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The family-wise error rate (FWER) has been widely used in genome-wideassociation studies. With the increasing availability of functional genomicsdata, it is possible to increase the detection power by leveraging thesegenomic functional annotations. Previous efforts to accommodate covariates inmultiple testing focus on the false discovery rate control whilecovariate-adaptive FWER-controlling procedures remain under-developed. Here wepropose a novel covariate-adaptive FWER-controlling procedure that incorporatesexternal covariates which are potentially informative of either the statisticalpower or the prior null probability. An efficient algorithm is developed toimplement the proposed method. We prove its asymptotic validity and obtain therate of convergence through a perturbation-type argument. Our numerical studiesshow that the new procedure is more powerful than competing methods andmaintains robustness across different settings. We apply the proposed approachto the UK Biobank data and analyze 27 traits with 9 million single-nucleotidepolymorphisms tested for associations. Seventy-five genomic annotations areused as covariates. Our approach detects more genome-wide significant loci thanother methods in 21 out of the 27 traits.

Covariate Adaptive Family-wise Error Rate Control for Genome-Wide Association Studies