Time-to-Event and Disease Progression Models

Understand how pharmacometric models extend beyond concentration and effect to capture event timing and disease dynamics.
Tip

What you’ll build today: a clear understanding of how pharmacometrics models when events happen and how disease evolves over time.

Learning Objectives

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

  • Define time-to-event (TTE) models
  • Understand disease progression models
  • Distinguish event timing vs continuous response
  • Recognize when these models are needed

Key Ideas

So far, you’ve seen:

  • PK → concentration
  • PD → effect

Now we extend further:

What happens over time at the clinical level?

This includes:

  • When an event occurs (e.g., death, relapse)
  • How disease changes over time

Extending the Modeling Chain

Pharmacometrics often expands from:

Dose
↓
PK
↓
PD
↓
Clinical Outcome

But clinical outcomes can appear in different forms:

  • continuous outcomes → disease progression
  • event outcomes → time-to-event

This allows pharmacometric models to connect biology to real patient outcomes.

Why This Lesson Matters

Not all outcomes are:

  • continuous (like concentration)
  • directly observable at every time

Many are:

  • discrete events
  • long-term disease changes

Example:

  • Time until tumor progression
  • Time until adverse event
  • Disease severity over months

Time-to-Event (TTE) Models

TTE models focus on:

When does an event occur?

Instead of modeling magnitude, we model:

  • probability of event over time

Hazard Concept

Key idea:

  • hazard = instantaneous risk of event

Conceptually:

\[ h(t) = \text{instantaneous event risk at time }t \]

Interpretation:

  • higher hazard → event more likely soon
  • lower hazard → event less likely soon

Worked Example: Event Timing

Interpretation:

  • early times → most individuals remain event-free
  • later times → more events accumulate

TTE models aim to explain and predict this behavior.

Disease Progression Models

These models describe:

How disease changes over time

Examples:

  • Tumor growth
  • Biomarker progression
  • Functional decline

Interpretation:

  • untreated → disease worsens over time
  • treatment → changes the trajectory

Insight

Disease progression provides the underlying trajectory, while treatment modifies it.

Note

Drug effect is often modeled as a deviation from natural disease progression.

Expanding the Idea

You can combine:

  • disease progression + treatment effect
  • exposure–response + time dynamics

This allows modeling:

  • slowing disease
  • delaying events
  • improving outcomes

Why This Matters for Decisions

These models support:

  • clinical trial endpoints
  • survival analysis
  • long-term predictions

Example:

  • Does treatment delay progression?
  • Does it improve survival?

Strategies

  • Use TTE for event-based outcomes
  • Use progression models for longitudinal disease
  • Combine with exposure when needed

Common Mistakes

  • Treating event timing like continuous data
  • Ignoring censoring
  • Misinterpreting hazard

Practice Problems

  1. What does a TTE model describe?
  2. What is disease progression?
  3. Why are these models important?
  1. Timing of events
  2. Change in disease over time
  3. They capture clinically meaningful outcomes

Summary

TTE and disease progression models:

  • extend PMx beyond PK/PD
  • focus on clinical outcomes
  • capture time dynamics
  • TTE = when events happen
  • Disease progression = how disease changes
  • Time is central
  • Combine with exposure when needed