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<h1 id="parent-fieldname-title" class="documentFirstHeading">
One-compartment open model
</h1>
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Filed under:
<span>
<a href="http://www.admb-project.org/@@search?Subject%3Alist=Differential%20equations" class="link-category" rel="tag">Differential equations</a><span class="separator">,</span>
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<a href="http://www.admb-project.org/@@search?Subject%3Alist=PK/DK" class="link-category" rel="tag">PK/DK</a>
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Fit mixed effects model to the classical "phenopharbital" model
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<div class="" id="parent-fieldname-text-fa2c8a6b-c991-4403-a3e2-38f3c700f46b">
Pinheiro
& Bates (2000, Ch. 6.4) fitted a so-called 'one-compartment open
model' to a dataset known as the 'phenopharbital data'. A patient is given
a dose <em>D</em> at time <em>t</em><sub>d</sub>, giving rise to a
phenopharbital concentration <em>c<sub>t</sub></em> at a later time
<em>t</em>:
<div><br />
<div align="center"><em>c<sub>t</sub></em> = <em>D/V</em>
exp[-<em>Cl/V</em>(<em>t</em>-<em>t</em><sub>d</sub>)],</div>
<div align="center"> </div>
where
<em>V</em> and <em>Cl</em> are parameters (the so-called 'Volume of
concentration' and the 'Clearance', respectively). Doses given at
different time points contribute additively to <em>c<sub>t</sub></em>.
<div><sub><br /></sub>
Pinheiro & Bates (2000) fitted a model with a linear predictor (and a
log-link) for each of the paramere <em>V</em> and <em>Cl</em>. Each of the
linear predictors contained one covariate <em>Wt</em> and one random
effect. A full description of the model can be found here <a href="one-compartment-open-model/pheno.pdf" class="internal-link" title="pheno.pdf">pheno.pdf</a> (quite old, so timing results mentioned are outdated).
<h3><br /></h3>
<div>Note: In this model the underlying ODE has an analytical solution, but in more general models it will not.</div>
<div> </div>
<h3>References</h3>
<div>
<div>Pinheiro, J., Bates, D.M. (2000), <em>Mixed-Effects Models in S and S-PLUS</em>. Statistics and Computing, Springer.</div>
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