Originally published as Genetics Published Articles Ahead of Print on October 3, 2005.

Genetics, Vol. 172, 687-691, January 2006, Copyright © 2006
doi:10.1534/genetics.105.049536

On the Sample Size Requirement in Genetic Association Tests When the Proportion of False Positives Is Controlled

Guohua Zou^*, and Yijun Zuo^*,1

^* Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824 and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China

¹ Corresponding author: Department of Statistics and Probability, Michigan State University, A440 Wells Hall, East Lansing, MI 48824.
E-mail: zuo{at}msu.edu

With respect to the multiple-tests problem, recently an increasing amount of attention has been paid to control the false discovery rate (FDR), the positive false discovery rate (pFDR), and the proportion of false positives (PFP). The new approaches are generally believed to be more powerful than the classical Bonferroni one. This article focuses on the PFP approach. It demonstrates via examples in genetic association studies that the Bonferroni procedure can be more powerful than the PFP-control one and also shows the intrinsic connection between controlling the PFP and controlling the overall type I error rate. Since controlling the PFP does not necessarily lead to a desired power level, this article addresses the design issue and recommends the sample sizes that can attain the desired power levels when the PFP is controlled. The results in this article also provide rough guidance for the sample sizes to achieve the desired power levels when the FDR and especially the pFDR are controlled.

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