On High-Dimensional Covariate Adjustment for Estimating Causal Effects in Randomized Trials with Survival Outcomes

The purpose of this work is to improve the efficiency in estimating the average causal effect (ACE) on the survival scale where right censoring exists and high-dimensional covariate information is available. We propose new estimators using regularized survival regression and survival Random Forest (RF) to adjust for the high-dimensional covariate to improve efficiency. We study the behavior of the adjusted estimators under mild assumptions and show theoretical guarantees that the proposed estimators are more efficient than the unadjusted ones asymptotically when using RF for the adjustment. In addition, these adjusted estimators are n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{n}$$\end{document}- consistent and asymptotically normally distributed. The finite sample behavior of our methods is studied by simulation. The simulation results are in agreement with the theoretical results. We also illustrate our methods by analyzing the real data from transplant research to identify the relative effectiveness of identical sibling donors compared to unrelated donors with the adjustment of cytogenetic abnormalities.