Specifying Models with Time Dependent Pharmacokinetic Parameters in NONMEM
Anne Brochot, Adrian Dunne, Italo Poggesi and An Vermeulen
Janssen Research & Development, a Division of Janssen Pharmaceutica, Belgium
Objectives: Time dependent parameters are sometimes required to describe the pharmacokinetics of a drug. NONMEM provides the user with a number of options in constructing a model with time dependent parameters. Two options using the PREDPP library were considered, one using the $PK block and the other using the $DES block. An example of time varying absorption previously presented [1,2] was investigated as well as other time varying pharmacokinetics.
Methods: The models studied have been implemented using either ADVAN6 ($DES implementation) or ADVAN1 to ADVAN4 ($PK implementation) in NONMEM (v. 7). The models have been fitted to simulated datasets and a comparison of the results was conducted.
Results: Depending on how the user introduces the time varying pharmacokinetic parameter, NONMEM will either use the analytic solution (ADVAN1 to ADVAN4) or numerically solve the differential equation(s) (ADVAN6). When using the analytic solution, NONMEM employs a step-function to approximate the change in the time varying parameter. How far this approximation differs from the real function depends on the number of TIME points included in the datafile. A large number of TIME records may provide a good approximation when using the analytic solution. However, if the individuals in the dataset differ with respect to their sampling times, then a different model will be fitted for each individual. The numerical solution using the NONMEM time variable T within $DES provides sufficient integration steps to make the solution independent of the TIME record chosen.
Conclusions: The analytic solution using ADVAN1 to ADVAN4 in NONMEM uses an approximation when parameters are varying with time. The numerical differential equation solver in NONMEM uses the desired model but it is more computer intensive. If the analytic solution is used, the introduction of a sufficient number of time points is required to have an acceptable approximation.
References:
[1] Iavarone et al., PAGE 19 (2010) Abstr 1856 [www.page-meeting.org/?abstract=1856].
[2] Petricoul O, Cosson V, Fuseau E, Marchand M. Population Models for drug absorption and enterohepatic recycling. Pharmacometrics: the science of quantitative pharmacology, 2007, Ette EI, Williams PJ (eds). John Wiley&Sons Inc.
