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One-compartment open model

Fit mixed effects model to the classical "phenopharbital" model
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 D at time td, giving rise to a phenopharbital concentration ct at a later time t:

ct = D/V exp[-Cl/V(t-td)],
 
where V and Cl are parameters (the so-called 'Volume of concentration' and the 'Clearance', respectively). Doses given at different time points contribute additively to ct.

Pinheiro & Bates (2000) fitted a model with a linear predictor (and a log-link) for each of the paramere V and Cl. Each of the linear predictors contained one covariate Wt and one random effect. A full description of the model can be found here pheno.pdf (quite old, so timing results mentioned are outdated).


Note: In this model the underlying ODE has an analytical solution, but in more general models it will not.
 

References

Pinheiro, J., Bates, D.M.  (2000), Mixed-Effects Models in S and S-PLUS. Statistics and Computing, Springer.