Optimal Concordant Tests

In meta-analyses, 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 a 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 exists no test that is uniformly most powerful; therefore, figuring out 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 a numeric simulation study and real data example.