Abstract
Combining information (p-values) obtained from individual studies to test whether there is an overall effect is an important task in statistical data analysis. Many classical statistical tests, such as chi-square tests, can be viewed as being a p-value combination approach. It remains challenging to find powerful methods to combine p-values obtained from various sources. In this paper, we study a class of p-value combination methods based on gamma distribution. We show that this class of tests is optimal under certain conditions and several existing popular methods are equivalent to its special cases. An asymptotically and uniformly most powerful p-value combination test based on constrained likelihood ratio test is then studied. Numeric results from simulation study and real data examples demonstrate that the proposed tests are robust and powerful under many conditions. They have potential broad applications in statistical inference.
Highlights
In statistical inference and decision making, it is critical but challenging to appropriately aggregate information from different sources. p-value combination approaches provide possible solutions
When the p-values to be combined are from certain type of distributions whose parameters are partially or fully unknown, asymptotically uniformly most powerful (UMP) tests based on constrained likelihood ratio test (CLRT) are proposed and studied
Let tCLRT,α0 be the observed statistic of test TCLRT,α0 ; the p-value of TCLRT,α0 is determined by the gamma distribution-based test TG(α0) = ∑in=1 FG−(1α0)(1 − Pi) as follows: Pr TCLRT,α0 > tCLRT,α0 =
Summary
In statistical inference and decision making, it is critical but challenging to appropriately aggregate information from different sources. p-value combination approaches provide possible solutions. The commonly used chi-square tests, including the likelihood ratio test, the score test, and the Wald test, with degrees of freedom (df) greater than one can be viewed as p-value combination methods, which are special cases of our proposed gamma distribution-based tests (see Section 2). When the p-values to be combined are from certain type of distributions whose parameters are partially or fully unknown, asymptotically UMP tests based on constrained likelihood ratio test (CLRT) are proposed and studied. The rest of the manuscript is organized as follows: In Section 2, we first introduce some existing popular p-value combination tests, describe our proposed tests based on gamma distributions, and study their connections to existing popular methods and their properties as of UMP tests.
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