Testing overall and moderator effects meta-regression

Random effects meta-regression is a technique to synthesize results of multiple studies. It allows for a test of an overall effect, as well as for tests of effects of study characteristics, that is, (discrete or continuous) moderator effects. We describe various procedures to test moderator effects: the z, t, likelihood ratio (LR), Bartlett-corrected LR (BcLR), and resampling tests. We compare the Type I error of these tests, and conclude that the common z test, and to a lesser extent the LR test, do not perform well since they may yield Type I error rates appreciably larger than the chosen alpha. The error rate of the resampling test is accurate, closely followed by the BcLR test. The error rate of the t test is less accurate but arguably tolerable. With respect to statistical power, the BcLR and t tests slightly outperform the resampling test. Therefore, our recommendation is to use either the resampling or the BcLR test. If these statistics are unavailable, then the t test should be used since it is certainly superior to the z test.