Sequential shrinkage estimation of variances in microarray data
by
Andrea Volodin
University of Regina, Sask., Canada
Coauthors: Abdulkadir Hussein

In detecting differentially expressed genes in microarray data, investigators usually deal with a large number of genes and small sample sizes for each gene due to the high cost of microarray plates. The homogeneity of variances across genes is desirable but uncertain, for if they were homogenous then one could pool their estimators to gain power. However, the small samples available do not allow verification of the hypothesis. Therefore, the problem is "to pool or not to pool" with "an eye on the cost per sample point (microarray)". Recently, (Cui et al. 2005) proposed James-Stein-type shrinkage estimator to do the first part of the problem. We are proposing here to use the estimator of (Cui et al. 2005) in a sequential fashion with a stopping rule obtained by minimizing a loss function of the form L + cn, accounting for the cost per microarray, where L could be either

quadratic or Stein (enthropy) loss function. Hence, one would borrow information across genes and at the same time would reduce the sample size required per gene.

Date received: February 18, 2007