Enhanced doubly robust estimate with semiparametric models for causal inference of survival outcome

In observational studies, the treatment assignment is typically not random. Even in randomized clinical trials, the randomization may be imperfect given the limitation of sample size. In these cases, traditional statistical methods may lead to biased estimates of treatment effects, and causal inference methods are needed to obtain unbiased estimates. The doubly robust estimator (DRE) is a recent development in causal inference, but the literature on DRE for survival data is very limited, and existing methods tend to have complicated forms and may not have double robustness in the original sense. Some are constructed based on the Nelson-Aalen estimator, and to our knowledge no DRE is constructed based on the Kaplan-Meier estimator. Furthermore, in these methods, the propensity score model is often subjectively specified with a logistic model. DRE can be seriously biased if the propensity score and outcome models are slightly misspecified. Here we propose a new semiparametric robust estimator that utilizes the Kaplan-Meier estimator and Stute weighted empirical form to address these issues. Our proposed estimator is not only doubly robust in the original sense but also enhances robustness with the use of semiparametric specification. The asymptotic properties of the proposed estimator are derived, and extensive simulation studies are conducted to evaluate its finite sample performance and compare it with existing methods. Finally, we apply our proposed method to a real clinical study.