Experiments to Determine Whether Recursive Partitioning (CART) or an Artificial Neural Network Overcomes Theoretical Limitations of Cox Proportional Hazards Regression

New computationally intensive tools for medical survival analyses include recursive partitioning (also called CART) and artificial neural networks. A challenge that remains is to better understand the behavior of these techniques in effort to know when they will be effective tools. Theoretically they may overcome limitations of the traditional multivariable survival technique, the Cox proportional hazards regression model. Experiments were designed to test whether the new tools would, in practice, overcome these limitations. Two datasets in which theory suggests CART and the neural network should outperform the Cox model were selected. The first was a published leukemia dataset manipulated to have a strong interaction that CART should detect. The second was a published cirrhosis dataset with pronounced nonlinear effects that a neural network should fit. Repeated sampling of 50 training and testing subsets was applied to each technique. The concordance index C was calculated as a measure of predictive accuracy by each technique on the testing dataset. In the interaction dataset, CART outperformed Cox (P less than 0.05) with a C improvement of 0.1 (95% Cl, 0.08 to 0.12). In the nonlinear dataset, the neural network outperformed the Cox model (P less than 0.05), but by a very slight amount (0.015). As predicted by theory, CART and the neural network were able to overcome limitations of the Cox model. Experiments like these are important to increase our understanding of when one of these new techniques will outperform the standard Cox model. Further research is necessary to predict which technique will do best a priori and to assess the magnitude of superiority.