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Due to rapid technological advances, a wide range of different measurementscan be obtained from a given biological sample including single nucleotidepolymorphisms, copy number variation, gene expression levels, DNA methylationand proteomic profiles. Each of these distinct measurements provides the meansto characterize a certain aspect of biological diversity, and a fundamentalproblem of broad interest concerns the discovery of shared patterns ofvariation across different data types. Such data types are heterogeneous in thesense that they represent measurements taken at very different scales ordescribed by very different data structures. We propose a distance-basedstatistical test, the generalized RV (GRV) test, to assess whether there is acommon and non-random pattern of variability between paired biologicalmeasurements obtained from the same random sample. The measurements enter thetest through distance measures which can be chosen to capture particularaspects of the data. An approximate null distribution is proposed to computep-values in closed-form and without the need to perform costly Monte Carlopermutation procedures. Compared to the classical Mantel test for associationbetween distance matrices, the GRV test has been found to be more powerful in anumber of simulation settings. We also report on an application of the GRV testto detect biological pathways in which genetic variability is associated tovariation in gene expression levels in ovarian cancer samples, and presentresults obtained from two independent cohorts.

A Distance-Based Test of Association Between Paired Heterogeneous Genomic Data