Comments on the rank product method for analyzing replicated experiments

Abstract

Breitling et al. introduced a statistical technique, the rank product method, for detecting differentially regulated genes in replicated microarray experiments. The technique has achieved widespread acceptance and is now used more broadly, in such diverse fields as RNAi analysis, proteomics, and machine learning. In this note, we relate the rank product method to linear rank statistics and provide an alternative derivation of distribution theory attending the rank product method.

Figure 1

Probability plots of the empirical distributions of the transformed RP statistics, based on 10000 simulations, versus corresponding quantiles of the approximating gamma distributions. A. n=10000 genes, k=3 replicates. B. n=10000 genes, k=5 replicates. C. n=10000 genes, k=10 replicates. D. n=5000 genes, k=3 replicates. E. n=5000 genes, k=5 replicates. F. n=5000 genes, k=10 replicates. G. n=30000 genes, k=3 replicates. H. n=30000 genes, k=5 replicates. I. n=30000 genes, k=10 replicates. Points should form approximately a straight line along the diagonal; departures from this straight line indicate departures from the specified distribution. In each instance, the approximating gamma distribution has scale parameter 1, and shape parameter equal to the number of replicates.