# Survival Forests under Test: Impact of the Proportional Hazards Assumption on Prognostic and Predictive Forests for ALS Survival

## TL;DR

This paper examines how the proportional hazards assumption influences the performance of various survival forest models for ALS, proposing new variants and analyzing their effectiveness through simulations and real data.

## Contribution

It introduces distributional and transformation survival forests and compares their theoretical and empirical performance against existing methods under non-proportional hazards.

## Key findings

- Log-rank splitting has low power in non-proportional hazards scenarios.
- Alternative split procedures can improve detection of complex survival patterns.
- New forest variants show promise in modeling ALS survival data.

## Abstract

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.