Power and sample size calculation for microarray studies

Microarray is a technology to screen a large number of genes to discover those differentially expressed between clinical subtypes or different conditions of human diseases. Gene discovery using microarray data requires adjustment for the large-scale multiplicity of candidate genes. The family-wise error rate (FWER) has been widely chosen as a global type I error rate adjusting for the multiplicity. Typically in microarray data, the expression levels of different genes are correlated because of coexpressing genes and the common experimental conditions shared by the genes on each array. To accurately control the FWER, the statistical testing procedure should appropriately reflect the dependency among the genes. Permutation methods have been used for accurate control of the FWER in analyzing microarray data. It is important to calculate the required sample size at the design stage of a new (confirmatory) microarray study. Because of the high dimensionality and complexity of the correlation structure in microarray data, however, there have been no sample size calculation methods accurately reflecting the true correlation structure of real microarray data. We propose sample size and power calculation methods that are useful when pilot data are available to design a confirmatory experiment. If no pilot data are available, we recommend a two-stage sample size recalculation based on our proposed method using the first stage data as pilot data. The calculated sample sizes are shown to accurately maintain the power through simulations. A real data example is taken to illustrate the proposed method.