next up previous
Next: Plotting Principal Tensor components Up: tr00dl2 Previous: Handling PTA-kmodes method


Using PTA-kmodes for PDY studies

Based on the previously described drug experiment our purpose is now to show some practical examples of using PTA-$k$modes as a method of extracting the main results for pharmaco-EEG studies. The first consideration when using a multiway method is to define the structure of the data or the structure of interest. The whole structure of the data contains:
  1. a spatial dimension,
  2. a time dimension,
  3. a variable dimension (e.g. frequency bands in absolute energy),
  4. a dose dimension,
  5. a subject dimension,
  6. a condition dimension (Rest or Vigilance Control)
When performing a PTA-$k$modes we are looking for links between these dimensions through optimisation of linear modelisations of each in order to maximise variability. From geometrical point of view one looks for decomposed tensors or rank one tensors (i.e. tensor product of linear modelisations on each mode) giving the best projection of the data according to least squares error. The sum of squares explained is the sum of the squared singular values obtained, and the decomposed tensors are the corresponding principal tensors.

Figure 2: choices of modes for PTA-$k$modes of pharmaco-EEG data.
\includegraphics[width=11cm]{ptak.ps}

Dimensions can be directly taken as modes or combined depending on focuses chosen for analysis. Figure fig.2 illustrates the main possible ways to organise the data to perform PTA-$k$modes for PDY studies, where each arrow means a mode of the tensor. After choosing the tensor to analyse (choices of modes), preprocessing (e.g. centring, reducing) can be done using or not metrics on each mode (choice of a global tensorial metric), added linear constraints on some modes is also possible. All of those offer flexibility. Pharmaco-EEG designs usually are cross-over designs, this makes possible the PTA-5modes shown on figure fig.2 which fully takes into account the repeated measure aspect of the design (one could also separate the sequence), but does not necessarily give a greater interest (see discussion). Secondly it also makes possible to build the subject*dose mode preferably with comparison to placebo (i.e. dose is in fact dose versus placebo). This will reduce subject variability effect. In the same manner Time mode is in fact often Time versus baseline. There after dose and Time will be considered respectively versus placebo and baseline.

Subsections
next up previous
Next: Plotting Principal Tensor components Up: tr00dl2 Previous: Handling PTA-kmodes method
Didier Leibovici 2001-09-04