Hierarchical neural networks for survival analysis.

Neural networks offer the potential of providing more accurate predictions of survival time than do traditional methods. Their use in medical applications has, however, been limited, especially when some data is censored or the frequency of events is low. To reduce the effect of these problems, we have developed a hierarchical architecture of neural networks that predicts survival in a stepwise manner. Predictions are made for the first time interval, then for the second, and so on. The system produces a survival estimate for patients at each interval, given relevant covariates, and is able to handle continuous and discrete variables, as well as censored data. We compared the hierarchical system of neural networks with a nonhierarchical system for a data set of 428 AIDS patients. The hierarchical model predicted survival more accurately than did the nonhierarchical (although both had low sensitivity). The hierarchical model could also learn the same patterns in less than half the time required by the nonhierarchical model. These results suggest that the use of hierarchical systems is advantageous when censored data is present, the number of events is small, and time-dependent variables are necessary.