Difference between revisions of "Overview"

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Data: concentrations at times $0, 1, \ldots 15$, from 6 patients who received each 100 mg at time $t=0$ (bolus intravenous):
 
Data: concentrations at times $0, 1, \ldots 15$, from 6 patients who received each 100 mg at time $t=0$ (bolus intravenous):
  
:[[Image:Intro1.png|center|900px]]
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:[[Image:Intro1.png|left|900px]]
 
 
  
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Goal of modelling: describe the variability of the data (structural, intra $\&$ inter variabilities) using a ''statistical model''.
 
Goal of modelling: describe the variability of the data (structural, intra $\&$ inter variabilities) using a ''statistical model''.

Revision as of 14:29, 4 February 2013

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 $k=0.279$:

Intro2.png