models which included main effects and interactions, when interactions exist. Using the EPILOG PLUS® PROC NEURAL utility, feed-forward back-propagation networks were examined under nine designs representing a variety of experimental conditions which varied (a) the number of inputs and interactions, (b) the degree of censoring, (c) proportional vs. non-proportional hazards, and (d) sample size. Minimization methods were implemented that efficiently determined optimal parameters. The C-index was used as a measure of performance. For the testing phase of the study, none of the NN methods outperformed Cox regression. Compared to Cox regression, the Faraggi–Simon, Buckley–James, and Liestol–Andersen–Andersen methods performed as well as Cox regression for 7,5 and 1 of the nine designs, respectively. The effect on performance of modeling interactions in Cox regression, varying the number of intervals in the Liestol–Andersen–Andersen method, and varying the NN architecture are also presented. The results of our study suggest that NNs can serve as effective methods for modeling right-censored data. However, the performance of the NN is somewhat variable, depending on the underlying data structure.