Multiple Testing: Further Development Of Theory And Methodology

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MULTIPLE TESTING: FURTHER DEVELOPMENT OF THEORY AND METHODOLOGY The primary goal of the investigator in this project is further development of statistical theory and methodology for problems in multiple hypothesis testing. Having realized that the traditional idea of controlling the familywise error rate (FWER) is too stringent to use when large number of hypotheses are tested, researchers have recently focused on defining less stringent error rates and developing methods that control them. The false discovery rate (FDR) is the first of these receiving considerable attention, even though there are still a number of important related issues that are yet to be answered. The probabilities of rejecting at least a number more than one and the false discovery proportion exceeding a certain threshold are the two most recently introduced concepts that generalize the FWER and represent meaningful alternatives to the FDR. While some methods controlling them have been suggested very recently, the potential to developing newer and more powerful procedures is revealed by some recent work by the investigator. The development of such new procedures and investigative studies comparing them to related methods, theoretically as well as empirically, will be one major thrust of the present research. When testing multiple null hypotheses against two-sided alternatives, making directional decisions for the alternative hypotheses corresponding to the rejected ones with a control of false directional rejections is often desired. While such a procedure has been recently put forward in the framework of the FDR, there is a good potential of developing newer procedures in light of some work of the investigator together with students and colleagues. The development of such new procedures will be the second major thrust of this research.The results from this research will be of importance to virtually any statistical investigation where questions are posed in terms of testing several hypotheses. One particular area of application is DNA microarrays which are a new and promising biotechnology that can monitor expression levels in cells for thousands of genes simultaneously. The identification of differentially expressed genes is an important and common question in these experiments. The biological question of differential expression is framed as a statistical problem of multiple hypotheses testing: the simultaneous test for each gene of the null hypothesis that the expression levels do not associate with the responses or covariates of interest. Developing a statistical procedure of discovering the genes that are differentially expressed by controlling statistical measures of false discoveries or false non-discoveries at a desired level is one of the central issues in such a problem. Another area of application is pharmaceutical investigations where multiple testing techniques are routinely used in dose-response study or in evaluating a drug's efficacy over a standard drug or placebo. This research has the potential to generate collaborations with researchers in the biopharmaceutical industry and medical schools. It would also benefit education through training of graduate students, incorporation of the developed methodologies in statistics courses, and writing textbooks.