  Testing of the disjunction hypothesis is appropriate when each gene or
location studied is associated with multiple $p$-values, each of which is of
individual interest. This can occur when more than one aspect of an underlying
process is measured. For example, cancer researchers may hope to detect genes
that are both differentially expressed on a transcriptomic level and show
evidence of copy number aberration. Currently used methods of $p$-value
combination for this setting are overly conservative, resulting in very low
power for detection. In this work, we introduce a method to test the
disjunction hypothesis by using cumulative areas from the Voronoi diagram of
two-dimensional vectors of $p$-values. Our method offers much improved power
over existing methods, even in challenging situations, while maintaining
appropriate error control. We apply the approach to data from two published
studies: the first aims to detect periodic genes of the organism
Schizosaccharomyces pombe, and the second aims to identify genes associated
with prostate cancer.
