Performance of Matching Methods as Compared With Unmatched Ordinary Least Squares Regression Under Constant Effects

Matching methods are assumed to reduce the likelihood of a biased inference compared with ordinary least squares (OLS) regression. Using simulations, we compared inferences from propensity score matching, coarsened exact matching, and unmatched covariate-adjusted OLS regression to identify which methods, in which scenarios, produced unbiased inferences at the expected type I error rate of 5%. We simulated multiple data sets and systematically varied common support, discontinuities in the exposure and/or outcome, exposure prevalence, and analytical model misspecification. Matching inferences were often biased in comparison with OLS, particularly when common support was poor; when analysis models were correctly specified and common support was poor, the type I error rate was 1.6% for propensity score matching (statistically inefficient), 18.2% for coarsened exact matching (high), and 4.8% for OLS (expected). Our results suggest that when estimates from matching and OLS are similar (i.e., confidence intervals overlap), OLS inferences are unbiased more often than matching inferences; however, when estimates from matching and OLS are dissimilar (i.e., confidence intervals do not overlap), matching inferences are unbiased more often than OLS inferences. This empirical "rule of thumb" may help applied researchers identify situations in which OLS inferences may be unbiased as compared with matching inferences.