# Modeling the Restricted Mean Survival Time Using Pseudo‐Value Random Forests

## TL;DR

This paper introduces a new method called pseudo-value random forest to estimate survival time in medical studies without relying on strict assumptions.

## Contribution

The paper introduces a non-parametric method for modeling restricted mean survival time using pseudo-values and random forests.

## Key findings

- PVRF provides accurate estimates of patient-specific survival times.
- The method performs well in detecting covariate effects in high-dimensional data.
- PVRF outperforms existing techniques in simulation and real-world breast cancer data.

## Abstract

The restricted mean survival time (RMST) has become a popular measure to summarize event times in longitudinal studies. Defined as the area under the survival function up to a time horizon τ>0, the RMST can be interpreted as the life expectancy within the time interval [0,τ]. In addition to its straightforward interpretation, the RMST allows for the definition of valid estimands for the causal analysis of treatment contrasts in medical studies. In this work, we introduce a non‐parametric approach to model the RMST conditional on a set of baseline variables (including, e.g., treatment variables and confounders). Our method is based on a direct modeling strategy for the RMST, using leave‐one‐out jackknife pseudo‐values within a random forest regression framework. In this way, it can be employed to obtain precise estimates of both patient‐specific RMST values and confounder‐adjusted treatment contrasts. Since our method (termed “pseudo‐value random forest”, PVRF) is model‐free, RMST estimates are not affected by restrictive assumptions like the proportional hazards assumption. Particularly, PVRF offers a high flexibility in detecting relevant covariate effects from higher‐dimensional data, thereby expanding the range of existing pseudo‐value modeling techniques for RMST estimation. We investigate the properties of our method using simulations and illustrate its use by an application to data from the SUCCESS‐A breast cancer trial. Our numerical experiments demonstrate that PVRF yields accurate estimates of both patient‐specific RMST values and RMST‐based treatment contrasts.