A statistical framework for biomarker discovery in metabolomic time course data

Motivation: Metabolomics is the study of the complement of small molecule metabolites in cells, biofluids and tissues. Many metabolomic experiments are designed to compare changes observed over time under two experimental conditions or groups (e. g. a control and drug-treated group) with the goal of identifying discriminatory metabolites or biomarkers that characterize each condition. A common study design consists of repeated measurements taken on each experimental unit thus producing time courses of all metabolites. We describe a statistical framework for estimating time-varying metabolic profiles and their within-group variability and for detecting between-group differences. Specifically, we propose (i) a smoothing splines mixed effects (SME) model that treats each longitudinal measurement as a smooth function of time and (ii) an associated functional test statistic. Statistical significance is assessed by a non-parametric bootstrap procedure. Results: The methodology has been extensively evaluated using simulated data and has been applied to real nuclear magnetic resonance spectroscopy data collected in a preclinical toxicology study as part of a larger project lead by the COMET (Consortium for Metabonomic Toxicology). Our findings are compatible with the previously published studies.