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Designed gene expression micro-array experiments, consisting of severaltreatment levels with a number of replicates per level, are analyzed byapplying simple tests for group differences at the per gene level. The genelevel statistics are sorted and a criterion for selecting important genes whichtakes into account multiplicity is applied. A caveat arises in that truesignals (genes truly over or under expressed) are "competing" with fairly largetype I error signals. False positives near the top of a sorted list can occurwhen genes having very small fold-change are compensated by small enoughvariance to yield a large test statistic. One of the first attempts around thiscaveat as the development of "significance analysis of micro-arrays (SAM)",which used a modified t-type statistic thresholded against its permutationdistribution. The key innovation of the modified t-statistic was the additionof a constant to the per gene standard errors in order to stabilize thecoefficient of variation of the resulting test statistic. Since then, severalauthors have proposed the use of shrinkage variance estimators in conjunctionwith t-type, and more generally, ANOVA type tests at the gene level. Our newapproach proposes the use of a shrinkage variance Hotelling T-squared statisticin which the per gene sample covariance matrix is replaced by a shrinkageestimate borrowing strength from across all genes. It is demonstrated that thenew statistic retains the F-distribution under the null, with added degrees offreedom in the denominator. Advantages of this class of tests are (i)flexibility in that a whole family of hypothesis tests is possible (ii) thegains of the above-mentioned earlier innovations are enjoyed more fully. Thispaper summarizes our results and presents a simulation study benchmarking thenew statistic against another recently proposed statistic.

The Shrinkage Variance Hotelling $T^2$ Test for Genomic Profiling Studies