Name: Hsueh

Firstname: Hueymiin

Title: Assistant Professor

Institution: National ChengChi University, Division of Statistics

Street: Chih-Nan Road, Section 2,

City: Taipei

Zip-Code: 11623

Country: Taiwan

Phone: 886-2-29393091-ext 81138

Fax: 886-2-29398024

Email: hsueh@nccu.edu.tw

Authors: James J. Chen and Hueymiin Hsueh

Title: Estimating the number of true null hypotheses in multiple testing problems

Abstract: A microarray experiment often involves comparisons of hundreds or thousands genes simultanuously. To control the overall Type I error rate or familywise error rate (FWE), a number of multiple comparison procedures (MCP) have been proposed. Benjamini and Hochberg (1995) suggested controlling the false discovery rate (FDR) as an alternative to control the FWE. However, the definition of the FDR was controvertible and the calculation of the FDR depends on the total number of true null hypotheses. We propose an applicable method to estimate the number of true null hypotheses. Simulation studies show that our estimation gives better performance than the graphical method proposed by Schweder and Spjotvoll (1982). Using the estimate in the Bonerroin-type FWE approach, the induced procedure is shown to have greater power and well-controlled FWE empirically. The formulas for several FDRs are given explicitly. A real microarray data set is given as an example to demonstrate the estimating procedure.

References: 1. Benjamini, Y. and Hochberg, Y.(1995) Controlling the False Discovery Rate : a Practical and Powerful Approach to Multiple Testing. J. R. Statist. Soc. B, 57, 289-300. 2.Schweder, T. and Spjotvoll, E. (1982) Plots of P-values to Evaluate Many Tests Simultaneously. Biometrika, 69, 493-502.