MOTIVATION: Due to rapid technological advances, a wide range of different measurements can be obtained from a given biological sample including single nucleotide polymorphisms, copy number variation, gene expression levels, DNA methylation and proteomic profiles. Each of these distinct measurements provides the means to characterize a certain aspect of biological diversity, and a fundamental problem of broad interest concerns the discovery of shared patterns of variation across different data types. Such data types are heterogeneous in the sense that they represent measurements taken at different scales or represented by different data structures. RESULTS: We propose a distance-based statistical test, the generalized RV (GRV) test, to assess whether there is a common and non-random pattern of variability between paired biological measurements obtained from the same random sample. The measurements enter the test through the use of two distance measures, which can be chosen to capture a particular aspect of the data. An approximate null distribution is proposed to compute P-values in closed-form and without the need to perform costly Monte Carlo permutation procedures. Compared with the classical Mantel test for association between distance matrices, the GRV test has been found to be more powerful in a number of simulation settings. We also demonstrate how the GRV test can be used to detect biological pathways in which genetic variability is associated to variation in gene expression levels in an ovarian cancer sample, and present results obtained from two independent cohorts. AVAILABILITY: R code to compute the GRV test is freely available from http://www2.imperial.ac.uk/∼gmontana

MOTIVATION: Time course gene expression experiments are performed to study time-varying changes in mRNA levels of thousands of genes. Statistical methods from functional data analysis (FDA) have recently gained popularity for modelling and exploring such time courses. Each temporal profile is treated as the realization of a smooth function of time, or curve, and the inferred curve becomes the basic unit of statistical analysis. The task of identifying genes with differential temporal profiles then consists of detecting statistically significant differences between curves, where such differences are commonly quantified by computing the area between the curves or the l₂ distance. RESULTS: We propose a general test statistic for detecting differences between gene curves, which only depends on a suitably chosen distance measure between them. The test makes use of a distance-based variance decomposition and generalizes traditional MANOVA tests commonly used for vectorial observations. We also introduce the visual l₂ distance, which is shown to capture shape-related differences in gene curves and is robust against time shifts, which would otherwise inflate the traditional l₂ distance. Other shape-related distances, such as the curvature, may carry biological significance. We have assessed the comparative performance of the test on realistically simulated datasets and applied it to human immune cell responses to bacterial infection over time.