Estimating restricted mean treatment effects with stacked survival models

TL;DR

This paper introduces a novel method using stacked survival models to estimate covariate-adjusted restricted mean survival differences, improving accuracy especially when proportional hazards assumptions are violated.

Contribution

It proposes a new estimator based on stacked survival models that enhances covariate adjustment in restricted mean survival time analysis, outperforming traditional methods under certain conditions.

Findings

The new estimator performs nearly as well as Cox regression under proportional hazards.

It significantly outperforms Cox when proportional hazards assumption is violated.

Application to lung transplant data demonstrates practical utility.

Abstract

The difference in restricted mean survival times between two groups is a clinically relevant summary measure. With observational data, there may be imbalances in confounding variables between the two groups. One approach to account for such imbalances is to estimate a covariate-adjusted restricted mean difference by modeling the covariate-adjusted survival distribution and then marginalizing over the covariate distribution. We demonstrate that the mean-squared error of the restricted mean difference is bounded by the mean-squared error of the covariate-adjusted survival distribution estimators. This implies that a better estimator of the covariate-adjusted survival distributions is associated with a better estimator of the restricted mean difference. Thus, this paper proposes estimating restricted mean differences with stacked survival models. Stacked survival models estimate a weighted average of several survival models by minimizing predicted error. By including a range of parametric and semi-parametric models, stacked survival models can effectively estimate a covariate-adjusted survival distribution and, therefore, the restricted mean treatment effect in a wide range of scenarios. We demonstrate through a simulation study that the new estimator can perform nearly as well as Cox regression when the proportional hazards assumption is satisfied and significantly better when proportional hazards is violated. The proposed estimator is also illustrated with data from the United Network for Organ Sharing to evaluate post-lung transplant survival between large and small-volume centers.