  Motivation: Algorithms for differential analysis of microarray data are vital
to modern biomedical research. Their accuracy strongly depends on effective
treatment of inter-gene correlation. Correlation is ordinarily accounted for in
terms of its effect on significance cut-offs. In this paper it is shown that
correlation can, in fact, be exploited {to share information across tests},
which, in turn, can increase statistical power.
  Results: Vastly and demonstrably improved differential analysis approaches
are the result of combining identifiability (the fact that in most microarray
data sets, a large proportion of genes can be identified a priori as
non-differential) with optimization criteria that incorporate correlation. As a
special case, we develop a method which builds upon the widely used two-sample
t-statistic based approach and uses the Mahalanobis distance as an optimality
criterion. Results on the prostate cancer data of Singh et al. (2002) suggest
that the proposed method outperforms all published approaches in terms of
statistical power.
  Availability: The proposed algorithm is implemented in MATLAB and in R. The
software, called Tellipsoid, and relevant data sets are available at
http://www.egr.msu.edu/~desaikey
