Margossian 2022 - Bayesian Pharmacometrics - Overview
Summary
Margossian, Zhang & Gillespie (CPT: Pharmacometrics & Systems Pharmacology, 2022; arXiv 2109.10184, “Part I”) is a worked tutorial on a full Bayesian workflow for pharmacokinetic/pharmacodynamic (PK/PD) models: a two-compartment oral-dose model, a hierarchical population model with allometric scaling, and a nonlinear Friberg-Karlsson PK/PD ODE system, in Stan with the Torsten extension. Takeaway: ODE likelihoods + hierarchical priors + posterior predictive checks + PSIS-LOO form a complete, reusable recipe.
Overview
Problem. Pharmacometric models are ODE systems driven by a clinical event schedule (doses, infusions, measurements). Mixed-effects (population) structure pools patients. Existing tools (NONMEM, Monolix, nlmixr) are specialized; the authors argue Stan’s flexibility (non-normal random effects, custom priors, multiple submodels) and diagnostics are valuable, and Torsten supplies event-schedule handling, analytic PK solvers and group parallelization.
What the paper builds.
- A single-patient linear two-compartment model with first-order absorption, lognormal residuals, 1200 mg q12h x 14 doses (simulated) (Margossian 2022 - Compartment Models and Event Schedules).
- The Stan program structure and the inference checks: , bulk/tail ESS, trace plots (Margossian 2022 - Stan Workflow and MCMC Diagnostics).
- Posterior predictive checks and leave-one-out comparison of one vs two compartments (Margossian 2022 - Posterior Predictive Checks and LOO).
- A hierarchical population model with allometric weight scaling and a flip-flop identifiability constraint (Margossian 2022 - Population Two-Compartment Model).
- A nonlinear PK/PD model (Friberg-Karlsson myelosuppression) solved with numerical ODE solvers, plus Torsten’s coupled solver (Margossian 2022 - Nonlinear PKPD and ODE Solvers).
Source Map
| Paper section | Covered in |
|---|---|
| 1 Introduction (why Stan, Torsten; NONMEM comparison) | this note; Margossian 2022 - Nonlinear PKPD and ODE Solvers (Sec. 5 discussion) |
| Bayesian inference notation and workflow; setting up Stan/Torsten | Margossian 2022 - Stan Workflow and MCMC Diagnostics |
| 2.1-2.2 Two-compartment model, event schedule (Table 1), statistical model and priors | Margossian 2022 - Compartment Models and Event Schedules |
| 2.3-2.4 Stan program blocks, calling from R | Margossian 2022 - Stan Workflow and MCMC Diagnostics |
| 2.5 Checking inference (, ESS; Table 2; Fig. 1) | Margossian 2022 - Stan Workflow and MCMC Diagnostics |
| 2.6-2.7 Posterior predictive checks, LOO (Figs. 2-4) | Margossian 2022 - Posterior Predictive Checks and LOO |
| 3 Population model (Figs. 5-6), NPDE/PIT remarks | Margossian 2022 - Population Two-Compartment Model |
| 4 Nonlinear PK/PD (Friberg-Karlsson, Figs. 7-8), ODE solving, coupled solvers | Margossian 2022 - Nonlinear PKPD and ODE Solvers |
| 5 Current/potential role, Part II preview | Margossian 2022 - Nonlinear PKPD and ODE Solvers |
Motivating PyMC examples
Listed at https://redam94.github.io/pymc-challenges/examples.html :
- E64 - Population pharmacokinetics: hierarchical compartment models and dosing decisions (theophylline, 12 subjects; warfarin PK/PD, 32 subjects): one-compartment oral model in closed form, hierarchical priors, dosing decisions from the posterior. See also Population PK Dosing Decisions from the Posterior (Concept Note).
- E54 (patch-clamp conductance model) and E50-E61 (reaction-diffusion, signaling) use the same pattern: mechanistic ODE/PDE as the likelihood mean plus a measurement model; see Likelihoods Built on Differential Equations (Concept Note).
Source substitution
The brief suggested this paper as the open popPK/NLME source (alternative: Gelman, Bois & Jiang 1996, JASA, not freely available). The classic Gelman-Bois-Jiang population PK paper is cited in the concept note but was not ingested.
Relevance to marketing measurement
Structurally this is a Bayesian hierarchical nonlinear model with latent dynamics driven by an intervention schedule: doses are ‘spend events’, compartments are carry-over stocks, clearance is decay. The pharmacometric practice of (i) putting hierarchical priors on log-scale mechanistic rates, (ii) checking with PPCs on new hypothetical subjects, and (iii) PSIS-LOO model comparison transfers to adstock/saturation MMMs with geo-level partial pooling; see Hierarchical Models and Bayesian Estimation and Priors for MMM. This is an analogy, not a claim from the paper.
Connections
HMC and Stan in Practice, Prior Predictive Checking, Posterior Predictive Checking, Overfitting and Information Criteria, Chen 2018 - Adjoint Sensitivity Method (sensitivities for the ODE gradients), Linear-Gaussian State-Space Models.
See Also
Chen 2018 - Neural ODEs - Overview, Izmailov 2021 - Bayesian Neural Network Posteriors - Overview.