Thresholding rules for recovering a sparse signal from microarray experiments

We consider array experiments that compare expression levels of a high number of genes in two cell lines with few repetitions and with no subject effect. We develop a statistical model that illustrates under which assumptions thresholding is optimal in the analysis of such microarray data. The results of our model explain the success of the empirical rule of two-fold change. We illustrate a thresholding procedure that is adaptive to the noise level of the experiment, the amount of genes analyzed, and the amount of genes that truly change expression level. This procedure, in a world of perfect knowledge on noise distribution, would allow reconstruction of a sparse signal, minimizing the false discovery rate. Given the amount of information actually available, the thresholding rule described provides a reasonable estimator for the change in expression of any gene in two compared cell lines.