Motivation: Analysis of variance (ANOVA)-type methods are the default tool for the analysis of data with multiple covariates. These tools have been generalized to the multivariate analysis of high-throughput biological datasets, where the main challenge is the problem of small sample size and high dimensionality. However, the existing multi-way analysis methods are not designed for the currently increasingly important experiments where data is obtained from multiple sources. Common examples of such settings include integrated analysis of metabolic and gene expression profiles, or metabolic profiles from several tissues in our case, in a controlled multi-way experimental setup where disease status, medical treatment, gender and time-series are usual covariates.
Results: We extend the applicability area of multivariate, multi-way ANOVA-type methods to multi-source cases by introducing a novel Bayesian model. The method is capable of finding covariate-related dependencies between the sources. It assumes the measurements consist of groups of similarly behaving variables, and estimates the multivariate covariate effects and their interaction effects for the discovered groups of variables. In particular, the method partitions the effects to those shared between the sources and to source-specific ones. The method is specifically designed for datasets with small sample sizes and high dimensionality. We apply the method to a lipidomics dataset from a lung cancer study with two-way experimental setup, where measurements from several tissues with mostly distinct lipids have been taken. The method is also directly applicable to gene expression and proteomics.
Availability: An R-implementation is available at http://www.cis.hut.fi/projects/mi/software/multiWayCCA/.