  Equivalence testing is of emerging importance in genomics studies but has
hitherto been little studied in this content. In this paper, we define the
notion of equivalence of gene expression and determine a `strength of evidence'
measure for gene equivalence. It is common practice in genome-wide studies to
rank genes according to observed gene-specific P-values or adjusted P-values,
which are assumed to measure the strength of evidence against the null
hypothesis of no differential gene expression. We show here, both empirically
and formally, that the equivalence P-value does not satisfy the basic
consistency requirements for a valid strength of evidence measure for
equivalence. This means that the widely-used q-value (Storey, 2002) defined for
each gene to be the minimum positive false discovery rate that would result in
the inclusion of the corresponding P-value in the discovery set, cannot be
translated to the equivalence testing framework. However, when represented as a
posterior probability, we find that the q-value does satisfy some basic
consistency requirements needed to be a credible measure of evidence for
equivalence. We propose a simple estimate for the q-value from posterior
probabilities of equivalence, and analyse data from a mouse stem cell
microarray experiment which demonstrate the theory and methods presented here.
