Deconfounding small quasi-experiments using propensity scores and other dimension reduction techniques
Ben Hansen, University of Michigan  *Yevgeniya Kleyman, University of Michigan 

Keywords: observational study, propensity score, covariate balance, matching, prognostic score, full matching

When the sample is small and the number of potential confounders large, propensity adjustment may seem to have little to offer. However, in combination with dimension reduction, flexible matching, formal diagnostics and simple post-matching adjustments, we find that it works surprisingly well. In our motivating example, a richly observed quasi-experiment comparing a faith-based and a conventional drug addiction treatment, close propensity score matching was not possible. Still, by matching relatively coarsely on the propensity score but also matching on other scores summarizing the covariate, it was possible to balance k=27 covariates with only n=67 subjects; closer propensity matching was no better in these terms, and worse in others. In a thorough simulation study, we offer a comparison to other natural approaches involving some but not all of our method's contributing techniques.

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