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A parametric model to estimate the proportion from true null using a distribution for p-values

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  • Yu, Chang
  • Zelterman, Daniel

Abstract

Microarray studies generate a large number of p-values from many gene expression comparisons. The estimate of the proportion of the p-values sampled from the null hypothesis draws broad interest. The two-component mixture model is often used to estimate this proportion. If the data are generated under the null hypothesis, the p-values follow the uniform distribution. What is the distribution of p-values when data are sampled from the alternative hypothesis? The distribution is derived for the chi-squared test. Then this distribution is used to estimate the proportion of p-values sampled from the null hypothesis in a parametric framework. Simulation studies are conducted to evaluate its performance in comparison with five recent methods. Even in scenarios with clusters of correlated p-values and a multicomponent mixture or a continuous mixture in the alternative, the new method performs robustly. The methods are demonstrated through an analysis of a real microarray dataset.

Suggested Citation

  • Yu, Chang & Zelterman, Daniel, 2017. "A parametric model to estimate the proportion from true null using a distribution for p-values," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 105-118.
    • Handle: RePEc:eee:csdana:v:114:y:2017:i:c:p:105-118
    DOI: 10.1016/j.csda.2017.04.008
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    1. Allison, David B. & Gadbury, Gary L. & Heo, Moonseong & Fernandez, Jose R. & Lee, Cheol-Koo & Prolla, Tomas A. & Weindruch, Richard, 2002. "A mixture model approach for the analysis of microarray gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 1-20, March.
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    6. Xiang, Qinfang & Edwards, Jode & Gadbury, Gary L., 2006. "Interval estimation in a finite mixture model: Modeling P-values in multiple testing applications," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 570-586, November.
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    Cited by:

    1. Chang Yu & Daniel Zelterman, 2020. "Distributions associated with simultaneous multiple hypothesis testing," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-17, December.

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