BioSysBio:abstracts/2007/Mattias Rantalainen

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Piecewise Multivariate Modelling of Short Time Series in Metabonomics

Author(s): Mattias Rantalainen, Olivier Cloarec, Johan Trygg*, Jeremy Nicholson, Elaine Holmes
Affiliations: Imperial College London, *Umea University
Contact:email: mattias dot rantalainen at imperial dot ac dot uk
Keywords: 'Multivariate' 'Time Series' 'Metabonomics'


Modelling time series of biological systems is essential for understanding their dynamics and their responses to perturbations. In metabonomic studies the time series are commonly usually fairly short (< 20 time points), the sampling rate is many times restricted due to experimental factors of the biological systems studied. Such data have previously often been modelled and visualised by Principal Component Analysis (PCA) as time-trajectories. Although this approach provides a general overview of the data, PCA does not explicitly model time related changes, but is rather maximising the modelled variance in the data, which is not necessarily time related. Here a multivariate approach with the objective to explicitly model the time-related variation in the data is described, aiming to increase the time resolution and opportunity to interpret and predict time related events.


Applying the proposed method for analysis of a short time-series from a NMR metabonomic study of Mercury Chloride toxicity in rat illustrates how time related changes can be modelled and interpreted by the proposed method. In addition we demonstrate how time predictions can be made.


Piecewise multivariate models are estimated to describe time related changes between neighbouring time frames over the time series. The set of local models describe the changes over the full time series. Although linear models are used in the local time frames, the framework encompasses the description and prediction of non-linear time related changes over the full time series. Recent development in the area of chemometrics [1] has opened up for estimation of multivariate models with predictive performance identical to Partial Least Squares, but reducing the number of components to interpret to a single component for a rank one problem, which we have here. Thus enabling straightforward piecewise modelling of time-series data with multicollinear variables, resulting in a highly transparent models ideal for interpretation.


For short multivariate time-series, when conventional statistical time-series analysis methods are not applicable, the proposed method provides a multivariate framework enabling interpretation and prediction of time-related biological variation in omics data sets.


[1] Trygg, J.; Wold, S., Orthogonal projections to latent structures (OPLS). Journal of Chemometrics 2002, 16, (3), 119-128.

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