A New Class of Shrinkage-Type Nonparametric Tests for Multiple Hypothesis Testing
Date Issued
2004
Date
2004
Author(s)
Ho, Hung-Chi
DOI
en-US
Abstract
Microarrays are a novel technology that permits us to measure the expression levels of thousands of genes simultaneously. A typical microarray experiment provides few, if any, replicates of expression indexes for a specific gene, but the number of genes is, on the contrary, enormous, say 5,000-30,000.
The main task of such an experiment is primarily to identify a few significant genes, say 1%, among a huge number of nonsignificant ones, raising a critical challenge to classical view of statistical inference. This identification process can be put in the framework of multiple testing problem. If R denotes the number of genes declared significant and V the number of falsely significant genes, then one of the major error rate quantities commonly used in multiple hypothesis testing is the positive false discovery rate (pFDR), defined as pFDR = E[V/R|R > 0]. On the other hand, the discovery rate (DR) is defined as the probability that a gene is declared significant. Under some regularity conditions, we provide a result for multiple hypothesis testing which is in the spirit of Neyman-Pearson Lemma; that is, a likelihood ratio test attains the maximum DR among all tests of pFDR less than or equal to that of this likelihood ratio test. The result is presented as Theorem 2 in Section 7. Bearing Theorem 2 in mind, an optimal route of data reduction is taken as a successful attempt in the process of achieving the same performance as a likelihood ratio test. While traditional methods of data reduction using means or t-statistics are generally unsatisfactory in the context of microarray experiments, strong model-based methods of analyzing microarray data are also too restricted. Therefore, we turn to nonparametric methods and present a modified version of the traditional sign test, the modified sign test (MST), as the dominant tone of this thesis and then extend its concept to obtain the modified Wilcoxon signed rank test (MWT).
Subjects
positive false discovery rate
shrinkage
multiple hypothesis testing
Type
thesis
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