Statistics and Its Interface

Volume 4 (2011)

Number 4

Spin–spin coupling information is crucial for unbiased NMR analysis in metabonomics

Pages: 443 – 450



Hsieh Fushing (Department of Statistics, University of California at Davis)

Hong-Dar Isaac Wu (Department of Applied Mathematics, National Chung-Hsing University, Taiwan)


We address the critical use of spin–spin coupling information for extracting unbiased concentration information of metabolites based on NMR spectroscopy. This coupling information reveals a truncating status due to binning and baseline correction, termed as vertical and horizontal truncations, which are typical operations needed in bin integration for area under spectral peaks. The likelihood function incorporating truncation status of the involved peak areas is analytically derived. We demonstrate that the maximum likelihood estimation (MLE) provides unbiased estimates of metabolite concentrations. When the information of truncation status is neglected, the extent of resultant bias is substantial. These results bear fundamental implications on reliability and validity of most of the popular statistical methodology in metabolomics, including the analysis of variance (ANOVA), principal component analysis (PCA) and multiple testings. For a multiple-response one-way ANOVA, a test statistic is proposed and implemented through a numerical study.


baseline correction, peak area, binning, truncation, maximum likelihood estimation, mixture model, heterogeneity, random effect, ANOVA

Published 17 November 2011