  The detection of differentially expressed (DE) genes is one of the most
commonly studied problems in bioinformatics. For example, the identification of
DE genes between distinct disease phenotypes is an important first step in
understanding and developing treatment drugs for the disease. It can also
contribute significantly to the construction of a discriminant rule for
predicting the class of origin of an unclassified tissue sample from a patient.
We present a novel approach to the problem of detecting DE genes that is based
on a test statistic formed as a weighted (normalized) cluster-specific contrast
in the mixed effects of the mixture model used in the first instance to cluster
the gene profiles into a manageable number of clusters. The key factor in the
formation of our test statistic is the use of gene-specific mixed effects in
the cluster-specific contrast. It thus means that the (soft) assignment of a
given gene to a cluster is not crucial. This is because in addition to class
differences between the (estimated) fixed effects terms for a cluster,
gene-specific class differences also contribute to the cluster-specific
contributions to the final form of the test statistic. The proposed test
statistic can be used where the primary aim is to rank the genes in order of
evidence against the null hypothesis of no DE. We also show how a P-value can
be calculated for each gene for use in multiple hypothesis testing where the
intent is to control the false discovery rate (FDR) at some desired level. With
the use of real and simulated data sets, we show that the proposed
contrast-based approach outperforms other methods commonly used for the
detection of DE genes both in a ranking context with lower proportion of false
discoveries and in a multiple hypothesis testing context with higher power for
a specified level of the FDR.
