Generalized coarsened confounding for causal effects: a large-sample framework

There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider a class of generalized coarsened procedures for confounding. At a high level, these procedures can be viewed as performing a clustering of confounding variables, followed by treatment effect and attendant variance estimation using the confounder strata. In addition, we propose two new algorithms for generalized coarsened confounding. While previous authors have developed some statistical properties for one special case in our class of procedures, we instead develop a general asymptotic framework. We provide asymptotic results for the average causal effect estimator as well as providing conditions for consistency. In addition, we provide an asymptotic justification for the variance formulae for coarsened exact matching. A bias correction technique is proposed, and we apply the proposed methodology to data from two well-known observational studies.