Dominic MH Tong (1), Jasmine H Hughes (1), Ron J Keizer (1)
(1) InsightRX, San Francisco, CA
Objectives: Model-informed precision dosing (MIPD) combines prior knowledge about drug pharmacokinetics/pharmacodynamics (PK/PD) with patient data to predict the likelihood of a patient experiencing a target drug exposure and/or toxicity. Current Bayesian clinical decision support tools typically rely on maximum a posteriori (MAP) estimation to make predictions and infer optimal future doses. MAP is known to be biased in some scenarios compared to full-Bayesian Hamiltonian Monte Carlo (HMC) approaches that sample from the posterior [1], and hence may not necessarily predict the most probable outcome nor quantify the risk of sub- or supratherapeutic drug exposure or of toxicity. Here, we compare methods that estimate the full posterior distribution to MAP to quantify the probability of pharmacokinetic target attainment or toxicity in three simulated clinical scenarios.
Methods: Target metrics were calculated for a full Bayes approach (HMC) and a MAP Bayes approach in three scenarios. The first scenario was a two-compartment linear PK model of vancomycin, with an exposure target of 400-600 ugh/mL AUC [2]. The second scenario was a nonlinear PK model of voriconazole, with target trough concentration > 1 ug/mL. The third scenario was a nonlinear PK/PD model of oncological chemotherapy, modeling the risk of neutropenia. We defined the acceptable level of toxicity to be a 10% or higher risk of stage 3 or 4 neutropenia (neutrophil count < 1.0 x 10^9 cells/L [3]).
HMC was implemented using the open source R package PKPDposterior [4], a light-weight API for using Torsten/Stan in MIPD scenarios [5, 6]. MAP estimation was performed using the BFGS method in R’s general purpose optim optimizer [7]. Probabilities of PK/PD target attainment or toxicity based on these MAP estimates were calculated using the open source PKPDsim framework according to two approaches for estimating uncertainty [8]: 1) the Delta method (“MAP delta”) and 2) via simulating variability by repeatedly drawing from the variance-covariance matrix at the maximum likelihood (“MAP sim”).
Results: Estimated AUC target attainment for vancomycin (median, IQR) was similar between MAP sim (72.5, 30.4-89%) and HMC (73.8, 36.5-90%), with MAP delta (31.9, 0.3-89.6%) under-predicting target attainment relative to HMC. Estimated target attainment for voriconazole was predicted to be lower using HMC (76, 49-98%) compared to MAP sim (100, 70-100%) or MAP delta (100, 80-100%). For the PK/PD neutropenia model, 12.5% of patients simulated would have a lower dose given using HMC than MAP, given an acceptable severe neutropenia risk (stage 3 or 4) of 10% or less. These PK results suggest that while MAP and HMC show good agreement in estimating target attainment in linear PK models, meaningful discrepancies in uncertainty may arise in nonlinear and/or PD modeling situations.
Conclusions: MAP-based Bayesian inference underestimates the spread in posterior distribution compared to full Bayesian estimation, especially in nonlinear PK/PD models. Differences in the probability of drug exposure target attainment or drug-related toxicity can have important ramifications on clinical decision-making.
References:
[1] Maier et al. CPT-PSP 2020. DOI: 10.1002/psp4.12492
[2] Rybak et al. Am J Health-Syst Pharm 2020. DOI: https://doi.org/10.1093/ajhp/zxaa036
[3] US National Institutes of Health. Common Terminology Criteria for Adverse Events 2017.
[4] Hughes et al. PAGE 2022 abstract.
[5] Stan Development Team. 2019. https://mc-stan.org
[6] Torsten Development Team. 2021. https://github.com/metrumresearchgroup/Torsten
[7] R Core Team (2020). https://www.R-project.org/
[8] Wicha et al. PAGE 2015.
Reference: PAGE 30 (2022) Abstr 10233 [www.page-meeting.org/?abstract=10233]
Poster: Methodology - Estimation Methods