Second-order indirect response modelling of complex biomarker dynamics

Objectives: Biomarker dynamics in response to drug action may not always be fully understood. Redundant pathways, tolerance, feedback and counter-regulation may be such that the response to a drug stimulus can show complex patterns [1-3]. This motivates the present work, where a new pharmacokinetic/pharmacodynamic (PK/PD) approach inspired by indirect response modelling (IRM) [4] and precursor-dependent IRM [5] is investigated. Methods: We propose a novel family of PK/PD models that feature a zero-order rate constant kin of precursor formation, and a first-order rate constant k of conversion from precursor to response. Drug concentration is assumed to modulate simultaneously kin and k (potentially by stimulation or inhibition) through specific SC50 or IC50 parameters. The rate of response dispersion can be assumed equal to k to reduce model complexity. The proposed models can structurally describe complex patterns, such as the combination of (i) inverse response (i.e. a drop of response levels immediately after dosing, followed by an increase above baseline level), (ii) fast achievement of peak response followed by slow return to baseline, after single dose, and (iii) average increase from baseline at steady-state, after repeated dosing. The mathematical properties of the proposed PK/PD models and the sensitivity of response profiles to parameter changes were investigated by simulation. Model identifiability was assessed using NONMEM version 7.1 [6] to perform parameter estimation. Results: In the sensitivity analysis, the new approach could describe a wide range of response profiles, following both single and repeated-dose administration. In particular, different real-life patterns of response could be reproduced. Simulations showed that, under a suitable study design, model parameters could be estimated with good precision. Moreover, the proposed approach was able to reconstruct both population and individual profiles. Conclusions: These results confirm the feasibility of a modeling approach for longitudinal data characterized by complex features. This approach extends and complements the well-known methodology of IRM [2,5], and is especially appealing when the mechanism of action of a drug is known (or assumed) to impact both the response itself and a precursor of response. Additionally, the proposed approach can be used effectively to describe inhibition of clearance for both a parent drug and its metabolite, in presence of a second drug that inhibits certain metabolic pathways (e.g. CYP3A4). References: [1] C. van Kesteren, A.S. Zandvliet, M.O. Karlsson et al. (2005). Semi-physiological model describing the hematological toxicity of the anti-cancer agent indisulam. Invest. New Drugs 23:225-234. [2] A. Russu, E. Marostica, S. Zamuner et al. (2012). A new, second-order indirect model of depression time course. Population Approach Group in Europe 21st Meeting, Abstract 2516. [3] I. Ortega Azpitarte, A. Vermeulen, V. Piotrovsky (2006). Concentration-response analysis of antipsychotic drug effects using an indirect response model. Population Approach Group in Europe 15th Meeting, Abstract 995. [4] N.L. Dayneka, V. Garg, W.J. Jusko (1993). Comparison of four basic models of indirect pharmacodynamic responses. J. Pharmacokinet. Biopharm. 21:457-478. [5] D.E. Mager, E. Wyska, W.J. Jusko (2003). Diversity of mechanism-based pharmacodynamic models. Drug Metab. Dispos. 31:510-519. [6] Beal, S.L., Sheiner, L.B., Boeckmann, A.J. (Eds.), 1989-2006. NONMEM Users Guides. Icon Development Solutions, Ellicott City, Maryland, USA.