Why the unrestricted weighted least squares should be routinely reported in medical meta-analyses

Abstract

The unrestricted weighted least squares (UWLS) meta-analysis estimator of mean effect is an alternative to the conventional random-effects model (RE). It is a weighted least squares regression estimator that can be represented as a multiplicative random-effects model. UWLS has been shown to fit medical research better than RE as measured by AIC/BIC widely across Cochrane Database of Systematic Reviews (CDSR). The independence of UWLS's mean and heterogeneity estimators provide small-sample advantages that RE does not possess. Large small-sample biases and uncertainty in RE's heterogeneity variance estimates explain most of RE's relatively poor fit along with RE's boundary problem, where RE's heterogeneity variance is estimated to be zero. We prove that UWLS almost always has superior fit at RE's boundary with uncommon exceptions. UWLS has also been found to have generally superior statistical properties: bias, MSE, and coverage relative to RE across 1,665 simulation designs compiled from four published studies authored by different teams of researchers. A recent study in this journal replicated UWLS's superior goodness of fit widely across both the CDSR and a new set of simulations. Due to reporting and interpretation errors, this recent study calls for the continued use of RE as the default meta-analysis estimator with limited applications of UWLS. We address this recent study's concerns and show why UWLS should be routinely reported in medical meta-analyses.