Population pharmacokinetics data are often modeled using nonlinear
mixed-effects models; nonlinear because the pharmacokinetic parameters
- rate constants, clearance rates, etc. - occur nonlinearly in the
model function and mixed-effects because the models involve both
fixed-effects parameters, applying to the population or well-defined
subsets of the population, and random effects associated with
particular experimental or observational units under study. Many
algorithms for estimating the parameters in such models have been
proposed and implemented but often the estimation algorithm is
confused with the parameter estimation criterion - maximum likelihood.
I suggest we concentrate on evaluating or approximating the
log-likelihood to be optimized and will describe how this is done in
the nlmer function in the lme4 package for R.