Statistical design of reverse dye microarrays

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.