Franziska Thoma (1,2), Manfred Opper (3), Jana de Wiljes (1), Niklas Hartung (1), Wilhelm Huisinga (1)
(1) Institute of Mathematics, University of Potsdam, Germany (2) Graduate Research Training Program PharMetrX: Pharmacometrics & Computational Disease Modelling, Freie Universität Berlin and University of Potsdam, Germany (3) Institute of Software Engineering and Theoretical Computer Science, Technische Universität Berlin
Introduction: In model-informed precision dosing, PK/PD models are used to predict therapy outcomes based on patient characteristics and data from therapeutic drug/biomarker monitoring (TDM). The individual model parameters are given by a statistical model based on estimates of the typical population mean and interindividual variability from prior population analyses. As these prior values are derived from clinical study data and thus a specific subpopulation, it is prudent to analyse whether the target population is sufficiently well represented by the prior information, as a bias may be introduced due to a population shift [1,2]. To avoid this, prior information should be updated by assimilating additional patient data [1].
A sequential Bayesian hierarchical modelling (sBHM) framework was introduced by Maier et al. [3]. The Bayesian part allows to account for uncertainty in the population parameters, while the specific sequential approach avoids the need to access individual patient data for updating the hyper-population parameters. Through analysis of a large virtual patient population using a semimechanistic PK/PD model of chemotherapy induced neutropenia [4], it was shown that the framework is able to correct for bias in the prior information when densely sampled TDM data is available. In a sparser TDM data situation, which is closer to clinical reality, bias was much less corrected for.
Objectives: To develop a simple hierarchical model representation and to study sequential and fully BHM approaches for their ability of bias correction for different data samplings and the impact of simplifying assumptions.
Methods: The sBHM framework [3] is based on a two-stage hierarchical approach as encountered in meta-analysis [5]. Therein, data from clinical studies is analysed independently in stage 1 to obtain posterior distributions for the individual model parameters via an MCMC approach. In stage 2, the joint posterior distribution of population and individual parameters is iteratively sampled using Gibbs sampling. The individual parameters are sampled from the posterior distributions of stage 1, but are now assumed to arise from a common distribution defined by the hyperparameters.
In using the sBHM approach in [3], the stage 1 analysis is not performed in batch, i.e. with data from a large number of patients simultaneously. Rather, for each patient at a time, it is processed in stages 1 and 2 as described, and the marginal posterior distribution of the population parameters is used to update the hyper-population parameters in a parametric approximation. This procedure allows carrying forward information from all previous patients without storing the data, while also ensuring that sampling in stage 2 can be performed in closed form. The distributional assumptions that are propagated may, however, introduce additional biases and thus restrict our ability to estimate the correct population parameters.
Results: We developed a simple and illustrative representation of a BHM that allowed us to easily analyse the performance of sequential and fully BHM approaches under different sampling scenarios and based on different numerical and analytical approximations. For this, we choose a classical Beta-Bernoulli model and allow for uncertainty in the population parameters (parameters of the beta distribution) by a hyperprior. Due to the similar underlying hierarchical structure, this model is suitable for evaluation of our hypotheses for the source of bias in the estimation of hyper-population parameters. Using generated data, we showed that the correct population parameters can be estimated in a fully BHM approach in both dense and sparse TDM data scenarios, allowing us to distinguish between estimation biases due to sparsity in the TDM data versus the distributional assumptions enforced within the sBHM approach.
Conclusions: To investigate the general BHM for estimation of population parameters, we have developed a simple representation using a Beta-Bernoulli-Hyperprior model. This allows us to study and explain different sampling and approximation methods within the sBHM framework as well as other methods like hierarchical particle filters for their performance and suitability in sequential modelling with the specific restrictions applying to data accessibility and storage.
References:
[1] Keizer, Ron J., et al. “Model‐informed precision dosing at the bedside: scientific challenges and opportunities.” CPT: pharmacometrics & systems pharmacology 7.12 (2018): 785-787.
[2] Polasek, Thomas M., Sepehr Shakib, and Amin Rostami-Hodjegan. “Precision dosing in clinical medicine: present and future.” Expert review of clinical pharmacology 11.8 (2018): 743-746.
[3] Maier, Corinna, et al. “A continued learning approach for model‐informed precision dosing: Updating models in clinical practice.” CPT: Pharmacometrics & Systems Pharmacology 11.2 (2022): 185-198.
[4] Henrich, Andrea, et al. “Semimechanistic bone marrow exhaustion pharmacokinetic/pharmacodynamic model for chemotherapy-induced cumulative neutropenia.” Journal of Pharmacology and Experimental Therapeutics 362.2 (2017): 347-358.
[5] Lunn, David, et al. “Fully Bayesian hierarchical modelling in two stages, with application to meta‐analysis.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 62.4 (2013): 551-572.
Reference: PAGE 30 (2022) Abstr 10188 [www.page-meeting.org/?abstract=10188]
Poster: Methodology - Estimation Methods