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。这些方法的核心是正性假设。违背正性假设会导致在估计感兴趣的平均因果效应（如平均处理效应（ATE）或处理组平均处理效应（ATT））时出现极端PS权重，从而使相关统计推断失效。为解决此问题，修剪或截断极端估计PS的方法被广泛采用。然而，这些方法需要事先指定阈值，有时还需额外指定平滑参数。尽管已有许多方法处理ATE估计中的缺乏正性问题，但令人惊讶的是，针对ATT的同一问题却鲜有研究。本文首先回顾了ATT估计中常用的方法（如修剪和截断），强调其背后的直观理解以阐明应用情境，并重点分析其主要局限性。随后，我们论证现有方法本质上仅针对缩放后的ATT（即将目标转向不同的兴趣参数），其中需明确缩放比例和目标群体。我们进一步提出一种基于PS权重的处理组平均因果效应替代方法，称为重叠加权处理组平均处理效应（OWATT）。所提方法的优势在于：无需预先选择阈值（或指定平滑参数），即可获得与修剪和截断方法相当甚至更优的结果。通过一系列蒙特卡洛模拟以及关于医疗支出种族差异的数据分析，验证了所提方法的性能。