摘要：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.
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