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Causal analysis of observational studies requires data that comprise of a set of covariates, a treatment assignment indicator, and the observed outcomes. However, data confidentiality restrictions or the nature of data collection may distribute these variables across two or more datasets. In the absence of unique identifiers to link records across files, probabilistic record linkage algorithms can be leveraged to merge the datasets. Current applications of record linkage are concerned with estimation of associations between variables that are exclusive to one file and not causal relationships. We propose a Bayesian framework for record linkage and causal inference where one file comprises all the covariate and observed outcome information, and the second file consists of a list of all individuals who receive the active treatment. Under certain ignorability assumptions, the procedure properly propagates the error in the record linkage process, resulting in valid statistical inferences. To estimate the causal effects, we devise a two-stage procedure. The first stage of the procedure performs Bayesian record linkage to multiply impute the treatment assignment for all individuals in the first file, while adjustments for covariates' imbalance and imputation of missing potential outcomes are performed in the second stage. This procedure is used to evaluate the effect of Meals on Wheels services on mortality and healthcare utilization among homebound older adults in Rhode Island. In addition, an interpretable sensitivity analysis is developed to assess potential violations of the ignorability assumptions.

A multiple imputation procedure for record linkage and causal inference to estimate the effects of home-delivered meals