The characteristics of the OPLS method have been investigated for the purpose of discriminant analysis (OPLS-DA). We demonstrate how class-orthogonal variation can be exploited to augment classification performance in cases where the individual classes exhibit divergence in within-class variation, in analogy with soft independent modelling of class analogy (SIMCA) classification. The prediction results will be largely equivalent to traditional supervised classification using PLS-DA if no such variation is present in the classes. A discriminatory strategy is thus outlined, combining the strengths of PLS-DA and SIMCA classification within the framework of the OPLS-DA method. Furthermore, resampling methods have been employed to generate distributions of predicted classification results and subsequently assess classification belief. This enables utilisation of the class-orthogonal variation in a proper statistical context. The proposed decision rule is compared to common decision rules and is shown to produce comparable or less class-biased classification results.

We describe here the implementation of the statistical total correlation spectroscopy (STOCSY) analysis method for aiding the identification of potential biomarker molecules in metabonomic studies based on NMR spectroscopic data. STOCSY takes advantage of the multicollinearity of the intensity variables in a set of spectra (in this case 1H NMR spectra) to generate a pseudo-two-dimensional NMR spectrum that displays the correlation among the intensities of the various peaks across the whole sample. This method is not limited to the usual connectivities that are deducible from more standard two-dimensional NMR spectroscopic methods, such as TOCSY. Moreover, two or more molecules involved in the same pathway can also present high intermolecular correlations because of biological covariance or can even be anticorrelated. This combination of STOCSY with supervised pattern recognition and particularly orthogonal projection on latent structure-discriminant analysis (O-PLS-DA) offers a new powerful framework for analysis of metabonomic data. In a first step O-PLS-DA extracts the part of NMR spectra related to discrimination. This information is then cross-combined with the STOCSY results to help identify the molecules responsible for the metabolic variation. To illustrate the applicability of the method, it has been applied to 1H NMR spectra of urine from a metabonomic study of a model of insulin resistance based on the administration of a carbohydrate diet to three different mice strains (C57BL/6Oxjr, BALB/cOxjr, and 129S6/SvEvOxjr) in which a series of metabolites of biological importance can be conclusively assigned and identified by use of the STOCSY approach.