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In observational study, the propensity score has the central role to estimatecausal effects. Since the propensity score is usually unknown, estimating byappropriate procedures is an indispensable step. A point to note that a causaleffect estimator might have some bias if a propensity score model wasmisspecified; valid model construction is important. To overcome the problem, avariety of interesting methods has been proposed. In this paper, we review fourmethods: using ordinary logistic regression approach; CBPS proposed by Imai andRatkovic; boosted CART proposed by McCaffrey and colleagues; a semiparametricstrategy proposed by Liu and colleagues. Also, we propose the novel robust twostep strategy: estimating each candidate model in the first step andintegrating them in the second step. We confirm the performance of thesemethods through simulation examples by estimating the ATE and ATO proposed byLi and colleagues. From the results of the simulation examples, the boostedCART and CBPS with higher-order balancing condition have good properties; boththe estimate of the ATE and ATO has the small variance and the absolute valueof bias. The boosted CART and CBPS are useful for a variety of estimands andestimating procedures.

Robust Estimating Method for Propensity Score Models and its Application to Some Causal Estimands: A review and proposal