A generalized weighting regression-derived meta-analysis estimator robust to small-study effects and heterogeneity

Heterogeneity and small-study effects are major concerns for the validity of meta-analysis. Although random effects meta-analysis provides a partial solution to heterogeneity, neither takes into account the presence of small-study effects, although they can rarely be ruled out with certainty. In this paper, we facilitate a better understanding of the properties of a recently described regression-based approach to deriving a meta-analysis estimator robust to small-study effects and unexplainable heterogeneity. The weightings of studies in the meta-analysis are derived algebraically for the regression model and compared with the weightings allocated to studies by fixed and random effects models. These weightings are compared in case studies with and without small-study effects. The presence of small-study effects causes pooled estimates from fixed and random effects meta-analyses to differ, potentially markedly, as a result of the different weights allocated to individual studies. Because random effects meta-analysis gives more weight to smaller studies, it becomes more vulnerable to the small-study effects. The regression approach gives heavier weight to the larger studies than either the fixed or random effects models, leading to its dominance in the estimated pooled effect. The weighting properties of the proposed regression-derived meta-analysis estimator are presented and compared with those of the standard meta-analytic estimators. We propose that there is much to recommend the routine use of this model as a reliable way to derive a pooled meta-analysis estimate that is robust to potential small-study effects, while still accommodating heterogeneity, even though uncertainty will often be considerably larger than for standard estimators.