Implication of differences in model parameterisation in osteoporosis
Stephan Schmidt (1), Teun Post (2), Massoud Boroujerdi (1), Lambertus A. Peletier (3), Meindert Danhof (1), Oscar Della Pasqua (1, 4)
(1) Division of Pharmacology, Leiden/Amsterdam Center for Drug Research, Leiden, The Netherlands, (2) Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3), Merck, Oss, The Netherlands, (3) Mathematical Institute, Leiden University, Leiden, The Netherlands, (4) Clinical Pharmacology Modelling & Simulation, GlaxoSmithKline, Stockley Park, UK
Objectives: The RANK-RANKL-OPG system was identified as a key player in the regulation of bone remodelling by osteoblasts (formation) and osteoclasts (resorption). Two models with partly conflicting RANK-RANKL-OPG parameterisations were proposed in the literature (Lemaire et al. (1) vs. Pivonka et al. (2)) to characterise osteoblast and osteoclast activity. The aim of our study was 1) to compare these two models and 2) to identify the parameterisation that best describes changes in bone turnover markers and bone mineral density (BMD).
Methods: Data from 767 healthy postmenopausal women, randomly assigned to treatment with tibolone (0.3, 0.625, 1.25, and 2.5mg) or placebo and supplemental calcium (500mg daily) (3), were analysed using a using a non-linear mixed effect modelling approach in NONMEM 6.2. Two mixture kinetic-pharmacodynamic (KPD) models with respective Lemaire and Pivonka RANK-RANKL-OPG parameterisations were fitted to the data. Bone-specific alkaline phosphatise, osteocalcin, urinary N-terminal collagen telopeptide and BMD in lumbar spine (L1-L4) and total hip were used as biomarker input. Model selection and validation were based on statistical and visual diagnostic criteria. Simulations (n = 500) using the final parameterisations of both models were performed at each dose level to evaluate the quality of the predictions for BMD in lumbar spine and total hip as the primary biomarkers.
Results: Both KPD models converged successfully and allowed for fitting of all bone turnover markers. While the parameterisation of the RANK-RANKL-OPG system required the incorporation of a mixture model to identify responders and non-responders to tibolone treatment, parameterisation according to Pivonka allowed using a simple regression model. Predictions from this latter model further indicated that poor response to treatment may be due to differences in maximum effect (Imax) rather than in concentrations necessary to reach the half-maximum effect (IC50). In addition, simulations of BMD in lumbar spine and total hip provided similar results for both models.
Conclusion: Based on parsimony principles and on simulation outcome, our findings indicate that parameterisation of the RANK-RANKL-OPG system according to Pivonka is superior to that of Lemaire. Future research will 1) evaluate the performance of this model to describe the effect of drugs with different mechanisms of action and 2) relate short-term changes in biomarkers to long-term fracture risk.
References:
[1] V. Lemaire et al. J Theor Biol 229 (2004) 293-309
[2] P. Pivonka et al. Bone 43 (2008) 249-263
[3] J.C. Gallagher et al. J Clin Endocrinol Metab 86 (2001) 4717-4726
