Artikel
Multiple test procedures based on a data-driven ordering of hypotheses with application to high-dimensional problems in gene expression analysis and association studies
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Autoren
Veröffentlicht: | 14. September 2004 |
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Gliederung
Text
Introduction
Modern experimental techniques in molecular biology/medicine or genetics allow the simultaneous analysis of an extremely high number of end-points. Examples hereof are the measurement of ten-thousands of genes using the micro-array technology or the multiple analysis of single nucleotide polymorphism (SNP) markers in genetic association studies.
To avoid false positive results in the statistical analysis (e.g. testing for differential gene expressions or detecting association of maker locus and disease phenotype) it is necessary to perform multiplicity adjustments of the test results. Classical adjustment methods (e.g. Bonferroni-Holm) are in most case far too conservative in these situations.
It could be shown that multiple test procedures, based on the theory of spherical distributions [Ref. 1], are able to improve the detection of significant results, still strictly keeping a given family wise type I error rate (FWE).
Methods
In the current work, these multiple procedures have been generalized for an application to a customized multivariate test of differential gene expression using the Affymetrix GeneChip® technology and for the analysis of multiple 2x2 contingence tables in genetic association studies.
With respect to the testing of differential gene expression we suggest the use of true multivariate information on expression intensities of individual genes analyzed by Affymetrix-type micro-arrays. In contrast to, firstly, construct an expression score, based on the different oligonucleotide (perfect- and mis-match) information and, secondly, perform a multiple test procedure, we suggest a multivariate test per gene, based on the complete perfect match information. The obtained P-values are analyzed according to multiple test procedures proposed by Kropf and Läuter [Ref. 2], or Westfall et al. [Ref. 3], using a data driven ordering of hypotheses.
Regarding the analysis of multiple 2x2 tables, it is proposed to apply individual exact Fisher tests using a hypothesis ordering based on the empirical marginal proportions.
Results
We show that the application of the multiple test procedures in both settings are able to keep a given FWE under each combination of true and false local hypotheses.
Furthermore, illustrated by examples on testing differential gene expression of tumor and healthy tissues within identical patients (dependent observations), between two groups of different patients (independent observations), and for testing of genetic association in a case control study, we could demonstrate an advantage of the proposed procedures with respect to the detection of significant effects compared to classical test strategies.
References
- 1.
- Läuter J, Glimm E, and Kropf S. Multivariate Tests Based on Left-Spherically Distributed Linear Scores. Annals of Statistics 1998; 26: 1972-1988
- 2.
- Kropf S and Läuter J. Multiple Tests of Different Sets of Variables Using Data-Driven Ordering of Hypotheses, with an Application to Gene Expression Data. Biometrical Journal 2002; 44 (7): 789-800
- 3.
- Westfall PH, Kropf S, and Finos L. Weighted FWE-controlling methods in high-dimensional situations. In: Benjamini Y, Bretz F, Sarkar SK (eds) Recent Developments in Multiple Comparison Procedures. IML Lecture Notes and Monograph series.2004 (accepted).