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Accurate and Efficient P-value Calculation via Gaussian Approximation: a Novel Monte-Carlo Method.


ABSTRACT: It is of fundamental interest in statistics to test the significance of a set of covariates. For example, in genome-wide association studies, a joint null hypothesis of no genetic effect is tested for a set of multiple genetic variants. The minimum p-value method, higher criticism, and Berk-Jones tests are particularly effective when the covariates with nonzero effects are sparse. However, the correlations among covariates and the non-Gaussian distribution of the response pose a great challenge towards the p-value calculation of the three tests. In practice, permutation is commonly used to obtain accurate p-values, but it is computationally very intensive, especially when we need to conduct a large amount of hypothesis testing. In this paper, we propose a Gaussian approximation method based on a Monte Carlo scheme, which is computationally more efficient than permutation while still achieving similar accuracy. We derive non-asymptotic approximation error bounds that could vanish in the limit even if the number of covariates is much larger than the sample size. Through real-genotype-based simulations and data analysis of a genome-wide association study of Crohn's disease, we compare the accuracy and computation cost of our proposed method, of permutation, and of the method based on asymptotic distribution.

SUBMITTER: Liu Y 

PROVIDER: S-EPMC6530914 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Accurate and Efficient <i>P</i>-value Calculation via Gaussian Approximation: a Novel Monte-Carlo Method.

Liu Yaowu Y   Xie Jun J  

Journal of the American Statistical Association 20180628 525


It is of fundamental interest in statistics to test the significance of a set of covariates. For example, in genome-wide association studies, a joint null hypothesis of no genetic effect is tested for a set of multiple genetic variants. The minimum <i>p</i>-value method, higher criticism, and Berk-Jones tests are particularly effective when the covariates with nonzero effects are sparse. However, the correlations among covariates and the non-Gaussian distribution of the response pose a great cha  ...[more]

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