Deborah Glueck
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Exact Power under Independence for the False Discovery Rate in Gene Expression Array Experiments

D. H. Glueck1, K. E. Muller2, A. Karimpour-Fard3 and L. Hunter4
1,3 Department of Preventive Medicine and Biometrics, University of Colorado Health Sciences Center, Denver, Colorado,80262, U. S. A. 
2 Department of Biostatistics, University of North Carolina, CB#7420, Chapel Hill, NC 27599-7420, U. S.A.
4 Department of Pharmacology, University of Colorado Health Sciences Center, Denver, Colorado,80262, U. S. A.

The false discovery rate is widely used for multiple comparison problems, including gene expression array studies. In that case, choosing the number of chips is an important but poorly treated problem. We have been unable to find published reports of analytic expressions for power and sample size for the false discovery rate. We derive the distribution of the total number of rejections, the number of false rejections conditioning on the total number of rejections, and the joint probability distribution of the number of total and false rejections. We demonstrate the results for independent but not identically distributed arbitrary distributions, and then describe the special case of independent and identically distributed distributions. Thus we provide methods for exact small sample power and sample size for gene expression array experiments, based on the common assumption of independence. The results also apply to any other use of false discovery rate which meets the same assumptions. Simulation studies are used to confirm the analytic results. An example is given for research on the genetic basis of breast cancer.


Graybill Conference
June 18-20, 2003
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Last Updated: Monday, April 21, 2003