Quick Calculation for Sample Size while Controlling False Discovery Rate with Application to Microarray Analysis
Sample size estimation is important in microarray or proteomic experiments since biologists can typically afford only a few repetitions. In the multiple testing problems involving these experiments, it is more powerful and more reasonable to control false discovery rate (FDR) or positive FDR (pFDR) instead of type I error, e.g., family-wise error rate (FWER) (Storey and Tibshirani, 2003). However, the traditional approach of estimating sample size is no longer applicable to controlling FDR, which has left most practitioners to rely on haphazard guessing. We propose a procedure to calculate sample size while controlling false discovery rate. Two major definitions of the false discovery rate (FDR in Benjamini and Hochberg, 1995, and pFDR in Storey, 2002) vary slightly. Our procedure applies to both definitions. The proposed method is straightforward to apply and requires minimal computation, as illustrated with two sample t-tests and F-tests. We have also demonstrated by simulation that, with the calculated sample size, the desired level of power is achievable by the q-value procedure (Storey, Taylor and Siegmund, 2004) when gene expressions are either independent or dependent.
This preprint was published as Peng Liu and J. T. Gene Hwang, "Quick calculation for sample size while controlling false discovery rate with application to microarray analysis", Bioinformatics (2007): 739-746, doi: 10.1093/bioinformatics/btl664