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：倾向性评分（PS）方法在因果推断中的应用已十分普遍。这类方法的核心是正定性假设。当正定性假设被违反时，在估计目标平均因果效应（如平均处理效应（ATE）或处理组平均处理效应（ATT））时会产生极端PS权重，导致相关统计推断失效。为解决这一问题，常采用对极端估计PS值进行截断或修剪的方法。然而，这类方法需要预先设定阈值，有时还需指定额外的平滑参数。尽管已有多种方法处理ATE估计中的正定性缺失问题，但令人惊讶的是，针对ATT中同类问题的研究却十分有限。本文首先梳理了ATT估计中广泛使用的修剪与截断方法，着重阐释其内在机理以深化应用认知，并指出其主要局限性。继而论证现有方法实际上只是针对缩放后的ATT（即改变了目标参数）进行估计，需要明确缩放比例和目标人群。在此基础上，我们提出一种基于PS权重的处理组平均因果效应替代估计量，称为重叠加权处理组平均处理效应（OWATT）。该方法的优势在于：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估计效果。通过蒙特卡洛模拟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。