Optimal matching with a variable number of controls vs. a fixed number of controls for a cohort study. trade-offs.

Matching is used to control for imbalances between groups, but the preferable strategy for matching is not always clear. We sought to compare two algorithms-optimal matching with a fixed number of controls (OMFC), and optimal matching with a variable number of controls (OMVC). We compared the degree of bias reduction and relative precision using Monte Carlo simulations. We systematically changed the magnitude of the matching variable difference, the variance ratios of the matching variable in the exposed and unexposed groups, the sample size, and the number of unexposed subjects available for matching. OMVC always produced larger removal of bias than the OMFC. The mean percentage reduction of bias was 38.3 with the OMFC and 52.6 with OMVC. OMVC increased the variance 6%. OMVC should be employed when researchers have access to a pool of unexposed subjects because it removes more bias with little loss in precision.