Filed under: Differential equations, PDK
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 _t_d, giving rise to a phenopharbital concentration ct at a later time t:
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 A full description of the model can be found here pheno.pdf (quite old, so timing results mentioned are outdated).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.
Pinheiro, J., Bates, D.M. (2000), Mixed-Effects Models in S and S-PLUS. Statistics and Computing, Springer.