Statistics and Its Interface

Volume 7 (2014)

Number 2

D_CDF test of negative log transformed p-values with application to genetic pathway analysis

Pages: 187 – 200

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n2.a4

Authors

Hongying Dai (Research Development and Clinical Investigation, Children’s Mercy Hospital, Kansas City, Missouri, U.S.A.; Dept. of Pediatrics and Dept. of Informatic Medicine and Personalized Health, University of Missouri, Kansas City, Mo., U.S.A.)

Richard Charnigo (Department of Statistics, University of Kentucky, Lexington, Ky, U.S.A.)

Abstract

In genetic pathway analysis and other high dimensional data analysis, thousands and millions of tests could be performed simultaneously. p-values from multiple tests are often presented in a negative log-transformed format. We construct a contaminated exponential mixture model for $-\mathrm{ln}(P)$ and propose a D_CDF test to determine whether some $-\mathrm{ln}(P)$ are from tests with underlying effects. By comparing the cumulative distribution functions (CDF) of $-\mathrm{ln}(P)$ under mixture models, the proposed method can detect the cumulative effect from a number of variants with small effect sizes. Weight functions and truncations can be incorporated to the D_CDF test to improve power and better control the correlation among data. By using the modified maximum likelihood estimators (MMLE), the D_CDF tests have very tractable limiting distributions under $H_0$. A copula-based procedure is proposed to address the correlation issue among p-values. We also develop power and sample size calculation for the D_CDF test. The extensive empirical assessments on the correlated data demonstrate that the (weighted and/or $c$-level truncated) D_CDF tests have well controlled Type I error rates and high power for small effect sizes. We applied our method to gene expression data in mice and identified significant pathways related the mouse body weight.

Keywords

D_CDF test, negative log transformed p-values, weight function, $c$-level truncated test, mixture model, modified maximum likelihood estimator (MMLE)

Full Text (PDF format)