A. Janssen1, F.C. Bennis2, M.H. Cnossen3, and R.A.A. Mathôt1 for the OPTI-CLOT study group and SYMPHONY consortium
1 Department of Clinical Pharmacology, Hospital Pharmacy, Amsterdam University Medical Center, Amsterdam, The Netherlands. 2 Quantitative Data Analytics Group, Department of Computer Science, VU Amsterdam, Amsterdam, The Netherlands 3 Department of Pediatric Hematology, Erasmus MC Sophia Children’s Hospital, Erasmus University Medical Center Rotterdam, The Netherlands
Introduction: Pharmacokinetic (PK) guided dosing is a common approach for personalising prophylactic treatment of haemophilia A patients receiving standard or extended half-life factor VIII (SHL/EHL-FVIII) concentrate. For these FVIII concentrates, population PK models are available that allow for dose individualization based on the determination of FVIII activity levels in serial blood samples. These population models are frequently used to develop limited sampling strategies (LSSs). Here, Monte Carlo simulations are performed and multiple combinations of sampling times are evaluated for their accuracy in predicting individual PK parameters. However, often only a limited number of time points are evaluated and only accuracy with respect to simulated concentrations is reported.
Aside from prediction accuracy, prediction uncertainty is also an interesting metric as it might be more informative in practice. Generally, we do not know the true concentration and so we might prefer a more certain prediction to one that was accurate in simulations. In this work, we used Markov chain Monte Carlo sampling to describe the posterior distribution of individual PK parameters after taking samples at specific time points. Since Bayesian inference is typically computationally intensive, we used Bayesian Optimization (BO) to more efficiently search optimal sampling times.
Objectives: Design a BO procedure for automatic determination of optimal sampling times based on a population PK model. Compare its accuracy to a published LSS.
Methods: EHL-FVIII activity time profiles were simulated for 500 severe haemophilia A patients. Typical and individual PK parameters were simulated based on a previous PK study [1]. Each virtual patient received a single dose of 50 IU/kg EHL-FVIII concentrate. A two compartment model with inter-individual variability on the clearance and central volume parameters was implemented in the Turing probabilistic programming system (version 0.17.4)[2]. Based on FVIII activity measurements, this model determines the posterior distribution of the individual random effect parameters ηi. Goal of the algorithm was to find time points which result in the lowest posterior variance of ηi. This variance represents the residual uncertainty of the PK parameters. First, we sampled FVIII levels with noise at five random time points. Next, we fit a Gaussian process (GP) to these points which learned to predict the variance of ηi for each time point. Then, the randomized upper confidence bound acquisition function was used to select five additional time points such that the GP reliably represented the variance of ηi as a function of time [3]. Finally, we selected the minimum of this function as the optimal time point and repeated the procedure for three total measurements.
We compared the accuracy of the suggested BO-LSS to a LSS from the literature [4]. In the latter, a sample was collected at t = 1h, and two samples at 24, 48, or 72h for children, adolescents, and adults, respectively. We reported the accuracy of predictions using the root mean squared error (RMSE), the accuracy of ηi MAP estimates using mean absolute error (MAE), and the posterior variance of ηi as a representation of residual uncertainty.
Results: The BO-LSS identified two samples at t = 1h and one sample at t = 48h as optimal for all patients, independent of age. Although both sampling strategies displayed similar accuracy with RMSE values of 0.042 IU/mL, the BO-LSS obtained slightly more accurate peak FVIII activity predictions (t < 4h; RMSE of 0.087 vs. 0.082 IU/mL). In addition, MAP estimates by the BO-LSS were slightly more accurate (MAE clearance: 0.17 vs. 0.18, central volume: 0.084 vs. 0.091). Residual uncertainty following the BO-LSS was lower for central volume (σ2: 0.0071 vs. 0.012), but higher for clearance (σ2: 0.01 vs. 0.0071).
The analysis also showed that as the number of samples increased, timing became less and less important for reducing uncertainty. Sample timing was crucial when taking a single sample, but did not affect the uncertainty reduction after taking samples at t = 1 and 48h.
Conclusions: BO allows for an automated approach to creating LSSs, evaluating all time points concurrently. It also allows for the quantification of the benefit of taking an additional sample on a per patient basis. By using residual uncertainty instead of accuracy the BO-LSS also produces an interpretable measure of performance for use in practice.
References: [1] Nestorov, Ivan, et al. “Population pharmacokinetics of recombinant factor VIII Fc fusion protein.” Clinical pharmacology in drug development 4.3 (2015): 163-174. [2] Ge, H., Xu, K., & Ghahramani, Z. (2018, March). “Turing: a language for flexible probabilistic inference.” International conference on artificial intelligence and statistics (pp. 1682-1690). PMLR. [3] Berk, J., Gupta, S., Rana, S., & Venkatesh, S. (2020). Randomised gaussian process upper confidence bound for bayesian optimisation. arXiv preprint arXiv:2006.04296. [4] McEneny-King, Alanna, et al. “Limited sampling strategies for accurate determination of extended half-life factor VIII pharmacokinetics in severe haemophilia A patients.” Haemophilia 27.3 (2021): 408-416.
Reference: PAGE 30 (2022) Abstr 10072 [www.page-meeting.org/?abstract=10072]
Poster: Methodology - Study Design