Simultaneous record linkage and causal inference with propensity score subclassification.

We develop methodology for causal inference in observational studies when using propensity score subclassification on data constructed with probabilistic record linkage techniques. We focus on scenarios where covariates and binary treatment assignments are in one file and outcomes are in another file, and the goal is to estimate an additive treatment effect by merging the files. We assume that the files can be linked using variables common to both files, eg, names or birth dates, but that links are subject to errors, eg, due to reporting errors in the linking variables. We develop methodology for cases where such reporting errors are independent of the other variables on the files. We describe conceptually how linkage errors can affect causal estimates in subclassification contexts. We also present and evaluate several algorithms for deciding which record pairs to use in estimation of causal effects. Using simulation studies, we demonstrate that case selection procedures can result in improved accuracy in estimates of treatment effects from linked data compared to using only cases known to be true links.