Evaluation of multiple variate selection methods from a biological perspective: a nutrigenomics case study

Genomics-based technologies produce large amounts of data. To interpret the results and identify the most important variates related to phenotypes of interest, various multivariate regression and variate selection methods are used. Although inspected for statistical performance, the relevance of multivariate models in interpreting biological data sets often remains elusive. We compare various multivariate regression and variate selection methods applied to a nutrigenomics data set in terms of performance, utility and biological interpretability. The studied data set comprised hepatic transcriptome (10,072 predictor variates) and plasma protein concentrations [2 dependent variates: Leptin (LEP) and Tissue inhibitor of metalloproteinase 1 (TIMP-1)] collected during a high-fat diet study in ApoE3Leiden mice. The multivariate regression methods used were: partial least squares "PLS"; a genetic algorithm-based multiple linear regression, "GA-MLR"; two least-angle shrinkage methods, "LASSO" and "ELASTIC NET"; and a variant of PLS that uses covariance-based variate selection, "CovProc." Two methods of ranking the genes for Gene Set Enrichment Analysis (GSEA) were also investigated: either by their correlation with the protein data or by the stability of the PLS regression coefficients. The regression methods performed similarly, with CovProc and GA performing the best and worst, respectively (R-squared values based on "double cross-validation" predictions of 0.762 and 0.451 for LEP; and 0.701 and 0.482 for TIMP-1). CovProc, LASSO and ELASTIC NET all produced parsimonious regression models and consistently identified small subsets of variates, with high commonality between the methods. Comparison of the gene ranking approaches found a high degree of agreement, with PLS-based ranking finding fewer significant gene sets. We recommend the use of CovProc for variate selection, in tandem with univariate methods, and the use of correlation-based ranking for GSEA-like pathway analysis methods.