Accurate differential analysis of microarray data strongly depends on effective treatment of intergene correlation. Such dependence is ordinarily accounted for in terms of its effect on significance cutoffs. In this paper, it is shown that correlation can, in fact, be exploited to share information across tests and reorder expression differentials for increased statistical power, regardless of the threshold. Significantly improved differential analysis is the result of two simple measures: (i) adjusting test statistics to exploit information from identifiable genes (the large subset of genes represented on a microarray that can be classified a priori as nondifferential with very high confidence], but (ii) doing so in a way that accounts for linear dependencies among identifiable and nonidentifiable genes. A method is developed that builds upon the widely used two-sample t-statistic approach and uses analysis in Hilbert space to decompose the nonidentified gene vector into two components that are correlated and uncorrelated with the identified set. In the application to data derived from a widely studied prostate cancer database, the proposed method outperforms some of the most highly regarded approaches published to date. Algorithms in MATLAB and in R are available for public download. 1. Preamble In certain ways, this paper represents a departure from current trends in scientific publishing. The Worldwide Web has made available extraordinary resources in the form of databases for comparative analysis of methods in bioinformatics and numerous other disciplines. The benefits of using common sets of real data to compare and contrast new algorithms are obvious. In some fields of investigation, especially, perhaps, research in early states of knowledge (e.g., genomics), there is an equally obvious drawback in using real data—that the “correct answers are not known,” making it difficult to ultimately interpret differences in performance as anything but differences. Lest the reader be preparing for an argument promoting classic simulation studies, we hasten to state at the outset that this argument is not forthcoming. Before the age of the internet, simulation studies using reasonably justified data models (Gaussian errors, etc.) were a time-honored standard in all areas of math, science, and engineering. The ready availability of rich data resources makes it irrational to advocate to a return to “pure simulation” using models that are untested against these existing data sets. The authors of this paper in no way promote a return to such methods and appeal to
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