Name: Kropf

Firstname: Siegfried

Title: Dr.

Institution: Otto von Guericke University, Institute for Biometry and Medical Informatics

Street: Leipziger Str. 44

City: Magdeburg

Zip-Code: D-39110

Country: Germany

Phone: +49-391-6713535

Fax: +49-391-6713536

Email: Siegfried.Kropf@medizin.uni-magdeburg.de

Authors: Kropf, Siegfried; Läuter, Jürgen; Eszlinger, Markus

Title: Multiple Comparisons with Gene Expression Arrays Using a Data Driven Ordering of Hypotheses

Abstract: Testing with a-priori ordered hypotheses and testing with alpha-adjustment are two well-known basic strategies for multiple comparison procedures. In the paper, a new strategy is proposed (Kropf, 2000, Kropf and Läuter, 2002), which derives an order of hypotheses (i.e., of genes) from the data in a first step and then carries out a sequential unadjusted testing in that order. The mathematical background is given by theorems for exact parametric multivariate tests (Läuter et al., 1998). The strategy can be adjusted for different statistical problems (one-sample problem, one-way layout, multifactorial designs, test for the quotient of expectations from two independent samples,...).

Further modifications and generalisations are directed towards the inclusion of sets of variables instead of single variables or modified order criteria for the hypotheses. We can also give a non-parametric counterpart of the procedure that is based on the independence of rank and order statistics for continuous data.

The procedures are demonstrated using data from patients with nodules in the thyroids. The expression values of 12,625 genes have been derived for 15 patients with so-called hot or cold nodules.

Results of simulation studies indicate that the new proposals have advantages compared to alternative procedures as Holm's procedure or resampling techniques (Westfall and Young, 1993, Dudoit et al., 2000) in small samples, which is a common situation in the analysis of gene expression data.

References: Dudoit, S., Yang, Y.H., Callow, M.J., and Speed, T.P., 2000: Statistical Methods for Identifying Differentially Expressed Genes in Replicated cDNA Microarray Experiments. Technical report # 578, Department of Biochemistry, Stanford University School of Medicine, Stanford, CA.

Kropf, S., 2000: High-dimensional multivariate Procedures in Medical Statistics (German: Hochdimensionale multivariate Verfahren in der medizinischen Statistik). Shaker Verlag, Aachen.

Kropf, S. and Läuter, J. 2002: Multiple Tests for Different Sets of Variables Using a Data-Driven Ordering of Hypotheses, with an Application to Gene Expression Data. Submitted to Biometrical Journal.

Läuter, J., Glimm, E., and Kropf, S., 1998: Multivariate Tests Based on Left-Spherically Distributed Linear Scores. Annals of Statistics 26, 1972-1988. Erratum: Annals of Statistics 27, 1441.

Westfall, P.H. and Young, S.S., 1993: Resampling-Based Multiple Testing. John Wiley & Sons, New York.