Survival Forests under Test: Impact of the Proportional Hazards Assumption on Prognostic and Predictive Forests for ALS Survival
This addresses limitations in survival modeling for ALS prognosis and treatment prediction, representing an incremental improvement to existing forest methods.
The study examined how the proportional hazards assumption affects prognostic and predictive survival models for ALS patients, finding that log-rank-based splitting in survival forests has low power in non-proportional hazards situations, which can be overcome by novel distributional and transformation survival forest variants.
We investigate the effect of the proportional hazards assumption on prognostic and predictive models of the survival time of patients suffering from amyotrophic lateral sclerosis (ALS). We theoretically compare the underlying model formulations of several variants of survival forests and implementations thereof, including random forests for survival, conditional inference forests, Ranger, and survival forests with $L_1$ splitting, with two novel variants, namely distributional and transformation survival forests. Theoretical considerations explain the low power of log-rank-based splitting in detecting patterns in non-proportional hazards situations in survival trees and corresponding forests. This limitation can potentially be overcome by the alternative split procedures suggested herein. We empirically investigated this effect using simulation experiments and a re-analysis of the PRO-ACT database of ALS survival, giving special emphasis to both prognostic and predictive models.