Index: Margossian 2022 - Bayesian Pharmacometrics Stan Torsten

Margossian 2022 - Bayesian Pharmacometrics Stan Torsten

Routing Summary

Full capture of Margossian, Zhang & Gillespie, Flexible and efficient Bayesian pharmacometrics modeling using Stan and Torsten, Part I (CPT:PSP 2022; arXiv 2109.10184): two-compartment PK, event schedules, Stan workflow and diagnostics, PPC and LOO, population model with allometric scaling, Friberg-Karlsson PK/PD with numerical and coupled ODE solvers. 6 notes.

• Need the paper on one page or a section map? → Margossian 2022 - Bayesian Pharmacometrics - Overview
• Need the compartment ODE, event-schedule variables, likelihood and priors? → Margossian 2022 - Compartment Models and Event Schedules
• Need Stan blocks, $\hat{R}$, ESS or Table 2? → Margossian 2022 - Stan Workflow and MCMC Diagnostics
• Need posterior predictive checks, PSIS-LOO or NPDE/PIT? → Margossian 2022 - Posterior Predictive Checks and LOO
• Need the hierarchical population model, allometric scaling or the flip-flop constraint? → Margossian 2022 - Population Two-Compartment Model
• Need the nonlinear PK/PD ODE, solver choice, coupled solvers, or the discussion? → Margossian 2022 - Nonlinear PKPD and ODE Solvers
• Need dosing decisions from the posterior (PTA)? → Population PK Dosing Decisions from the Posterior (Concept Note)

Concept Map

Concept	Note	Type	Depends On	Key Result
Two-compartment oral model	Margossian 2022 - Compartment Models and Event Schedules	definition	linear ODE	$\hat{c}=u_{cent}/V_{cent}$, lognormal error
Event schedule (evid, addl, ii, ss)	Margossian 2022 - Compartment Models and Event Schedules	definition	NONMEM	doses and samples as rows
$\hat{R}$ and ESS	Margossian 2022 - Stan Workflow and MCMC Diagnostics	definition	MCMC	$n_{eff}\approx 100$ usually enough
Posterior predictive check	Margossian 2022 - Posterior Predictive Checks and LOO	algorithm	generated quantities	simulate $\tilde{y}$ from the posterior
PSIS-LOO	Margossian 2022 - Posterior Predictive Checks and LOO	definition	importance sampling	two-compartment beats one
Population model	Margossian 2022 - Population Two-Compartment Model	definition	hierarchical priors	${\vartheta }_j\sim \text{logN}(\log {\vartheta }_{pop},\Omega )$
Flip-flop constraint	Margossian 2022 - Population Two-Compartment Model	definition	identifiability	$k_a>{\lambda }_1$
Friberg-Karlsson model	Margossian 2022 - Nonlinear PKPD and ODE Solvers	definition	PK model	feedback $({\text{Circ}}_0/y_{circ}{)}^{\gamma }$, $E_{drug}=\min (\alpha \hat{c},1)$
Coupled solver	Margossian 2022 - Nonlinear PKPD and ODE Solvers	definition	one-way coupling	analytic PK + numerical PD

Notes

• Margossian 2022 - Bayesian Pharmacometrics - Overview — CONTAINS: question, five builds, Source Map, motivating example E64, marketing analogy.
• Margossian 2022 - Compartment Models and Event Schedules — CONTAINS: ODE system, Table 1, likelihood and priors, matrix-exponential code with verified profile.
• Margossian 2022 - Stan Workflow and MCMC Diagnostics — CONTAINS: HMC requirements, Stan blocks, $\hat{R}$/ESS, full Table 2 with interpretation.
• Margossian 2022 - Posterior Predictive Checks and LOO — CONTAINS: PPC algorithm, PSIS-LOO, one vs two compartments, NPDE/PIT remarks.
• Margossian 2022 - Population Two-Compartment Model — CONTAINS: population model, allometry, flip-flop, priors, PPC for new patients, noncentered PyMC sketch.
• Margossian 2022 - Nonlinear PKPD and ODE Solvers — CONTAINS: FK equations, solving ODEs in Stan, coupled solvers, discussion, verified nadir simulation.

Sources

Margossian 2022 - Bayesian Pharmacometrics with Stan and Torsten. Part II (divergences, prior predictive checks, solver tuning) is not covered.

See Also

Hierarchical Models, HMC and Stan in Practice, Chen 2018 - Adjoint Sensitivity Method.