Bioinformatics Advance Access published online on March 30, 2006
Bioinformatics, doi:10.1093/bioinformatics/btl109
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1 Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada
* To whom correspondence should be addressed.
Motivation: The parametric F-test has been widely used in the analysis of factorial microarray experiments to assess treatment effects. However, the normality assumption is often untenable for microarray experiments with small replications. Therefore, permutation based methods are called for help to assess the statistical significance. The distribution of the F-statistics across all the genes on the array can be regarded as a mixture distribution with a proportion of statistics generated from the null distribution of no differential gene expression whereas the other proportion of statistics generated from the alternative distribution of genes differentially expressed. This results in the fact that the permutation distribution of the F statistics may not approximate well to the true null distribution of the F statistics. Therefore, the construction of a proper null statistic to better approximate the null distribution of F statistic is of great importance to the permutation based multiple testing in microarray data analysis. Results: In this paper, we extend the ideas of constructing null statistics based on pairwise differences to neglect the treatment effects (Efron et al., 2001; Zhao and Pan, 2003; Pan, 2003) from the two-sample comparison problem to the multifactorial balanced or unbalanced microarray experiments. A null statistic based on a subpartition method is proposed and its distribution is employed to approximate the null distribution of the F statistic. The proposed null statistic is able to accommodate unbalance in the design and is also corrected for the undue correlation between its numerator and denominator. In the simulation studies and real biological data analysis, the number of true positives and the false discovery rate of the proposed null statistic are compared with those of the permutated version of the F statistic. It has been shown that our proposed method has a better control of the false discovery rates and a higher power than the standard permutation method to detect differentially expressed genes because of the better approximated tail probabilities. Availability: R codes available upon request.
Received December 14, 2005
Revised February 28, 2006
Accepted March 19, 2006
Article
Construction of null statistics in permutation based multiple testing for multi-factorial microarray experiments
Xin Gao 1 *
Xin Gao, E-mail: xingao{at}mathstat.yorku.ca
Abstract
Associate Editor: Joaquin Dopazo
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