The bounds of meta-analytics and an alternative method

Abstract

OBJECTIVES Meta-analysis is a statistical appraisal of the data analytic implications of published articles ( Y ), estimating parameters including the odds ratio and relative risk. This information is helpful for evaluating the significance of the findings. The Higgins I 2 index is often used to measure heterogeneity among studies. The objectives of this article are to amend the Higgins I 2 index score in a novel and innovative way and to make it more useful in practice. METHODS Heterogeneity among study populations can be affected by many sources, including the sample size and study design. They influence the Cochran Q score and, thus, the Higgins I 2 score. In this regard, the I 2 score is not an absolute indicator of heterogeneity. Q changes by bound as Y increases unboundedly. An innovative methodology is devised to show the conditional and unconditional probability structures. RESULTS Various properties are derived, including showing that a zero correlation between Q and Y does not necessarily mean that they are independent. A new alternative statistic, S 2 , is derived and applied to mild cognitive impairment and coronavirus disease 2019 vaccination for meta-analysis. CONCLUSIONS A hidden shortcoming of the Higgins I 2 index is overcome in this article by amending the Higgins I 2 score. The usefulness of the proposed methodology is illustrated using 2 examples. The findings have potential health policy implications.