Relaxed covariate overlap and margin-based causal effect estimation

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.