This article examines the performance of the updated quality effects (QE) estimator for meta-analysis of heterogeneous studies. It is shown that this approach leads to a decreased mean squared error (MSE) of the estimator while maintaining the nominal level of coverage probability of the confidence interval. Extensive simulation studies confirm that this approach leads to the maintenance of the correct coverage probability of the confidence interval, regardless of the level of heterogeneity, as well as a lower observed variance compared to the random effects (RE) model. The QE model is robust to subjectivity in quality assessment down to completely random entry, in which case its MSE equals that of the RE estimator. When the proposed QE method is applied to a meta-analysis of magnesium for myocardial infarction data, the pooled mortality odds ratio (OR) becomes 0.81 (95% CI 0.61-1.08) which favors the larger studies but also reflects the increased uncertainty around the pooled estimate. In comparison, under the RE model, the pooled mortality OR is 0.71 (95% CI 0.57-0.89) which is less conservative than that of the QE results. The new estimation method has been implemented into the free meta-analysis software MetaXL which allows comparison of alternative estimators and can be downloaded from www.epigear.com.
Keywords: Fixed effects; Heterogeneity; Meta-analysis; Quality effects; Quasi-likelihood; Random effects.
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