  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.
