Modeling a time-dependent absorption constant: a trick and some considerations
Laura Iavarone, Marianna Machin, Marta Neve, Roberto Gomeni, Stefano Zamuner, Italo Poggesi
Clinical Pharmacology Modeling and Simulation, GlaxoSmithKline Neurosciences CEDD Verona (Italy)
Background: Simple first-order absorption models are often inadequate to describe the absorption processes. In addition, the inclusion of a lag-time parameter in the model typically results in difficulties in the parameter estimation. To overcome some of these problems, we found beneficial to describe the absorption rate constant (ka) as a time-dependent function using, for example, a sigmoidal Emax relationship [ka(t)=ka*tc/(t50c+tc)]. Alternative models, i.e. those considering single or double Weibull distributions, have been proposed in the literature [1, 2]. In general, all these models are implemented in NONMEM using differential equations (ADVAN6) . Interestingly, we observed that they could also be directly implemented using the corresponding built-in PK models (e.g., ADVAN2/ADVAN4).
Objectives: In this communication we present the results obtained using the two approaches and we describe some practical considerations for their implementation in NONMEM.
Methods: The models including a) the Emax or b) the single Weibull distribution have been implemented for 1- and 2-compartment open models using either ADVAN6 or ADVAN2/ADVAN4 models in NONMEM (v. 6). The models have been fitted to real and simulated datasets.
Results: The simulated datasets obtained using either ADVAN6 or ADVAN2/ADVAN4 models were equivalent. Furthermore, the same model parameters were estimated by fitting the models to real or synthetic datasets. The implementation with ADVAN2/ADVAN4 resulted in considerably shorter run-times; sometimes it appeared less robust than the one based on differential equations in case of identifiability problems, likely due to the different parameterization. For both implementations, when a repeated-dose schedule is considered, caution should be taken to provide an appropriate number of datapoints over time (i.e. few missing observations for each dosing event) to allow NONMEM to correctly take into account the amount provided by all the individual doses.
Conclusions: Some atypical absorption processes can be implemented in NONMEM either using user-defined differential equations or the corresponding built-in pharmacokinetic models. In both cases, for repeated administration, an appropriate number of datapoints is required to allow the software to correctly handle the dosing events.
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