Simple Robust Estimating Method for Propensity Score Models and its Application to Some Causal Estimands

To estimate causal effects accurately, adjusting covariates is one of the important steps in observational study. When all covariates are observed, the covariates can be adjusted, and an unbiased estimator for causal effects can be obtained. In this situation, the propensity score has the central role to estimate the causal effects. Recently, some causal estimands, the target population of causal effects estimation, are considered which depend on the "true" propensity score. A point to note that an interested estimands might have some bias if a propensity score model was misspecified. In this paper, we consider a multiply robust estimator for the propensity score. In brief, we prepare some candidate models, and construct an estimating equation including the candidate models at once. Some theoretical properties are proved, and we consider application examples for propensity score estimations when the average treatment effects for the overlap population is central interest.