Sequential prediction bounds for identifying differentially expressed genes in replicated microarray experiments

Microarrays are new biotechnological devices that permit the simultaneous evaluation of expression levels of thousands of genes in one or more tissue samples. We develop a new method for identifying differentially expressed genes in replicated cDNA and oligonucleotide microarray experiments. The method is based on a nonparametric prediction interval which is computed as an order statistic of n control measurements and is applied sequentially to a series of p replicate sets of experimental measurements, each of size ni. We illustrate how reasonable experiment-wise false positive and false negative rates can be attained for any practical number of genes based on manipulating the order statistics, n, p and ni. The method is used to identify gene expression levels that are associated with a pathological condition beyond chance expectations given the large number of genes tested. We illustrate use of the method on replicated gene expression data in tumor and normal colon tissues, and compare it to an alternative approach based on permutation tests.