In observational studies, the propensity score plays a central role in estimating causal effects of interest. The inverse probability weighting (IPW) estimator is commonly used for this purpose. However, if the propensity score model is misspecified, the IPW estimator may produce biased estimates of causal effects. Previous studies have proposed some robust propensity score estimation procedures. However, these methods require considering parameters that dominate the uncertainty of sampling and treatment allocation. This study proposes a novel Bayesian estimating procedure that necessitates probabilistically deciding the parameter, rather than deterministically. Since the IPW estimator and propensity score estimator can be derived as solutions to certain loss functions, the general Bayesian paradigm, which does not require the considering the full likelihood, can be applied. Therefore, our proposed method only requires the same level of assumptions as ordinary causal inference contexts. The proposed Bayesian method demonstrates equal or superior results compared to some previous methods in simulation experimentss, and is also applied to real data, namely the Whitehall dataset.

翻译：在观察性研究中，倾向得分在估计目标因果效应中起着核心作用。逆概率加权（IPW）估计器通常用于此目的。然而，若倾向得分模型设定错误，IPW估计器可能产生有偏的因果效应估计。先前研究已提出若干稳健的倾向得分估计方法，但这些方法需考虑主导抽样与治疗分配不确定性的参数。本研究提出一种新颖的贝叶斯估计方法，该方法要求以概率方式而非确定性方式决定参数。由于IPW估计器与倾向得分估计器可推导为特定损失函数的解，无需考虑完整似然函数的通用贝叶斯范式得以适用。因此，我们提出的方法仅需与常规因果推断情境相同层级的假设。仿真实验表明，所提出的贝叶斯方法相较于既有方法具有相当或更优的表现，并成功应用于真实数据（即Whitehall数据集）。