Sieve estimation of the average treatment effect on log survival time

Propensity scores have been extensively utilized to investigate causal effects in observational studies. When the outcome is subject to right censoring, we propose a method that combines the propensity score sieve approach with log-rank regression to estimate treatment effects, which subsumes the propensity score covariate adjustment method as a special case. Compared to inverse probability weighting and double robust methods, our approach is less sensitive to extreme propensity scores and does not require modeling the distribution of censoring times given the covariates. We establish the consistency and asymptotic normality of the proposed estimator and assess its finite-sample performance through simulation studies. Finally, we apply our method to a real dataset from the German Breast Cancer Study Group.