Combining extremal Z-scores in meta-analysis

In the realm of modern medicine, the results of meta-analysis are typically presented in the form of statistics, confidence intervals, or <i>p</i> values to assess the magnitude, stability, and significance of experimental results. When confronted with a significant number of aggregate values, such as the Z-score, the utilization of statistical test approaches is of paramount importance. In this article, we introduce a novel test for integrating maximum and minimum Z-scores for meta-analysis. We deduce the asymptotic distribution of our proposed test under certain regular conditions and the null hypothesis. We explore the theoretical powers of our proposed test for several scenarios under the alternative hypothesis. Furthermore, in order to comprehensively evaluate the effectiveness of the test method proposed in this article, we conduct a comparative analysis of the efficacy with the existing test methods at the theoretical level. Both extensive simulation outcomes and real data analysis results demonstrate that our proposed test can effectively control empirical type-1 error rates and achieve desirable powers. Our proposed methodology can be adopted with ease and convenience.