Sample Size Calculation for Microarray Experiments

Abstract

Before conducting a microarray experiment, one important issue that needs to be decided is the number of arrays required in order for the results to be statistically interpretable. Microarray experiments often involve screening of hundreds or thousands of genes; in a typical experiment, only a fraction of genes is expected to be differentially expressed. In addition, the measured intensities among different genes may be correlated. Since a large number of tests are made, sample size calculation must take into account the multiple testing problem. Depending on the experimental objectives, sample size calculations can be based on one of the three specified measures for identification: sensitivity, true discovery, and accuracy rates. Here we formulate the sample size problem as: the number of arrays needed in order to achieve the desired fraction of the specified measure e.g., sensitivity, at the desired family-wise power at the given type I error and (standardized) effect size. We present a general approach for estimating sample size under the independent and equally- correlated models using the binomial and beta-binomial models, respectively. Sample size needed for two-sample z-test is computed; the computed theoretical numbers agree well with the results using the Monte Carlo simulation. The proposed approach is applicable to other tests such as two-sample t-test or k- sample ANOVA F-test.