Relaxed covariate overlap and margin-based causal effect estimation

TL;DR

This paper introduces the concept of relaxed covariate overlap, linking it to the machine learning margin, to enable causal effect estimation even when traditional positivity assumptions are violated.

Contribution

It proposes a new balance condition called relaxed covariate overlap, extending causal inference methods to cases with limited treatment positivity.

Findings

The approach allows causal inference without strict positivity assumptions.

It connects covariate balance to the machine learning margin.

Illustrated with two real-world examples.

Abstract

In most nonrandomized observational studies, differences between treatment groups may arise not only due to the treatment but also because of the effect of confounders. Therefore, causal inference regarding the treatment effect is not as straightforward as in a randomized trial. To adjust for confounding due to measured covariates, a variety of methods based on the potential outcomes framework are used to estimate average treatment effects. One of the key assumptions is treatment positivity, which states that the probability of treatment is bounded away from zero and one for any possible combination of the confounders. Methods for performing causal inference when this assumption is violated are relatively limited. In this article, we discuss a new balance-related condition involving the convex hulls of treatment groups, which I term relaxed covariate overlap. An advantage of this concept is that it can be linked to a concept from machine learning, termed the margin. Introduction of relaxed covariate overlap leads to an approach in which one can perform causal inference in a three-step manner. The methodology is illustrated with two examples.