In observational studies, the propensity score plays a central role in estimating causal effects of interest. The inverse probability weighting (IPW) estimator is especially commonly used. 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; these methods, however, require consideration of parameters that dominate the uncertainty of sampling and treatment allocation. In this manuscript, we propose a novel Bayesian estimating procedure that necessitates deciding the parameter probability, rather than deterministically. Since both the IPW estimator and the propensity score estimator can be derived as solutions to certain loss functions, the general Bayesian paradigm, which does not require the consideration of the full likelihood, can be applied. In this sense, our proposed method only requires the same level of assumptions as ordinary causal inference contexts.

翻译：在观察性研究中，倾向性评分在估计目标因果效应中发挥着核心作用。其中，逆概率加权（IPW）估计量尤为常用。然而，当倾向性评分模型设定错误时，IPW估计量可能产生有偏的因果效应估计。已有研究提出了一些稳健的倾向性评分估计方法，但这些方法需要考虑主导抽样与处理分配不确定性的参数。本文提出了一种新颖的贝叶斯估计方法，该方法需要对参数概率进行决策，而非确定性决策。由于IPW估计量与倾向性评分估计量均可视为某些损失函数的解，无需考虑完全似然的通用贝叶斯范式在此适用。从该意义上讲，我们提出的方法仅需要与普通因果推断语境相同水平的假设条件。