Figure 4.

Distribution of propensity score matching (PSM), coarsened exact matching (CEM), and ordinary least squares (OLS) regression point estimates in data structures where the relationships between the confounders and the outcome are quadratic. A) “Confounder-outcome quadratic, good support” data structure (data structure 3); B) “confounder-outcome quadratic, poor support” data structure (data structure 4). PSM, CEM, and OLS point estimates were unbiased, on average; however, the distribution of PSM point estimates was larger than that of CEM or OLS estimates, particularly when common support was poor. Our proposed empirical “rule of thumb” indicates that OLS inferences are unbiased more often than matching inferences in these scenarios; that is, the OLS type I error rate approximates 5%, while the PSM and CEM type I error rates vary from the expected value of 5%. See Table 1 for more information.