Introduction

When a compound is expecting to show some central nervous system (CNS) activity, its potentials still need to be well established for the drug to be classified properly before thinking about therapeutic effect. For that purpose pharmaco-dynamic (PDY) studies are required and currently involve electro-encephalographic signal recording (EEG) of healthy subjects according to a crossover design wherein each period includes repeated measures of EEG (days, times). Spatio-temporal distributions of parameters (frequency bands of the signal) are of interest for differences between placebo and verum doses. Links with additional variables such as neurocognitive variables (psychometric tests) can also be explored and will be addressed briefly in the discussion as well as a current interest on looking at pharmaco-kinetic parameters conjointly. The data-recording methodology and the quantification of the EEG-signal used for the dataset analysed thereafter is fully described in [17]. A collection and quantification of EEG-data, for each of the 28 leads (international 10/20 system is complemented to 28 leads with B1, FC1, FC2, B2, W1, PC1, PC2, W2). At each time of measurement, EEGs are taken under 3 minutes vigilance controlled (VC) recording condition (subjects push two knobs with their eyes closed), followed by 3 minutes resting (R) recording condition (subjects relax with their eyes closed). After filtering and digitisation and artefact removal procedure completed, energy spectra ($\mu V^2$) is calculated, for each 2 second period over a frequency range of 0.5 to 32Hz, using the Fast Fourier Transform (FFT), and then averaged for each subject and each recording condition. Each mean energy spectra is averaged by standard frequency EEG bands : $\delta$ (0.5-3.5Hz), $\theta$(4-7.5Hz), $\alpha_1$ (8-9.5Hz), $\alpha_2$ (10-12.5Hz), $\beta_1$ (13-17.5Hz), $\beta_2$ (18-20.5Hz), $\beta_3$ (21-32Hz) and Total (0.5-32Hz). Absolute energies and relative energies (percentage of the Total band energy) are considered. The alpha slow wave index ( $ASI=\frac{\alpha }{\left(\delta +\theta\right)}$), the mean frequency (GMF) and the mean complexity (GCO) of the EEG spectrum are also calculated. The whole process will then analyse at each time of measurement(typically $10$ not regularly spaced measures): 28 leads$\times$(2 absolute or % $\times$(7 bands)+1 total+3 synthetic variables) $\times$2 conditions $=$28 locations$\times$18 parameters$\times$2 conditions $=$1008 variables measured say $10$ times on say $12$ subjects. In fact only $7$ parameters generated the $18$. This methodology was conducted for the following pharmaco-dynamic study (PDY),a placebo-controlled, double-blind trial, with randomisation of 12 healthy male subjects into a 4 periods and 4 treatments cross-over design. Each received a single morning dose of 10, 30, 90mg of compound or placebo and wake-EEG was performed on day 1 before administration and 0.5, 1, 1.5, 2, 2.5, 3, 4, 6, hours post-dosing and on day 2: 24 and 36 hours post-dosing. Blood was sampled for determination of drug plasma concentration and endocrinological assessments on day 1 before administration and then 1, 2, 4, 6 hours post-dosing and on day 2: 24 and 36 hours post-dosing. The interest is in knowing if the compound has an effect? which dose? (dose effect?), at what point in time does it happen? where is it located on the scalp? for which frequency band or pattern of frequency band does this affect? To answer these questions, parametric and non-parametric testing methods have been routinely implemented. In the first place some weaknesses of these mainly univariate methods will be pointed out before introducing our proposed method involving multiway data analysis methods. The main method applied here was theoretically exposed in [16]. The purpose of this paper is show how to modify and apply it in this context. This involves different methods which are related to existing approaches in multidimensional analysis (two-way analysis), and thereby extending them to multiway data. An important generalisation is about Correspondence Analysis extended from the analysis of $2$ variables to $k$ variables enabling to break down the lack of complete independence into additive components relating to different level of interactions between the variables.