Karsten Kuritz1, Daniel Kaschek1, Daniel Lill1, Nathalie Gobeau2
1IntiQuan AG, 2MMV Medicines for Malaria Venture
Background Poor-identifiability of parameters pose a major challenge in population modeling, slowing down model development and potentially leading to unreliable models. For example, when using the Stochastic Approximation Expectation Maximization (SAEM) algorithm, common in industry-standard software like NONMEM and Monolix, non-identifiability can lead to convergence issues and unreliable Fisher information matrices. The reported, large RSE in such cases may not reflect potential non-linearities of the likelihood function. In trial simulations, this might lead to predictions involving extreme parameter values, compromising the reliability of simulation outcomes. While advanced tools used in quantitative systems pharmacology (QSP) employ gradient-based methods and profile likelihoods for efficient parameter estimation and assessment of identifiability issues, these methods do not generally account for inter-individual variability, critical for population modeling. Aim •To present a framework for population modeling that supports profile-likelihood-based decision-making during model development. •To demonstrate the application of this framework through a realistic PK/PD model development example. Methods To address parameter identifiability during model development, we employed a deterministic trust-region algorithm that utilizes first- and second-order derivatives of the log-likelihood function. These derivatives were computed using analytically derived sensitivity equations [1], ensuring robustness and precision during optimization. The availability of both gradient and Hessian information allows for more sophisticated statistical methods, such as likelihood profiling [2]. Inter-individual variability was incorporated using a penalized maximum likelihood approach, equivalent to maximum a posteriori (MAP) estimation in a Bayesian context. This approach is computationally inexpensive compared to the SAEM algorithm while still providing reasonable individual parameter estimates. The framework is implemented in an industry-ready software package. Results We applied this approach in a pharmacometric workflow for malaria where the drug’s killing rate of was related to drug concentration using an Emax model [3]. When using standard SAEM methods, the Hill coefficient was non-identifiable, as indicated by large RSEs. Simulations with uncertainty from such a model would produce predictions with Hill coefficient values ranging from unrealistically low to excessively high. By employing profile-likelihood analysis, we found the likelihood profile for the Hill parameter to be right-open, indicating that values below 3 are unsupported by the data, while values above 4 are equally likely. We proceeded by fixing the Hill coefficient at 4, resulting in a well-identifiable model that takes individual variability in Emax and EC50 into account. Conclusion The proposed framework offers a robust and efficient approach to addressing poor parameter identifiability in population models. By utilizing profile-likelihood analysis, we were able to detect and correct non-identifiable parameters early in the model development process, ensuring reliable predictions based on well-supported parameter values. This framework, implemented in an industry-ready software package, significantly speeds up model development and improves the overall reliability of pharmacometric analyses.
[1] A. Raue, M. Schilling, J. Bachmann, A. Matteson, M. Schelker, D. Kaschek, S. Hug, C. Kreutz, B.D. Harms, F.J. Theis, U. Klingmuller, J. Timmer. Lessons learned from quantitative dynamical modeling in systems biology. PLoS ONE 8, 2013 [2] C. Kreutz, A. Raue, D. Kaschek, J. Timmer. Profile likelihood in systems biology. FEBS Journal 280, 2013, 2564-2571 [3] B.E. Barber, R. Webster, A.J. Potter, S. Llewellyn, N. Sahai, I. Leelasena, S. Mathison, K. Kuritz, J. Flynn, S. Chalon, A.C. Marrast, N. Gobeau, J.J. Moehrle. Characterising the blood-stage antimalarial activity of pyronaridine in healthy volunteers experimentally infected with Plasmodium falciparum. Int J Antimicrob Agents 64, 2024, 107196
Reference: PAGE 33 (2025) Abstr 11518 [www.page-meeting.org/?abstract=11518]
Poster: Methodology - Estimation Methods