Causal effect estimation in survival analysis with high dimensional confounders.

With the ever advancing of modern technologies, it has become increasingly common that the number of collected confounders exceeds the number of subjects in a data set. However, matching based methods for estimating causal treatment effect in their original forms are not capable of handling high-dimensional confounders, and their various modified versions lack statistical support and valid inference tools. In this article, we propose a new approach for estimating causal treatment effect, defined as the difference of the restricted mean survival time (RMST) under different treatments in high-dimensional setting for survival data. We combine the factor model and the sufficient dimension reduction techniques to construct propensity score and prognostic score. Based on these scores, we develop a kernel based doubly robust estimator of the RMST difference. We demonstrate its link to matching and establish the consistency and asymptotic normality of the estimator. We illustrate our method by analyzing a dataset from a study aimed at comparing the effects of two alternative treatments on the RMST of patients with diffuse large B cell lymphoma.