An integration test based only on the maximum and minimum Z-scores for meta analysis

Abstract

Purpose: In modern medical field, one may encounter many summary values such as Z-scores and p-values. There have existed many integration methods for p-values, and there also existed some integration methods for Z-scores. Although there is a test which can integrate the maximum and minimum values from a large number of related Z-score values, but the distribution function of this test method is very complex and it is difficult to compute its p value. Methods: In this paper, we propose a new test to integrate the maximum and minimum Z-scores for meta analysis. We derive the asymptotic distribution of our proposed test under some regular conditions and null hypothesis. We investigate theoretical powers of our proposed test for some settings under alternative hypothesis. Results: We compare powers of our proposed test to existing tests theoretically. Both extensive simulation results and real data analysis results show that our proposed test can control empirical type-1 error rates well and gain desirable powers. Conclusion: Our proposed method can be adopted easily and conveniently.