PLS-ROG: Partial least squares with rank order of groups

Abstract

Partial least squares (PLS) have been used widely in metabolomics. Partial least squares can distinguish between groups but do not always reflect rank order of groups (eg, severity of diseases). We extended PLS by adding a differential penalty between mean of groups in PLS subspace. We named this method partial least squares with rank order of groups (PLS-ROG). The PLS-ROG can distinguish between groups and also can reflect rank order of groups. The selection of metabolites associated with a biological phenotype is highly important in metabolomics. The PLS-ROG scores are represented as linear combinations of weight and the level of each metabolite. The weight is proportional to the correlation coefficient between the score of the response variable and the metabolite level when each metabolite level is scaled to unit variance. Using this feature, we selected significantly correlated metabolites based on the scores by applying statistical hypothesis testing of factor loading in PLS-ROG. To demonstrate the practical application of PLS-ROG for metabolomic data analysis, we applied PLS-ROG 2 case studies. The PLS-ROG scores tended to be associated with the biological phenotype that we focused attention on. Metabolites correlated with PLS-ROG scores were selected, and some of these metabolites were consistent with the metabolites reported in the previously published studies from which we sourced the metabolome data. The results suggest that PLS-ROG and its statistical hypothesis testing of factor loading can be useful to interpret metabolome data with rank order of groups.