  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.
