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Ph.D. Forsvar: Functional Data Analysis applied in Chemometrics – with focus on NMR Nutrimetabolomics

Date Friday, February 13, 2015, 13:15 - 15:00
Location Auditorium 10, H.C. Ørsted Instituttet, Universitetsparken 5, 2100 Copenhagen OE

Invitation til Martha Mullers ph.d. forsvar d. 13. februar 2015.

Martha Muller

Department of Mathematical Sciences, University of Copenhagen

will defend her PhD thesis entitled

“Functional Data Analysis applied in Chemometrics – with focus on NMR Nutrimetabolomics”

Friday, February 13, 2015 at 13:15 in auditorium 10, H.C. Ørsted Instituttet, Universitetsparken 5, 2100 Copenhagen OE.

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 study design, 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 peaks with 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 in chemometrics, with the benefits of no strong assumptions regarding neighboring 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 of biomarkers of food consumption and metabolic phenotype, and personalized nutrition for prevention and treatment.