Random Survival Forests › Summary

A random survival forest extends the random forest to right-censored outcomes by replacing the two ingredients that cannot see censoring. The split criterion becomes the log-rank statistic, which compares the observed and expected number of deaths on either side of a candidate threshold at every event time and standardizes by the hypergeometric variance. The leaf prediction becomes the Nelson–Aalen estimator, which accumulates the increments $d/Y$ over the leaf's own risk sets and is then exponentiated to give a survival function. Bootstrap sampling and random feature subsampling carry over, while out-of-bag prediction and scoring must respect censoring and leakage constraints. The ensemble is the average of the trees' cumulative hazards, exponentiated once at the end.

The reason to use it is flexibility. The model does not require proportional hazards or linear covariate effects, it discovers interactions and thresholds without being told about them, and censored observations contribute to applicable risk sets while they remain under observation in a sampled tree. The reasons to be careful are the price of that flexibility: the predictions are step functions rather than smooth curves, their flat tails supply no learned extrapolation past the last observed event, the risk score is a rank-order summary on an arbitrary scale rather than a hazard ratio, and the method does not solve informative censoring. OOB predictions can support internal assessment under the same censoring and leakage constraints as other evaluation, and partial dependence can describe an average fitted response, but the result is a description of a relationship rather than a formal test of it.

The natural next step is to grow trees sequentially. Gradient boosting adds fitted components to reduce a chosen training objective, using gradients or related working responses. Improvement depends on the loss, step size, and fitted component, and better training loss does not guarantee better held-out prediction. Boosted Trees develops that construction. Survival boosting can use survival-specific objectives such as Cox partial likelihood; it need not reuse the log-rank splitting criterion used here.