Nonparametric relevance-shifted multiple testing procedures for the analysis of high-dimensional multivariate data with small sample sizes
Creators: name: Frömke, C.
name: Hothorn, Ludwig A.
name: Kropf, S.
Publisher: name: London : BioMed Central Ltd.
Year: 2008
Subjects: subject: Familywise error rate
subject: Location parameters
subject: Multiple testing problems
subject: Multivariate data
subject: Parameter spaces
subject: Second procedures
subject: Several variables
subject: Small Sample Size
subject: Algorithms
subject: Statistical tests
subject: analytical error
subject: article
subject: data analysis
subject: mathematical analysis
subject: mathematical computing
subject: medical research
subject: methodology
subject: microarray analysis
subject: multivariate analysis
subject: nonparametric test
subject: null hypothesis
subject: rank sum test
subject: sample size
subject: simulation
subject: statistical significance
subject: algorithm
subject: biological model
subject: computer simulation
subject: DNA microarray
subject: gene expression profiling
subject: signal processing
subject: statistical analysis
subject: statistical model
subject: Computer Simulation
subject: Data Interpretation, Statistical
subject: Gene Expression Profiling
subject: Models, Biological
subject: Models, Statistical
subject: Multivariate Analysis
subject: Oligonucleotide Array Sequence Analysis
subject: Sample Size
subject: Signal Processing, Computer-Assisted
subject: Dewey Decimal Classification::500 | Naturwissenschaften
subject: Dewey Decimal Classification::500 | Naturwissenschaften::570 | Biowissenschaften, Biologie

description: Background: In many research areas it is necessary to find differences between treatment groups with several variables. For example, studies of microarray data seek to find a significant difference in location parameters from zero or one for ratios thereof for each variable. However, in some studies a significant deviation of the difference in locations from zero (or 1 in terms of the ratio) is biologically meaningless. A relevant difference or ratio is sought in such cases. Results: This article addresses the use of relevance-shifted tests on ratios for a multivariate parallel two-sample group design. Two empirical procedures are proposed which embed the relevance-shifted test on ratios. As both procedures test a hypothesis for each variable, the resulting multiple testing problem has to be considered. Hence, the procedures include a multiplicity correction. Both procedures are extensions of available procedures for point null hypotheses achieving exact control of the familywise error rate. Whereas the shift of the null hypothesis alone would give straight-forward solutions, the problems that are the reason for the empirical considerations discussed here arise by the fact that the shift is considered in both directions and the whole parameter space in between these two limits has to be accepted as null hypothesis. Conclusion: The first algorithm to be discussed uses a permutation algorithm, and is appropriate for designs with a moderately large number of observations. However, many experiments have limited sample sizes. Then the second procedure might be more appropriate, where multiplicity is corrected according to a concept of data-driven order of hypotheses.