A novel Bayesian approach to quantify clinical variables and to determine their spectroscopic counterparts in 1H NMR metabonomic data

Abstract

Background: A key challenge in metabonomics is to uncover quantitative associations between multidimensional spectroscopic data and biochemical measures used for disease risk assessment and diagnostics. Here we focus on clinically relevant estimation of lipoprotein lipids by 1H NMR spectroscopy of serum.

Results: A Bayesian methodology, with a biochemical motivation, is presented for a real 1H NMR metabonomics data set of 75 serum samples. Lipoprotein lipid concentrations were independently obtained for these samples via ultracentrifugation and specific biochemical assays. The Bayesian models were constructed by Markov chain Monte Carlo (MCMC) and they showed remarkably good quantitative performance, the predictive R-values being 0.985 for the very low density lipoprotein triglycerides (VLDL-TG), 0.787 for the intermediate, 0.943 for the low, and 0.933 for the high density lipoprotein cholesterol (IDL-C, LDL-C and HDL-C, respectively). The modelling produced a kernel-based reformulation of the data, the parameters of which coincided with the well-known biochemical characteristics of the 1H NMR spectra; particularly for VLDL-TG and HDL-C the Bayesian methodology was able to clearly identify the most characteristic resonances within the heavily overlapping information in the spectra. For IDL-C and LDL-C the resulting model kernels were more complex than those for VLDL-TG and HDL-C, probably reflecting the severe overlap of the IDL and LDL resonances in the 1H NMR spectra.

Conclusion: The systematic use of Bayesian MCMC analysis is computationally demanding. Nevertheless, the combination of high-quality quantification and the biochemical rationale of the resulting models is expected to be useful in the field of metabonomics.

Figure 1

The quantitative performance of the Bayesian models. The results of the Bayesian models for the VLDL-TG (n = 75) (orange), IDL-C (n = 72) (lime), LDL-C (n = 72) (sherry) and HDL-C (n = 67) (olive). The correlation coefficients (R) shown are between predictions and observations (for predictive R-values see Results and discussion). The straight black lines show a 1:1-relationship and are drawn only to guide the eye.

Figure 2

The kernel distributions in the Bayesian models. The marginal posterior distribution for the number of kernels in the Bayesian models for the VLDL-TG (orange), IDL-C (lime), LDL-C (sherry) and HDL-C (olive).

Figure 3

A representative ¹H NMR spectrum of serum and the spectroscopic characteristics of the Bayesian model kernels. Illustration of the aliphatic spectral region of a representative experimental ¹H NMR spectrum (black) together with the main Bayesian model kernels for the VLDL-TG (orange), IDL-C (lime), LDL-C (sherry) and HDL-C (olive). The assignments for the resonances refer to fatty acids in triglycerides, cholesterol compounds and phospholipids in various lipoprotein particles, the cholesterol backbone -C(18)H₃ and the -N(CH₃)₃ groups of surface phospholipids. Thus, it should be noted that all the lipoprotein fractions present in serum contribute to all of these resonances. The insets show the choline -N(CH₃)₃ region and the lipid (-CH₂-)_n region in mode detail. The highest intensity kernel for each lipoprotein fraction was scaled to 1.0. The dotted horizontal line shows the zero level.