title: The method of averaging applied to pharmacokinetic/pharmacodynamic indirect response models.
abstract: The computational effort required to fit the pharmacodynamic (PD) part of a pharmacokinetic/pharmacodynamic (PK/PD) model can be considerable if the differential equations describing the model are solved numerically. This burden can be greatly reduced by applying the method of averaging (MAv) in the appropriate circumstances. The MAv gives an approximate solution, which is expected to be a good approximation when the PK profile is periodic (i.e. repeats its values in regular intervals) and the rate of change of the PD response is such that it is approximately constant over a single period of the PK profile. This paper explains the basis of the MAv by means of a simple mathematical derivation. The NONMEM® implementation of the MAv using the abbreviated FORTRAN function FUNCA is described and explained. The application of the MAv is illustrated by means of an example involving changes in glycated hemoglobin (HbA1c%) following administration of canagliflozin, a selective sodium glucose co-transporter 2 inhibitor. The PK/PD model applied to these data is fitted with NONMEM® using both the MAv and the standard method using a numerical differential equation solver (NDES). Both methods give virtually identical results but the NDES method takes almost 8 h to run both the estimation and covariance steps, whilst the MAv produces the same results in less than 30 s. An outline of the NONMEM® control stream and the FORTRAN code for the FUNCA function is provided in the appendices.
authors.affiliation: Model Based Drug Development, Janssen Research & Development, A Division of Janssen Pharmaceutica NV, Beerse, Belgium, adrian.dunne@tacatraining.com.
authors.forename: Adrian
authors.initials: A
authors.lastname: Dunne
authors.forename: Willem
authors.initials: W
authors.lastname: de Winter
authors.forename: Chyi-Hung
authors.initials: CH
authors.lastname: Hsu
authors.forename: Shiferaw
authors.initials: S
authors.lastname: Mariam
authors.forename: Martine
authors.initials: M
authors.lastname: Neyens
authors.forename: José
authors.initials: J
authors.lastname: Pinheiro
authors.forename: Xavier
authors.initials: X
authors.lastname: Woot de Trixhe
mesh_terms: D000068896:Canagliflozin / Q000097:blood / Q000493:pharmacokinetics* / Q000494:pharmacology*; D019295:Computational Biology / Q000379:methods*; D006442:Glycated Hemoglobin / Q000032:analysis; D006801:Humans; D007004:Hypoglycemic Agents / Q000097:blood / Q000493:pharmacokinetics* / Q000494:pharmacology*; D008954:Models, Biological; D000077203:Sodium-Glucose Transporter 2 Inhibitors; D012984:Software
chemical_list: D000068896:Canagliflozin; D006442:Glycated Hemoglobin; D007004:Hypoglycemic Agents; D000077203:Sodium-Glucose Transporter 2 Inhibitors; C517652:hemoglobin A1c protein, human