We have been working on permutational multiple testing with multivariate multiple group data. This problem is compounded by two types of multiplicity, and requires different types of permutational approaches for different hypotheses. It is shown that under a certain multivariate assumption, it is possible to use full closure over all of the hypotheses. A shortcut test is found, which results in a procedure with improved power over existing procedures. A manuscript is currently under review. This methodology will be useful in the analysis of genetic association studies with large numbers of SNPs under study and several types of hypotheses of interest (case-control, mother-control, triad). Another project is focused on methods to compare several different classifiers. Often in clinical research, one constructs a classifier for some condition or disease based on easily observable covariates. There could be several ways to construct a classifier of the condition. The problem is to compare the correct classification rate of each pair of classifiers. We are currently writing a paper on methodology to do this while controlling the familywise error rate.

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Westfall, Peter H; Troendle, James F (2008) Multiple testing with minimal assumptions. Biom J 50:745-55