Optimal concordant tests

Music City Center 

In meta-analysis, unlike model-based methods, such as fixed- or random-effect models, the p-value combining methods are distribution-free and robust. How to appropriately and powerfully combine p-values obtained from various sources remains an important but challenging topic in statistical inference. For cases where all or the majority of the individual alternative hypotheses have the same but unknown direction, concordant tests based on one-sided p-values can substantially improve the detecting power. However, there exist no uniformly most powerful tests; therefore, how to choose a robust and powerful test to combine one-sided p-values for a given data set is desirable. In this paper, we propose and study a class of gamma distribution-based concordant tests. Those concordant tests are optimal under specific conditions. An asymptotically optimal concordant test is also studied. The excellent performances of the proposed tests were demonstrated through numeric simulation study and real data example.

chi-square test

constrained likelihood ratio test

gamma distribution

meta-analysis

uniformly most powerful test 

International Chinese Statistical Association