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Causal inference in observational studies typically requires makingcomparisons between groups that are dissimilar. For instance, researchersinvestigating the role of a prolonged duration of breastfeeding on childoutcomes may be forced to make comparisons between women with substantiallydifferent characteristics on average. In the extreme there may existneighborhoods of the covariate space where there are not sufficient numbers ofboth groups of women (those who breastfed for prolonged periods and those whodid not) to make inferences about those women. This is referred to as lack ofcommon support. Problems can arise when we try to estimate causal effects forunits that lack common support, thus we may want to avoid inference for suchunits. If ignorability is satisfied with respect to a set of potentialconfounders, then identifying whether, or for which units, the common supportassumption holds is an empirical question. However, in the high-dimensionalcovariate space often required to satisfy ignorability such identification maynot be trivial. Existing methods used to address this problem often requirereliance on parametric assumptions and most, if not all, ignore the informationembedded in the response variable. We distinguish between the concepts of"common support" and common causal support." We propose a new approach foridentifying common causal support that addresses some of the shortcomings ofexisting methods. We motivate and illustrate the approach using data from theNational Longitudinal Survey of Youth to estimate the effect of breastfeedingat least nine months on reading and math achievement scores at age five or six.We also evaluate the comparative performance of this method in hypotheticalexamples and simulations where the true treatment effect is known.

annals of applied statistics/the annals of applied statistics

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