  A two-groups mixed-effects model for the comparison of (normalized)
microarray data from two treatment groups is considered. Most competing
parametric methods that have appeared in the literature are obtained as special
cases or by minor modification of the proposed model. Approximate maximum
likelihood fitting is accomplished via a fast and scalable algorithm, which we
call LEMMA (Laplace approximated EM Microarray Analysis). The posterior odds of
treatment $\times$ gene interactions, derived from the model, involve shrinkage
estimates of both the interactions and of the gene specific error variances.
Genes are classified as being associated with treatment based on the posterior
odds and the local false discovery rate (f.d.r.) with a fixed cutoff. Our
model-based approach also allows one to declare the non-null status of a gene
by controlling the false discovery rate (FDR). It is shown in a detailed
simulation study that the approach outperforms well-known competitors. We also
apply the proposed methodology to two previously analyzed microarray examples.
Extensions of the proposed method to paired treatments and multiple treatments
are also discussed.
