Conclusion

The aim of this paper was to describe a general framework of multiway multidimensional analysis as a tool to analyse pharmaco-EEG data. The multiway method chosen enables data reduction of the complex structure of the data, providing a quantified hierarchy of effects (sets of linear components on each mode). The $subject*dose$ component can then be used for testing the drug effect with any cross-over analysis. Even with simple preprocessing the method performed well in extracting main variability features of the data but also revealed outliers. The existence of outliers seems to be an important aspect of this kind of data because of a strong subject variability of EEG recordings associated associated with drug intake. Without discussing sample size required for this type of analysis, (which would need to be fully addressed) this puts into question the use of subjects as a mode (or combined with doses) in the analysis and enforce to use summaries across subjects. Centring , scaling, and interactions removal were used to try to avoid outliers. Another approach was to represent doses by a summary measure across subjects (mean, median, trimean) and do the analysis with this mode. A larger sample would reduce outlier problem but would also improve estimation of the summaries. Analysing robust summaries may be interesting when comparing or classifying different drugs if the same design was used but not necessarily on the same subjects. Supplementary points technique can confirm and add more information on dispersion of the evolution of the dose-time profiles. The method described here can involve the use of metrics as in generalised multidimensional analysis, e.g. discriminant analysis. Note that the problem in pharmaco-EEG analysis is not necessarily a discriminant one as in the first place the neuro-pharmacist wants to identify effects of the drug and only secondly dose pattern effects. Correspondence Analysis on $k$ modes was introduced as a particular PTA-$k$modes of a $(k + 1)$ uple. This method seem very well suited to pharmaco-EEG data as conditional independence can be analysed and quantified. Complete independence, two way interactions, three way interactions take part of the same analysis, and are in turn also decomposed as sum of Principal Tensors. Analysing the links between pharmaco-dynamic variables and pharmaco-kinetic variables has not been investigated in this paper, but implementing for example inter-battery analysis ideas ([21]) with PTA-$k$modes seems straightforward. An expending literature about multiway PLS (Partial Least Squares) is worth reading for this purpose.