Product Engineer PumasAI Uppsala, Uppsala Lan, Sweden
Disclosure(s):
David Müller-Widmann, PhD: No relevant disclosure to display
Objectives: Typically, quantitative systems pharmacology (QSP) models and nonlinear mixed effects (NLME) models of pharmokinetics (PK) and pharmacodynamics (PD) are used at different stages of the drug development process.
In this case study, we combine these two modeling approaches in an NLME-based PK/PD model whose dynamics are governed by the QSP model ("NLME-QSP model").
We analyze the feasibility of parameter inference of the NLME-QSP model using first-order conditional estimation (FOCE).
Methods: The study is performed with an NLME-QSP model that combines a PK model of teriparatide, consisting of fixed and random effects, a QSP model of the relation between teriparatide concentration and calcium and parathyroid hormone (PTH) concentration, and a residual error model.
As QSP model the model of calcium homeostasis and bone remodeling by Peterson and Riggs (2010) is chosen which notably was the first QSP model used by FDA to analyze appropriateness of a proposed dosage regimen.
In addition to PK parameters of teriparatide, in the NLME-QSP model parameters of the QSP model are exposed that are most sensitive to the derived quantities .
Sensitivity of the QSP model's parameters is analyzed by a local sensitivity analysis of all parameters followed by a global sensitivity analysis (Sobol' method) of a subset of most sensitive parameters.
Pumas is used to fit the NLME-QSP model to calcium and PTH concentration measurements of subjects treated with teriparatide.
Results: Parameter estimation with the NLME-QSP model is feasible and can be performed successfully.
One challenge of NLME-QSP model, inherited from its QSP model, is that many parameter configurations give rise to complex ("stiff") dynamics on largely different timescales.
Hence, in general, for sufficiently accurate and efficient simulation algorithms specialized for stiff differential equations are required.
Together with the high dimension of the QSP model, this leads to considerably larger simulation times than for comparable compartmental PK/PD models.
The computational cost is further increased in model fitting with FOCE using gradient-based optimization algorithms.
Additionally, the large number of parameters of the QSP model puts constraints on the design of the NLME-QSP model:
Exposing too many parameters can lead to problems due to non-obvious parameter interactions and dependencies, overfitting, high computational cost (in particular with forward-mode differentiation used in Pumas), and the high dimension of the parameter space.
This problem is alleviated in the case study by selecting a subset of sensitive parameters.
The sensitivity analysis of the QSP model's parameters had to be performed in two stages since a joint global sensitivity analysis was not computationally feasible.
Conclusions: The case study shows that NLME-based PK models and QSP models can be combined in an NLME-QSP model that is amenable to successful albeit challenging parameter estimation.
Citations: [1] Peterson, M. and Riggs, M. (2010), A physiologically based mathematical model of integrated calcium homeostasis and bone remodeling. Bone, Volume 46, Issue 1, p. 49-63. https://doi.org/10.1016/j.bone.2009.08.053
[2] Peterson, M. and Riggs, M. (2015), FDA advisory meeting clinical pharmacology review utilizes a quantitative systems pharmacology (QSP) model: A watershed moment?. CPT Pharmacometrics & Systems Pharmacology, Volume 4, Issue 3, p. 189-192. https://doi.org/10.1002/psp4.20
[3] FDA, CDER (2002), Forteo summary basis of approval. Forteo [teriparatide (rDNA origin)] injection. Company: Eli Lilly and Company. Application No. 021318. Approval Date: 11/26/2002.
[4] Jansen, M.J.W. (1999), Analysis of variance designs for model output. Computer Physics Communications, Volume 117, Issues 1–2, p. 35-43. https://doi.org/10.1016/S0010-4655(98)00154-4
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