Exploratory analysis of multiple omics datasets using the adjusted RV coefficient

The integration of multiple high-dimensional data sets (omics data) has been a very active but challenging area of bioinformatics research in recent years. Various adaptations of non-standard multivariate statistical tools have been suggested that allow to analyze and visualize such data sets simultaneously. However, these methods typically can deal with two data sets only, whereas systems biology experiments often generate larger numbers of high-dimensional data sets. For this reason, we suggest an explorative analysis of similarity between data sets as an initial analysis steps. This analysis is based on the RV coefficient, a matrix correlation, that can be interpreted as a generalization of the squared correlation from two single variables to two sets of variables. It has been shown before however that the high-dimensionality of the data introduces substantial bias to the RV. We therefore introduce an alternative version, the adjusted RV, which is unbiased in the case of independent data sets. We can also show that in many situations, particularly for very high-dimensional data sets, the adjusted RV is a better estimator than previously RV versions in terms of the mean square error and the power of the independence test based on it. We demonstrate the usefulness of the adjusted RV by applying it to data set of 19 different multivariate data sets from a systems biology experiment. The pairwise RV values between the data sets define a similarity matrix that we can use as an input to a hierarchical clustering or a multidimensional scaling. We show that this reveals biological meaningful subgroups of data sets in our study.