Overview

In the following sections we introduce a formalism to describe the individual models and to calculate some useful information (confidence intervals, Fisher information Matrix, etc.) about the descriptors. The implementation of such formalism in a software and the corresponding results will be also illustrated.

Let us start our discussion with a couple of examples.

Data: concentrations at times $0, 1, \ldots 15$, from 6 patients who received each 100 mg at time $t=0$ (bolus intravenous):

Goal of modelling: describe the variability of the data (structural, intra $\&$ inter variabilities) using a statistical model.

The classical individual approach derives a model for a unique individual.

• Predicted concentration at time $t$:

\( f(t ; V,k) = \frac{D}{V} \ e^{-k \, t} \)

• Observed concentration at time $t_j$, $j=1, 2, \ldots, 15$:

\( y_j = f(t_j ; V,k) + \varepsilon_j \)

Observed concentrations from individual 1 and predicted concentration profile obtained with $V=10.5$ and $k=0.279$: