Mann-Whitney Type Tests for Microarray Experiments: TheRPackagegMWT

Abstract

We present the R package gMWT which is designed for the comparison of several treatments (or groups) for a large number of variables. The comparisons are made using certain probabilistic indices (PI). The PIs computed here tell how often pairs or triples of observations coming from different groups appear in a specific order of magnitude. Classical two and several sample rank test statistics such as the Mann-Whitney-Wilcoxon, Kruskal-Wallis, or Jonckheere-Terpstra test statistics are simple functions of these PI. Also new test statistics for directional alternatives are provided. The package gMWT can be used to calculate the variable-wise PI estimates, to illustrate their multivariate distribution and mutual dependence with joint scatterplot matrices, and to construct several classical and new rank tests based on the PIs. The aim of the paper is first to briefly explain the theory that is necessary to understand the behavior of the estimated PIs and the rank tests based on them. Second, the use of the package is described and illustrated with simulated and real data examples. It is stressed that the package provides a new flexible toolbox to analyze large gene or microRNA expression data sets, collected on microarrays or by other high-throughput technologies. The testing procedures can be used in an eQTL analysis, for example, as implemented in the package GeneticTools.

Rumen Microbiota Predicts Feed Efficiency of Primiparous Nordic Red Dairy Cows

“…Highly abundant genes were determined by applying a trimmed mean of M-values normalization (TMM) to the data and filtering out genes with a total sum of standardized values smaller than the 95% quantile across the total sum of all abundances. In total, 1.2 MM filtered genes were evaluated for differential abundances using a generalized Mann–Whitney test for directional alternatives as described by Fischer et al [ 70 ] and implemented in the R-package gMWT [ 71 ]. Let , , and be the cumulative distribution functions of abundances for a specific gene (double index omitted for simplicity) for the groups L-, M-, and H-REI, then, the underlying directional testing problem is vs. and with being the stochastic ordering that is not equal for at least one comparison.…”

MiRNA Profiles in Lymphoblastoid Cell Lines of Finnish Prostate Cancer Families

“…A new generalisation of Mann-Whitney type tests was applied to identify differentially expressed probes in the three-group comparison. The same generalisation was used for the eQTL analysis (for details see [ 15 ] and [ 16 ]).…”

“…Test results with p-value less than 0.01 were considered to be significant. The test method is implemented in the R-package gMWT [ 16 ], and the package GeneticTools exploits this test method for eQTL testing. Both packages are freely available from the Comprehensive R Archive Network (CRAN).…”

“… Independent of the health status of each individual, the expression values are grouped according to the genotype groups of the surrounding SNPs and then tested for differential expression between those groups. (Figure taken from [ 16 ]) …”

Rank-Based Procedures in Factorial Designs: Hypotheses About Non-Parametric Treatment Effects

“…The obviously appealing property that this estimator is obtained from the ranks of the observations mainly contributed to the popularity of the test based on it, the so-called Wilcoxon-Mann-Whitney test. Moreover, as pointed out by Acion et al (2006), the intuitive quantity w has several desirable and meaningful properties as a reasonable effect for the description of the treatment and is widely accepted in practice, see e.g., Brumback et al (2006), Kieser et al (2013), De Neve et al (2014, Fischer et al (2014), Fischer and Oja (2015) and Vermeulen et al (2015). In addition, this effect is used for assessing the accuracy of diagnostic tests in medicine since it is equal to the area under the receiver operating characteristic (ROC)-curve, see Bamber (1975) and in factorial diagnostic designs see, e.g., Kaufmann et al (2005), Lange (2008), Brunner and Zapf (2013), and Zapf et al (2016).…”