Highlighting Relationships Between Heterogeneous Biological Data Through Graphical Displays Based on Regularized Canonical Correlation Analysis

Abstract

Biological data produced by high throughput technologies are becoming more and more abundant and are arousing many statistical questions. This paper addresses one of them; when gene expression data are jointly observed with other variables with the purpose of highlighting significant relationships between gene expression and these other variables. One relevant statistical method to explore these relationships is Canonical Correlation Analysis (CCA). Unfortunately, in the context of postgenomic data, the number of variables (gene expressions) is usually greater than the number of units (samples) and CCA cannot be directly performed: a regularized version is required. We applied regularized CCA on data sets from two different studies and show that its interpretation evidences both previously validated relationships and new hypothesis. From the first data sets (nutrigenomic study), we generated interesting hypothesis on the transcription factor pathways potentially linking hepatic fatty acids and gene expression. From the second data sets (pharmacogenomic study on the NCI-60 cancer cell line panel), we identified new ABC transporter candidate substrates which relevancy is illustrated by the concomitant identification of several known substrates. In conclusion, the use of regularized CCA is likely to be relevant to a number and a variety of biological experiments involving the generation of high throughput data. We demonstrated here its ability to enhance the range of relevant conclusions that can be drawn from these relatively expensive experiments.

Gene-Metabolite Expression in Blood Can Discriminate Allergen-Induced Isolated Early from Dual Asthmatic Responses

“…Age and sex have been adjusted for in all comparisons (discovery and validation). Regularized Canonical Correlation Analysis (RCCA), an extension of CCA [38], highlights the correlation between two data sets where the number of variables (genes/metabolites) is much larger than the sample size (see Section 3 in [39]). RCCA in the mixOmics package was used in order to identify highly correlated clusters of differentially expressed genes and metabolites in ERs and DRs, respectively.…”

Visualising associations between paired ‘omics’ data sets

“…Such methodologies include regularized and sparse variants of Canonical Correlation Analysis (CCA) [1-5] and Partial Least Squares (PLS) regression [6,7] - also referred as projection-based methods . These multivariate approaches aim at unravelling the correlation structure between two sets of data measured on the same samples.…”

“…In this article, we propose to revisit some graphical outputs mostly dedicated to exploratory approaches to highlight associations between two different types of biological entities. We have improved Correlation Circles plots, Relevance Networks and Clustered Image Maps (CIM) to be specifically adapted to the results of our previously published CCA or PLS methods [1,4,7]. These graphical outputs are implemented in the package a that is dedicated to the integrative analysis of ‘omics’ data [12].…”

“…Most importantly, the high dimensionality and the insufficient sample size lead to computational problems as CCA requires the computation of the inverse of the covariance matrices of X and Y . To circumvent this problem, regularized CCA (rCCA) has been recently proposed by [1] when dealing with ill-conditioned covariance matrices by adding a regularization term on their diagonal. Sparse PLS (sPLS) has been recently proposed to perform simultaneous variable selection in the two data sets [4,7].…”

“…These methodologies require to choose or tune the number of dimensions d , the regularization parameters for rCCA and the number of variables to select in both data sets for sPLS. Guidelines to choose these parameters are discussed in [1,7]. The biological relevancy of rCCA and sPLS has been recently demonstrated in several biological studies [13-18].…”