Random forests for survival analysis using maximally selected rank statistics

The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption is not always fulfilled. An alternative approach is random forests for survival outcomes. The standard split criterion for random survival forests is the log-rank test statistics, which favors splitting variables with many possible split points. Conditional inference forests avoid this split point selection bias. However, linear rank statistics are utilized in current software for conditional inference forests to select the optimal splitting variable, which cannot detect non-linear effects in the independent variables. We therefore use maximally selected rank statistics for split point selection in random forests for survival analysis. As in conditional inference forests, p-values for association between split points and survival time are minimized. We describe several p-value approximations and the implementation of the proposed random forest approach. A simulation study demonstrates that unbiased split point selection is possible. However, there is a trade-off between unbiased split point selection and runtime. In benchmark studies of prediction performance on simulated and real datasets the new method performs better than random survival forests if informative dichotomous variables are combined with uninformative variables with more categories and better than conditional inference forests if non-linear covariate effects are included. In a runtime comparison the method proves to be computationally faster than both alternatives, if a simple p-value approximation is used.