The use of propensity score (PS) methods has become ubiquitous in causal inference. At the heart of these methods is the positivity assumption. Violation of the positivity assumption leads to the presence of extreme PS weights when estimating average causal effects of interest, such as the average treatment effect (ATE) or the average treatment effect on the treated (ATT), which renders invalid related statistical inference. To circumvent this issue, trimming or truncating the extreme estimated PSs have been widely used. However, these methods require that we specify a priori a threshold and sometimes an additional smoothing parameter. While there are a number of methods dealing with the lack of positivity when estimating ATE, surprisingly there is no much effort in the same issue for ATT. In this paper, we first review widely used methods, such as trimming and truncation in ATT. We emphasize the underlying intuition behind these methods to better understand their applications and highlight their main limitations. Then, we argue that the current methods simply target estimands that are scaled ATT (and thus move the goalpost to a different target of interest), where we specify the scale and the target populations. We further propose a PS weight-based alternative for the average causal effect on the treated, called overlap weighted average treatment effect on the treated (OWATT). The appeal of our proposed method lies in its ability to obtain similar or even better results than trimming and truncation while relaxing the constraint to choose a priori a threshold (or even specify a smoothing parameter). The performance of the proposed method is illustrated via a series of Monte Carlo simulations and a data analysis on racial disparities in health care expenditures.

翻译：倾向性得分（PS）方法在因果推断中的应用已变得极为普遍。这些方法的核心在于正性假设。正性假设被违反时，在估计感兴趣的平均因果效应（如平均处理效应（ATE）或已处理组的平均处理效应（ATT））过程中会出现极端的PS权重，从而导致相关统计推断失效。为规避此问题，学界广泛采用对极端估计PS进行修剪或截断的方法。然而，这些方法要求我们预先指定阈值，有时还需设定额外平滑参数。尽管已有诸多方法解决ATE估计中的正性缺乏问题，但令人惊讶的是，针对ATT的同类问题研究甚少。本文首先系统梳理ATT估计中常用的修剪与截断方法，着重阐释这些方法背后的直觉以增进对其应用的理解，并揭示其主要局限性。进而提出当前方法实际上只是针对缩放后的ATT目标估计量（即改变了原本的目标参数），其中缩放尺度与目标人群均需明确指定。我们进一步提出一种基于PS权重的替代方案——重叠加权已处理组平均处理效应（OWATT），用于估计已处理组的平均因果效应。该方法的核心优势在于：无需预先设定阈值（甚至无需指定平滑参数）即可获得与修剪/截断法相当甚至更优的结果。通过蒙特卡洛模拟系列实验及医疗支出种族差异的实证数据分析，验证了所提方法的有效性。