E. Olofsen
Department of Anesthesiology, Leiden University Medical Center, Leiden, The Netherlands
Objectives: Tornoe et al. introduced the application of stochastic differential equations to pharmacokinetic-pharmacodynamic (PK-PD) modeling in NONMEM.[1] One of their examples was to identify a time-varying absorption rate. When during drug absorption both pharmacokinetic and pharmacodynamic data are available, but not necessarily sampled at coinciding time instants, the questions arise (1) if these can be analyzed simultaneously and (2) how this would affect PK and PD parameter estimation.
Methods: A three-compartmental model, consisting of an absorption, disposition, and effect compartment was implemented in NONMEM incorporating a Kalman filter with (A) bivariate PK and PD feedback, (B1) alternating univariate PK and PD feedback, or (B2) idem, but with PK and PD information only fed back to the respective PK and PD parts of the model. The state (co)variance matrix was integrated using eqs(3) from Jorgensen et al.[2] Model versions B were fitted to simulated single-subject data, generated with various values of the blood-effect-site equilibration rate (ke0), to assess bias and standard error of model parameters. The absorption rate (ka) and ke0 were governed by stochastic differential equations. At the first sampling time a PD measurement was generated, a PK measurement at the next, et cetera.
Results: Kalman filter A and B1 configurations yielded identical parameter estimates when the PK and PD sampling times coincided (only NONMEM’s S matrices differed fittingly). In the setting of a randomly varying ka but constant ke0, simultaneous PK and PD analysis increased the precision of the estimates of ke0 (configuration B1 versus B2). Except when ke0 was relatively small, the improvement approached the expected one based on the increased number of measurements (and measurement noise levels).
Conclusions: PK and PD data can be analyzed simultaneously using an “alternating Kalman filter” configuration, which has the advantage that the PK and PD sampling times do not need to coincide. This approach is similar to “sequential processing” [3], with missing data. When ke0 is identified as being essentially constant, simultaneous analysis may decrease its estimation error.
References:
[1] CW Tornoe et al., Pharm. Res. 22:1247, 2005.
[2] JB Jorgensen et al., Proc. Am. Control Conference: 3706, 2007.
[3] BDO Anderson and JB Moore, Optimal filtering, Prentice Hall, 1979.
Reference: PAGE 22 (2013) Abstr 2696 [www.page-meeting.org/?abstract=2696]
Poster: Estimation methods