In observational study, the propensity score has the central role to estimate causal effects. Since the propensity score is usually unknown, estimating by appropriate procedures is an indispensable step. A point to note that a causal effect estimator might have some bias if a propensity score model was misspecified; valid model construction is important. To overcome the problem, a variety of interesting methods has been proposed. In this paper, we review four methods: using ordinary logistic regression approach; CBPS proposed by Imai and Ratkovic; boosted CART proposed by McCaffrey and colleagues; a semiparametric strategy proposed by Liu and colleagues. Also, we propose the novel robust two step strategy: estimating each candidate model in the first step and integrating them in the second step. We confirm the performance of these methods through simulation examples by estimating the ATE and ATO proposed by Li and colleagues. From the results of the simulation examples, the boosted CART and CBPS with higher-order balancing condition have good properties; both the estimate of the ATE and ATO has the small variance and the absolute value of bias. The boosted CART and CBPS are useful for a variety of estimands and estimating procedures.

翻译：在观察研究中,倾向性评分具有估计因果关系的核心作用。由于倾向性评分通常不为人知,因此通过适当程序估算是一个不可或缺的步骤。一个要点是,如果偏向性评分模型被错误地指定,因果关系估计者可能会有某些偏差;有效的模型构建很重要。为了克服问题,提出了各种有趣的方法。在本文件中,我们审查了四种方法:使用普通后勤回归法;Imai和Ratkovic提议的CBPS;McAffrey和同事提议的CART;McCARTy和同事提议的半对称战略;刘和同事提议的半对称战略。此外,我们提出了新颖的稳健的两步战略:在第一步估算每个候选人模型,并在第二步中将其整合。我们通过模拟示例,通过估算李和同事提议的ATE和ATTO,来确认这些方法的绩效。根据模拟实例,提升的CART和CBPS的平衡条件具有良好的特性;对ATE和ATO的估计具有小的差异和绝对的偏差值。增强的CART和CBPS程序对各种估计是有用的。