Collaborative Research: New Directions for Research on Some Large-Scale Multiple Testing Problems

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The paradigm shift of hypothesis testing from single to multiple hypotheses, often large number of them, in statistical applications to modern scientific investigations, such as brain imaging, microarray analysis, astronomy, atmospheric science, drug discovery and many others, has generated tremendous upsurge of research in the field of large-scale multiple testing in the last one and half decades. Nevertheless, some fundamentally important theoretical as well as methodological issues arising in many of these investigations still remain to be fully addressed before developing the necessary statistical tools. For instance, in clinical pharmacogenomics involving multiple testing, methods controlling false discoveries are yet to be developed in non-asymptotic setting when these hypotheses are tested group sequentially which is often required in order to meet economical and ethical concerns, or when these hypotheses belong to tree-structured hierarchical families which often happens due to importance based ordering of different sets of hypotheses. Also, in many practical applications of multiple testing where the order in which the tests are to be performed is pre-specified or can be assessed based on available data, but the potential improvements of the existing FDR methodologies exploiting this pre-ordering are yet to be explored. The project seeks to develop new and innovative multiple testing methods tackling these outstanding and related issues by focusing on the following three broad areas of research: (i) group sequential multiple testing, (ii) fixed sequence multiple testing, and (iii) testing multiple families of hypotheses. The project covers a wide spectrum of important multiple testing problems statisticians face in many practical settings. These problems are new and pose several technical challenges, as the existing theory and methodologies on multiple testing controlling false discoveries need to be extended from the framework of single stage or single family to that of multiple stages or multiple families. The proposed research has the potential to open up the door for research on multiple testing in newer directions. It not only aims at advancing the theory of multiple testing but also pays special attention to applications of the developed theories. This project is expected to have a broad impact on the theory and practice of statistics. It aims at modernizing the field of statistics by advancing research in areas of importance in modern scientific experiments, and thus can benefit the society. For instance, the project can potentially pave the way for novel techniques to address statistical issues faced in modern drug discoveries and biomedical experiments. It would also benefit education through training of graduate students and incorporation of the developed methodologies in statistics courses. The results will be disseminated through presentations and discussions at national and international conferences, and visits to other institutions. The software to be developed under this project will be made available, free of charge, to the scientific community.