MOTIVATION: In microarray experiments investigators sometimes wish to pool RNA samples before labeling and hybridization due to insufficient RNA from each individual sample or to reduce the number of arrays for the purpose of saving cost. The basic assumption of pooling is that the expression of an mRNA molecule in the pool is close to the average expression from individual samples. Recently, a method for studying the effect of pooling mRNA on statistical power in detecting differentially expressed genes between classes has been proposed, but the different sources of variation arising in microarray experiments were not distinguished. Another paper recently did take different sources of variation into account, but did not address power and sample size for class comparison. In this paper, we study the implication of pooling in detecting differential gene expression taking into account different sources of variation and check the basic assumption of pooling using data from both the cDNA and Affymetrix GeneChip microarray experiments. RESULTS: We present formulas for the required number of subjects and arrays to achieve a desired power at a specified significance level. We show that due to the loss of degrees of freedom for a pooled design, a large increase in the number of subjects may be required to achieve a power comparable to that of a non-pooled design. The added expense of additional samples for the pooled design may outweigh the benefit of saving on microarray cost. The microarray data from both platforms show that the major assumption of pooling may not hold. SUPPLEMENTARY INFORMATION: Supplementary material referenced in the text is available at http://linus.nci.nih.gov/brb/TechReport.htm.

MOTIVATION: In cDNA microarray experiments all samples are labelled with either Cy3 dye or Cy5 dye. Certain genes exhibit dye bias-a tendency to bind more efficiently to one of the dyes. The common reference design avoids the problem of dye bias by running all arrays 'forward', so that the samples being compared are always labelled with the same dye. But comparison of samples labelled with different dyes is sometimes of interest. In these situations, it is necessary to run some arrays 'reverse'-with the dye labelling reversed-in order to correct for the dye bias. The design of these experiments will impact one's ability to identify genes that are differentially expressed in different tissues or conditions. We address the design issue of how many specimens are needed, how many forward and reverse labelled arrays to perform, and how to optimally assign Cy3 and Cy5 labels to the specimens. RESULTS: We consider three types of experiments for which some reverse labelling is needed: paired samples, samples from two predefined groups, and reference design data when comparison with the reference is of interest. We present simple probability models for the data, derive optimal estimators for relative gene expression, and compare the efficiency of the estimators for a range of designs. In each case, we present the optimal design and sample size formulas. We show that reverse labelling of individual arrays is generally not required.