期刊
JOURNAL OF BIOPHARMACEUTICAL STATISTICS
卷 15, 期 5, 页码 783-797出版社
TAYLOR & FRANCIS INC
DOI: 10.1081/BIP-200067778
关键词
distribution-free; exchangeable random variables; false discovery rate; gene expression; microarray; multiple testing; nonparametric methods; normalization; rank methods; SAM; statistical analysis
资金
- NATIONAL HEART, LUNG, AND BLOOD INSTITUTE [U01HL066678, R01HL072358] Funding Source: NIH RePORTER
- NATIONAL HUMAN GENOME RESEARCH INSTITUTE [R01HG002510] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF DIABETES AND DIGESTIVE AND KIDNEY DISEASES [U01DK063665] Funding Source: NIH RePORTER
- NHGRI NIH HHS [HG02510] Funding Source: Medline
- NHLBI NIH HHS [HL66678, HL72358] Funding Source: Medline
- NIDDK NIH HHS [DK63665] Funding Source: Medline
This article proposes nonparametric inference procedures for analyzing microarray gene expression data that are reliable, robust, and simple to implement. They are conceptually transparent and require no special-purpose software. The analysis begins by normalizing gene expression data in a unique way. The resulting adjusted observations consist of gene-treatment interaction terms ( representing differential expression) and error terms. The error terms are considered to be exchangeable, which is the only substantial assumption. Thus, under a family null hypothesis of no differential expression, the adjusted observations are exchangeable and all permutations of the observations are equally probable. The investigator may use the adjusted observations directly in a distribution-free test method or use their ranks in a rank-based method, where the ranking is taken over the whole data set. For the latter, the essential steps are as follows: 1. Calculate a Wilcoxon rank-sum difference or a corresponding Kruskal-Wallis rank statistic for each gene. 2. Randomly permute the observations and repeat the previous step. 3. Independently repeat the random permutation a suitable number of times. Under the exchangeability assumption, the permutation statistics are independent random draws from a null cumulative distribution function (c.d.f.) approximated by the empirical c.d.f. Reference to the empirical c.d.f. tells if the test statistic for a gene is outlying and, hence, shows differential expression. This feature is judged by using an appropriate rejection region or computing a p-value for each test statistic, taking into account multiple testing. The distribution-free analog of the rank-based approach is also available and has parallel steps which are described in the article. The proposed nonparametric analysis tends to give good results with no additional refinement, although a few refinements are presented that may interest some investigators. The implementation is illustrated with a case application involving differential gene expression in wild-type and knockout mice of an E. coli lipopolysaccharide (LPS) endotoxin treatment, relative to a baseline untreated condition.
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