On the use of balancing scores and matching in testing for exposure effect in case-control studies

Balancing scores, especially the propensity score, are widely used to adjust for measured confounders in prospective studies. In case-control studies, the distribution of the exposure and outcome given the covariates is distorted when there is an exposure effect, due to the selection process. Therefore, it is less obvious how to estimate balancing scores. Extensive simulations revealed several interesting findings on the use of estimated balancing scores in testing for exposure effect. First, that with the aid of an estimated balancing score obtaining matched sets with a low absolute standardized difference in covariate means was far easier than without the aid of an estimated balancing score. Second, that the approach for estimating the balancing score matters, and that several potential approaches result in an inflation of the type I error probability. Third, that the strategy by which we adjust for difference in estimated balancing scores across groups can have a great effect on the power of the test for exposure effect. In particular, in our simulations, the full matching strategy on cavariates and on the estimated balancing score resulted in better power than the strategy of covariate adjustment or inverse probability weighting. We show the usefulness of full matching with the aid of our recommended approach to estimating the balancing score in a case-control study.