Improved One-Class Modeling of High-Dimensional Metabolomics Data via Eigenvalue-Shrinkage

• Main Authors: Alberto Brini, Vahe Avagyan, Ric C. H. de Vos, Jack H. Vossen, Edwin R. van den Heuvel, Jasper Engel
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Metabolites
• Subjects: high-dimensional data; one-class model; untargeted metabolomics; mahalonobis distance; eigenvalue-shrinkage; critical value
• Online Access: https://www.mdpi.com/2218-1989/11/4/237

One-class modelling is a useful approach in metabolomics for the untargeted detection of abnormal metabolite profiles, when information from a set of reference observations is available to model “normal” or baseline metabolite profiles. Such outlying profiles are typically identified by comparing the distance between an observation and the reference class to a critical limit. Often, multivariate distance measures such as the Mahalanobis distance (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>MD</mi></mrow></semantics></math></inline-formula>) or principal component-based measures are used. These approaches, however, are either not applicable to untargeted metabolomics data, or their results are unreliable. In this paper, five distance measures for one-class modeling in untargeted metabolites are proposed. They are based on a combination of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>MD</mi></mrow></semantics></math></inline-formula> and five so-called eigenvalue-shrinkage estimators of the covariance matrix of the reference class. A simple cross-validation procedure is proposed to set the critical limit for outlier detection. Simulation studies are used to identify which distance measure provides the best performance for one-class modeling, in terms of type I error and power to identify abnormal metabolite profiles. Empirical evidence demonstrates that this method has better type I error (false positive rate) and improved outlier detection power than the standard (principal component-based) one-class models. The method is illustrated by its application to liquid chromatography coupled to mass spectrometry (LC-MS) and nuclear magnetic response spectroscopy (NMR) untargeted metabolomics data from two studies on food safety assessment and diagnosis of rare diseases, respectively.