  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 forests
(SRF) to make the adjustment for the high dimensional covariates to improve
efficiency. We study the behavior of the adjusted estimator under mild
assumptions and show theoretical guarantees that the proposed estimators are
more efficient than the unadjusted ones asymptotically when using SRF for
adjustment. In addition, these adjusted estimators are $\sqrt{n}$- consistent
and asymptotically normally distributed. The finite sample behavior of our
methods are studied by simulation, and the 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.
