Pharmacokinetics (PK) describes what the body does to a drug — absorption, distribution, metabolism, and elimination — while pharmacodynamics (PD) describes what the drug does to the body — the relationship between drug concentration and effect. Together, PK/PD modeling is essential for determining appropriate dosing regimens. Bayesian methods, particularly hierarchical (population) models, have become the standard approach because they naturally handle the sparse, unbalanced data typical of clinical settings.
Population PK/PD Modeling
In a population PK model, each patient's parameters (clearance, volume of distribution, absorption rate) are drawn from a population distribution. The hierarchical structure allows information to flow both ways: population data inform individual estimates, and individual data refine population parameters. This is precisely the partial pooling that Bayesian hierarchical models provide.
Population level: θᵢ = g(covariatesᵢ, β) + ηᵢ
where ηᵢ ~ N(0, Ω) and εᵢⱼ ~ N(0, σ²)
θᵢ = individual PK parameters, β = population fixed effects, Ω = between-subject variability
The nonlinear mixed-effects model (NLME) is the traditional frequentist approach, implemented in NONMEM software. The Bayesian alternative, implemented in tools like Stan, Pumas, and BUGS, offers several advantages: natural handling of complex models, exact uncertainty quantification through posterior distributions, and the ability to incorporate informative priors from previous studies.
Bayesian Individualized Dosing
The clinical power of Bayesian PK/PD lies in therapeutic drug monitoring (TDM). When a patient has one or two drug concentration measurements, Bayesian estimation combines these sparse data with the population prior to produce an individualized posterior distribution for that patient's PK parameters. This posterior then drives dose adjustments to target a therapeutic concentration range. Software tools like MwPharm, InsightRX, and DoseMeRx implement this approach at the bedside.
Bayesian TDM is most critical for drugs with narrow therapeutic indices — where the difference between an effective dose and a toxic dose is small. Aminoglycoside antibiotics, vancomycin, immunosuppressants (tacrolimus, cyclosporine), and chemotherapy agents all benefit from Bayesian dose individualization. For these drugs, population-based dosing leads to unacceptable rates of toxicity or treatment failure, and Bayesian methods measurably improve patient outcomes.
Dose-Response Modeling
Bayesian PD models characterize the relationship between drug exposure and clinical response. The Emax model — relating concentration to effect through a maximum effect and an EC50 parameter — is commonly fit within a Bayesian framework. Model uncertainty about the dose-response curve shape can be addressed through Bayesian model averaging across candidate models (linear, log-linear, Emax, sigmoid Emax), providing more robust predictions for dose selection in Phase II trials.
"The Bayesian approach to PK/PD modeling is not merely a statistical preference — it is a clinical necessity for drugs where getting the dose wrong means the difference between cure and catastrophe." — Roger Jelliffe, pioneer of Bayesian therapeutic drug monitoring
Current Frontiers
Physiologically-based pharmacokinetic (PBPK) models, which simulate drug disposition through mechanistic organ-level compartments, are increasingly calibrated using Bayesian methods. Machine learning combined with Bayesian PK/PD enables model-informed precision dosing in real time. And Bayesian optimal design methods guide the selection of sampling times in PK studies, minimizing patient burden while maximizing information about key parameters.