Modeling for Pharmacometrics

A PMx-first modeling sequence in R: from questions and assumptions to hierarchical nonlinear models, diagnostics, and professional modeling judgment.
Tip

How to use this section:
These lessons build a modeling ladder — from simple exploratory tools to nonlinear mixed-effects models. The goal is not just to fit models, but to think clearly about structure, variability, and decision relevance.

Learning Objectives

By the end of this module, you will be able to:

  • Translate PMx questions into structured quantitative models.
  • Move deliberately from exploratory (lm, nls) to hierarchical (lme, nlme) thinking.
  • Understand pooling vs grouped vs mixed-effects modeling.
  • Parameterize PK models using CL/V form and interpret derived quantities (e.g., \(k_e\), half-life).
  • Evaluate model diagnostics responsibly.
  • Recognize when classical tools are sufficient — and when they are not.
  • Articulate modeling limitations and justify escalation to advanced PMx frameworks.

Why Modeling Matters in PMx

Before building a full population PK model, you should be able to answer:

  • What scientific decision does this model inform?
  • What structural assumptions are plausible from the data?
  • Where does variability originate (between-subject, residual, design)?
  • Are patterns consistent across individuals?
  • Are parameters biologically interpretable?
  • What would make this model misleading?

Modeling is not equation-fitting.
It is structured scientific reasoning.

Warning

A model that fits well but answers the wrong question is worse than no model at all.
Start with the decision, then build the simplest defensible structure.

The Modeling Ladder in This Module

This module is intentionally ordered. Each lesson builds on the previous one.

  1. Why We Model: Questions, Assumptions, and Decisions
  2. A Minimal Modeling Workflow in R
  3. Linear Models as First-Pass PK/PD Insight
  4. Nonlinear Modeling with nls(): Dose-Response and Saturation
  5. Variability and Hierarchy: Mixed-Effects Intuition
  6. Mixed-Effects Models in Practice with lme()
  7. Nonlinear Mixed-Effects Modeling with nlme()
  8. Diagnostics, Limitations, and Transition to Advanced PMx Frameworks

Datasets Used

Throughout this module, we primarily use:

  • Theoph (base R) for concentration–time modeling
  • PBG (nlme package) for dose–response modeling

These are intentionally well-behaved teaching datasets that allow you to focus on modeling logic rather than data chaos.

What This Module Emphasizes

This section emphasizes:

  • Clear scientific questions before modeling
  • Structural thinking before statistical complexity
  • CL/V parameterization for interpretability
  • Hierarchical modeling for realistic variability
  • Diagnostics as tools for trust
  • Modeling judgment as a professional skill

What This Module Is Not

This module is not:

  • A full population PK course
  • A simulation workflow course
  • A Bayesian modeling course
  • A regulatory reporting manual

Those build directly on this foundation.

After This Module

You will be prepared to:

  • Approach nlmixr2, mrgsolve, or Bayesian tools with structural clarity
  • Interpret variability components meaningfully
  • Debug models systematically
  • Communicate modeling decisions clearly to interdisciplinary teams

Exploratory and classical modeling are not stepping stones to discard —
they are the conceptual core of responsible PMx work.