Average treatment effect on the treated, under lack of positivity

TL;DR

This paper addresses the challenge of estimating the average treatment effect on the treated (ATT) under lack of positivity, proposing a new overlap weighting method that avoids arbitrary threshold choices and improves estimation accuracy.

Contribution

The paper introduces the overlap weighted average treatment effect on the treated (OWATT), a novel method that relaxes threshold selection and enhances causal effect estimation under positivity violations.

Findings

OWATT performs comparably or better than trimming and truncation methods.

The method is validated through simulations and real data analysis.

OWATT reduces bias and variance in ATT estimation.

Abstract

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.