Assessing lack of common support in causal inference using Bayesian nonparametrics: Implications for evaluating the effect of breastfeeding on children's cognitive outcomes

Abstract

Causal inference in observational studies typically requires making comparisons between groups that are dissimilar. For instance, researchers investigating the role of a prolonged duration of breastfeeding on child outcomes may be forced to make comparisons between women with substantially different characteristics on average. In the extreme there may exist neighborhoods of the covariate space where there are not sufficient numbers of both groups of women (those who breastfed for prolonged periods and those who did not) to make inferences about those women. This is referred to as lack of common support. Problems can arise when we try to estimate causal effects for units that lack common support, thus we may want to avoid inference for such units. If ignorability is satisfied with respect to a set of potential confounders, then identifying whether, or for which units, the common support assumption holds is an empirical question. However, in the high-dimensional covariate space often required to satisfy ignorability such identification may not be trivial. Existing methods used to address this problem often require reliance on parametric assumptions and most, if not all, ignore the information embedded in the response variable. We distinguish between the concepts of "common support" and common causal support." We propose a new approach for identifying common causal support that addresses some of the shortcomings of existing methods. We motivate and illustrate the approach using data from the National Longitudinal Survey of Youth to estimate the effect of breastfeeding at least nine months on reading and math achievement scores at age five or six. We also evaluate the comparative performance of this method in hypothetical examples and simulations where the true treatment effect is known.