Many benefits can be gained if multi-factorial diseases with a high incidence and prevalence are better understood. Sophisticated approaches like multilevel analyses are needed to discover subtle differences between healthy people and people at the onset of disease in these types of studies. Multilevel analysis generates different sub-models for each level of variation. For instance, within and between subject variation can be split and analyzed separately if the two factors are orthogonal (i.e., not confounded). In the present paper, the benefits of a multilevel approach in multi-way analysis (nPLS-DA) will be described for the analysis of metabolomics data of a double blinded, randomized, parallel intervention trial with twenty slightly overweight men, whom received a diclofenac or placebo treatment for nine days. Blood samples were taken on multiple time points on 5 treatment days.
The cross-validated error rate for classifying subjects in the correct treatment group for the multilevel nPLS-DA was compared with the error rate from the ordinary nPLS-DA. 42.1% of the subjects were misclassified using ordinary nPLS-DA, whereas only 5% were misclassified using the multilevel approach. Metabolites which contributed in different ways to treatment group differences could be determined and used for biological interpretation.
The multilevel multi-way technique turned out to be a much stronger tool for modeling differences between treatment groups than the ordinary method. The metabolites that contributed most to treatment differences were not only statistically, but also biologically relevant. The multilevel approach found the effects that were better interpretable, whereas the ordinary nPLS-DA failed to do so. The methodology that was described in this paper is not only limited to human intervention studies, but can be used also for studies with a similar data structure. The multilevel approach is able to investigate effects on all levels of variation of every well designed study, hence improving the interpretability of the results.