Bioequivalence, bootstrapping and case-deletion diagnostics in a biologic: a model-based analysis of the effect of formulation differences in a monoclonal antibody
Justin J Wilkins, Aurélie Gautier, Phil J Lowe
Modeling & Simulation, Novartis Pharma AG, Basel, Switzerland
Objectives: The primary objective of this work was to ascertain, through an integrated PK/PD model-based approach, whether the pharmacokinetics of a monoclonal antibody in development and the pharmacodynamic responses of free and total IgE to this drug were similar for three different formulations - a reference formulation (A), and two alternatives (B and C). Difficulties in obtaining estimates of model parameter precision necessitated the use of resampling-based diagnostics.
Methods: Two studies employing an open-label, randomized, two-parallel-group, single subcutaneous injection design were used in the analysis, providing a total of 74 subjects with formulation A (study 1), 89 on formulation B (79 in study 1 and 10 in study 2), and 29 on formulation C (study 2). A previously-published instantaneous equilibrium drug-ligand binding and turnover population model  was adapted in NONMEM VI to allow estimation of the effects of formulation and study on key model parameters relative to formulation A, in a proportional manner such that an effect of zero would deliver an estimated parameter value of unity - allowing intutive estimation of the relative bioequivalence of formulations B and C for each parameter. Case-deletion diagnostics and bootstrapping were used at key decision points in model-building to detect influential outlying individuals, to provide accurate estimates of parameter confidence intervals, and to gauge model robustness.
Results: The core model parameter estimates were well-estimated and consistent with those obtained previously. The bootstrapping and case-deletion diagnostic procedures identified a significant study effect on the volumes of distribution of IgG, IgE and receptor-ligand complex, as well as absorption rate and binding constant. For formulation B, all ratio parameters were close to unity, with bootstrap-derived 90% confidence intervals within the range 0.80-1.25. With formulation C, the confidence intervals were outside the acceptance range of 0.80-1.25, such that bioequivalence with formulation A could not be shown.
Discussion: The model-based approach was effective in showing bioequivalence between the formulations A and B, but the low number of patients treated with formulation B in study 2 were not sufficient to allow successful bridging, clearly shown by the wide confidence intervals on the ratio parameters for formulation C. Case-deletion diagnostics and bootstrapping identified significant differences, previously undetected, in volume- and binding-related parameter estimates between studies, which produced a significant change in in the overall results of the modeling exercise when properly accounted for.
Conclusions: A model-based approach to showing bioavailability through parameter similarity was shown to be effective given sufficient appropriate data. Bootstrapping and case-deletion diagnostics were pivotal in highlighting previously-unidentified study differences, justifying the significant amounts of time required for their use.
 Hayashi N, Tsukamoto Y, Sallas WM, Lowe PJ. A mechanism-based binding model for the population pharmacokinetics and pharmacodynamics of omalizumab. Brit J Clin Pharmacol 2006;63: 548-561.