Testing the disjunction hypothesis using Voronoi diagrams with applications to genetics

Abstract

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.

Large-Scale Simultaneous Inference with Hypothesis Testing: Multiple Testing Procedures in Practice

“…In statistics, the field of multiple comparisons is currently very prolific resulting in a continuous stream of novel findings [76][77][78][79]. Unfortunately, this area is very technical making it difficult for the non-expert to follow.…”

Multiple testing approaches for hypotheses in integrative genomics

“…Ideally, for integrative genomics problems, it would be ideal to keep the correlation structure within the p value vector in order to account for the fact that platform measurements are correlated. The approach in Phillips and Ghosh (2014) does this. However, in the work of Chi (2008) makes the more restrictive assumption of the components of the p-vector being independent under the null.…”

Tessellation

“…Cell areas from the Voronoi diagram generated by these vectors of p ‐values take the place of univariate spacings in the original procedure, resulting in an approach that accounts for the two‐dimensional nature of these vectors. The procedure offers a gain in power over the existing method that simply collapses vectors of p ‐values into a single statistic based on the maximum p ‐value …”