Functional Data Analysis applied in Chemometrics - with focus on NMR Nutri-metabolomics

Abstract:

Metabolomics studies the ‘unique chemical fingerprints’ that cellular processes create. These ‘fingerprints’ can be measured in biofluids like blood and urine and can be used to study the influence of nutrition on human metabolism. For each sample that is chemically analysed with nuclear magnetic resonance (NMR) we obtain a spectrum containing hundreds of peak patterns (metabolites) constructed by tens of thousands of data values. These data are typically analysed with standard chemometric methods and do not explore the rich functional nature of spectral data.

We explore functional data analysis (FDA) as a method to analyse NMR spectral data in metabolomics. In FDA, the data are curves instead of data points. We apply wavelet-based functional mixed model methodology. We use bootstrap based inference to estimate the difference in means between groups in the longitudinal functional model. This approach allows us to respect the studydesign, while modelling the NMR spectra as functions. We model nonparametric fixed and random effect functions that enable us to incorporate covariates and repeated measurements in one model. We investigate NMR spectral regions that are significantly different for gender and diet culture groups. Furthermore, we illustrate the rich nature of functional derivatives in simulated NMR peakswith characteristic Lorentzian line shape. Using phase-plane plots to explore the anatomy of NMR peaks, we introduce the novelty of heart plots for spectral data. These methods are also applicable to other spectral data, e.g. mass spectrometry or infrared.

 FDA provides access to many functional equivalents of methods currently used inchemometrics, with the benefits of no strong assumptions regarding neighbouring observations. FDA also provides access to the data's derivatives and opens up the ability to analyse information that is otherwise locked away in the data. The use of FDA in metabolomics can make a valuable contribution to the emerging technology in personalised medicine and health care, including discovery ofbiomarkers of food consumption and metabolic phenotype, and personalized nutrition for prevention and treatment. 

Advisor: Prof. Anders Tolver, Math, University of Copenhagen

Assessment committee:

Ass.Prof. Bo Markussen (chairman), MATH, University of Copenhagen

Prof. Sara Sjöstedt de Luna , Umeå University, Sweden

Ass. Prof. Ron Wehrens  Biometris/biosciences, Netherlands