Quick Calculation for Sample Size while Controlling False Discovery Rate with Application to Microarray Analysis

1 Summary. Sample size estimation is important in microarray or proteomic experiments since biologists can typically afford only a few repetitions. Classical procedures to calculate sample size are based on controlling type I error, e.g., family-wise error rate (FWER). In the context of microarray and other large-scale genomic data, it is more powerful and more reasonable to control false discovery rate (FDR) or positive FDR (pFDR)(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 However, the traditional approach of estimating sample size is no longer applicable to controlling FDR, which has left most practitioners to rely on haphazard guessing.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.