On the propensity score weighting analysis with survival outcome: Estimands, estimation, and inference.

Propensity score analysis is widely used in observational studies to adjust for confounding and estimate the causal effect of a treatment on the outcome. When the outcome is survival time, there are special considerations on the definition of the causal estimand, point, and variance estimation that have not been thoroughly studied in the literature. We investigate propensity score analysis of survival data with a class of weighting methods. We consider the following estimands in the two-sample context: average survival time, restricted average survival time, survival probability, survival quantile, and the marginal hazard ratio. We propose a unified analytic framework to obtain the point and variance estimators. The proposed methodology properly adjusts for the sampling variability in the estimated propensity scores. Extensive simulations show that the point and variance estimators possess desired finite sample properties and demonstrate better numerical performance than some existing weighting and matching methods commonly used in the literature. The proposed methodology is illustrated with data from a breast cancer study.