Relaxed covariate overlap and margin-based causal effect estimation
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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, and methods for performing causal inference when this assumption is violated are relatively limited. In this article, we explore the issue of covariate overlap and discuss a new condition involving overlap in the convex hulls of treatment groups, which we term relaxed covariate balance. 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 we can perform causal inference in a three-step manner. The methodology is illustrated with two examples.
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