title: Nonparametric methods for microarray data based on exchangeability and borrowed power.
abstract: 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.
authors.affiliation: Department of Medicine, Brigham and Women's Hospital, Boston, Massachusetts, USA. meiling@channing.harvard.edu
authors.forename: Mei-Ling Ting
authors.initials: ML
authors.lastname: Lee
authors.forename: G A
authors.initials: GA
authors.lastname: Whitmore
authors.forename: Harry
authors.initials: H
authors.lastname: Björkbacka
authors.forename: Mason W
authors.initials: MW
authors.lastname: Freeman
mesh_terms: D000818:Animals; D003627:Data Interpretation, Statistical; D015870:Gene Expression / Q000187:drug effects; D020869:Gene Expression Profiling / Q000706:statistics & numerical data; D008070:Lipopolysaccharides / Q000494:pharmacology; D008264:Macrophages / Q000187:drug effects / Q000378:metabolism; D051379:Mice; D018345:Mice, Knockout; D046228:Microarray Analysis / Q000706:statistics & numerical data*; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis / Q000706:statistics & numerical data; D018709:Statistics, Nonparametric
chemical_list: D008070:Lipopolysaccharides