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The problems of large-scale multiple testing are often encountered in modernscientific researches. Conventional multiple testing procedures usually sufferconsiderable loss of testing efficiency due to the lack of consideration ofcorrelations among tests. In fact, the appropriate use of correlationinformation not only enhances the efficacy of multiple testing but alsoimproves the interpretability of the results. Since the disease- ortrait-related single nucleotide polymorphisms (SNPs) often tend to be clusteredand exhibit serial correlations, the hidden Markov model (HMM) based multipletesting procedure has been successfully applied in genome-wide associationstudies (GWAS). It is important to note that modeling the entire chromosomeusing one HMM is somewhat rough. To overcome this issue, this paper employs thehierarchical hidden Markov model (HHMM) to describe local correlations amongtests and develops a multiple testing procedure that can not only automaticallydivide different class of chromosome regions, but also takes into account localcorrelations among tests. Theoretically, it is shown that the proposed multipletesting procedure is valid and optimal in some sense. Then a data-drivenprocedure is developed to mimic the oracle version. Extensive simulations andthe real data analysis show that the novel multiple testing procedureoutperforms its competitors.

Multiple Testing in Genome-Wide Association Studies via Hierarchical Hidden Markov Models