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Testing of the disjunction hypothesis is appropriate when each gene orlocation studied is associated with multiple $p$-values, each of which is ofindividual interest. This can occur when more than one aspect of an underlyingprocess is measured. For example, cancer researchers may hope to detect genesthat are both differentially expressed on a transcriptomic level and showevidence of copy number aberration. Currently used methods of $p$-valuecombination for this setting are overly conservative, resulting in very lowpower for detection. In this work, we introduce a method to test thedisjunction hypothesis by using cumulative areas from the Voronoi diagram oftwo-dimensional vectors of $p$-values. Our method offers much improved powerover existing methods, even in challenging situations, while maintainingappropriate error control. We apply the approach to data from two publishedstudies: the first aims to detect periodic genes of the organismSchizosaccharomyces pombe, and the second aims to identify genes associatedwith prostate cancer.

Testing the disjunction hypothesis using Voronoi diagrams with applications to genetics