Sample Size Estimation while Controlling False Discovery Rate for Microarray Experiments Using the ssize.fdr Package

Abstract

Microarray experiments are becoming more and more popular and critical in many biological disciplines. As in any statistical experiment, appropriate experimental design is essential for reliable statistical inference, and sample size has a crucial role in experimental design. Because microarray experiments are rather costly, it is important to have an adequate sample size that will achieve a desired power without wasting resources. For a given microarray data set, thousands of hypotheses, one for each gene, are simultaneously tested. Storey and Tibshirani (2003) argue that controlling false discovery rate (FDR) is more reasonable and more powerful than controlling family-wise error rate (FWER) in genomic data. However, the most common procedure used to calculate sample size involves controlling FWER, not FDR. Liu and Hwang (2007) describe a method for a quick sample size calculation for microarray experiments while controlling FDR. In this paper, we introduce the R package ssize.fdr which implements the method proposed by Liu and Hwang (2007). This package can be applied for designing one-sample, two-sample, or multi-sample experiments. The practitioner defines the desired power, the level of FDR to control, the proportion of non-differentially expressed genes, as well as effect size and variance. More specifically, the effect size and variance can be set as fixed or random quantities coming from appropriate distributions. Based on user-defined parameters, this package creates plots of power vs. sample size. These plots allow for visualization of trade-offs between power and sample size, in addition to the changes between power and sample size when the user-defined quantities are modified. For more in-depth details and evaluation of this sample size calculation method, please refer to Liu and Hwang (2007).