Balancing false positives and false negatives for the detection of differential expression in malignancies

A basic problem of microarray data analysis is to identify genes whose expression is affected by the distinction between malignancies with different properties. These genes are said to be differentially expressed. Differential expression can be detected by selecting the genes with P-values (derived using an appropriate hypothesis test) below a certain rejection level. This selection, however, is not possible without accepting some false positives and negatives since the two sets of P-values, associated with the genes whose expression is and is not affected by the distinction between the different malignancies, overlap. We describe a procedure for the study of differential expression in microarray data based on receiver-operating characteristic curves. This approach can be useful to select a rejection level that balances the number of false positives and negatives and to assess the degree of overlap between the two sets of P-values. Since this degree of overlap characterises the balance that can be reached between the number of false positives and negatives, this quantity can be seen as a quality measure of microarray data with respect to the detection of differential expression. As an example, we apply our method to data sets studying acute leukaemia.