title: Fisher's method of combining dependent statistics using generalizations of the gamma distribution with applications to genetic pleiotropic associations.
abstract: A classical approach to combine independent test statistics is Fisher's combination of $p$-values, which follows the $\chi ^2$ distribution. When the test statistics are dependent, the gamma distribution (GD) is commonly used for the Fisher's combination test (FCT). We propose to use two generalizations of the GD: the generalized and the exponentiated GDs. We study some properties of mis-using the GD for the FCT to combine dependent statistics when one of the two proposed distributions are true. Our results show that both generalizations have better control of type I error rates than the GD, which tends to have inflated type I error rates at more extreme tails. In practice, common model selection criteria (e.g. Akaike information criterion/Bayesian information criterion) can be used to help select a better distribution to use for the FCT. A simple strategy of the two generalizations of the GD in genome-wide association studies is discussed. Applications of the results to genetic pleiotrophic associations are described, where multiple traits are tested for association with a single marker.
authors.affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Qizhai
authors.initials: Q
authors.lastname: Li
authors.forename: Jiyuan
authors.initials: J
authors.lastname: Hu
authors.forename: Juan
authors.initials: J
authors.lastname: Ding
authors.forename: Gang
authors.initials: G
authors.lastname: Zheng
mesh_terms: D003627:Data Interpretation, Statistical; D058685:Genetic Pleiotropy / Q000235:genetics*; D055106:Genome-Wide Association Study / Q000592:standards*; D006801:Humans; D008957:Models, Genetic; D016008:Statistical Distributions
keywords: Dependent tests; Fisher's combination; Gamma distributions; Genetic pleiotropic associations; Genome-wide association studies; Type I error