Bayesian and non-Bayesian analysis of mixed-effects PK/PD models based on differential equations

Compartmental analysis is used to model dynamic biological systems and widely applied to study the kinetics of drugs in the body. We used compartmental mixed-effects modeling, which quantifies the between- and within-subject variability, to analyze population data based on a pharmacokinetic model where predictions were obtained from a solution of a system of ordinary differential equations (ODEs). Non-Bayesian software (nlmeODE in R, or, NLINMIX with ODEs in SAS) and Bayesian software (WBDiff in WinBUGS) enabled the mixed-effect analysis of complicated systems of ODEs with and without a closed-form solution. Our aim was to use simulation data and real data from the glucose-insulin minimal model study to illustrate the applicability of Bayesian and non-Bayesian methods for compartmental analysis of population data. Our results indicated that the two methods are numerically stable and provided accurate parameter estimates for the simulation data based on the standard PK/PD model. However, in the analysis of glucose-insulin minimal model, the Bayesian method was preferred, since it provided a satisfactory solution (statistically) to the minimal model without approximation by linearization required by the non-Bayesian algorithm.