Regression-Assisted Bayesian Record Linkage for Causal Inference in Observational Studies with Covariates Spread Over Two Files.

We consider causal inference for observational studies with data spread over two files. One file includes the treatment, outcome, and some covariates measured on a set of individuals, and the other file includes additional causally-relevant covariates measured on a partially overlapping set of individuals. By linking records in the two databases, the analyst can control for more covariates, thereby reducing the risk of bias compared to using only one file alone. When analysts do not have access to a unique identifier that enables perfect, error-free linkages, they typically rely on probabilistic record linkage to construct a single linked data set, and estimate causal effects using these linked data. This typical practice does not propagate uncertainty from imperfect linkages to the causal inferences. Further, it does not take advantage of relationships among the variables to improve the linkage quality. We address these shortcomings by fusing regression-assisted, Bayesian probabilistic record linkage with causal inference. The Markov chain Monte Carlo sampler generates multiple plausible linked data files as byproducts that analysts can use for multiple imputation inferences. Here, we show results for two causal estimators based on propensity score overlap weights. Using simulations and data from the Italy Survey on Household Income and Wealth, we show that our approach can improve the accuracy of estimated treatment effects.