Why Simulate?

Understand why simulation is central to pharmacometric modeling and how it differs from estimation.
Tip

Big picture: Estimation learns from observed data. Simulation uses a model to explore what could happen.

Learning Objectives

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

  • explain why pharmacometricians simulate
  • distinguish estimation from simulation
  • describe what-if questions
  • understand prediction versus observation
  • connect simulation to model-informed decisions

Key Ideas

  • estimation uses data to learn model parameters
  • simulation uses a model to generate predictions
  • simulation explores scenarios
  • simulation supports decisions

Setup

library(tidyverse)
library(rxode2)

This lesson uses a simple simulated PK model.

No estimation is performed.

New Tools Introduced in This Module

This module introduces simulation tools from rxode2.

Think of them as three connected pieces.

Function Role
rxode2() defines the model
et() defines events and scenarios
rxSolve() generates simulated outcomes

Conceptually:

Model

+

Scenario

↓

Simulation

Example:

pk_model <- rxode2(...)

ev <- et(...)

sim <- rxSolve(pk_model, ev)

Interpretation:

rxode2()
↓
Defines system behavior


et()
↓
Defines what happens


rxSolve()
↓
Computes predictions

In later lessons, rxSolve() will also simulate directly from fitted nlmixr2 models.

Estimation versus Simulation

Estimation asks:

Given data, what parameters explain the observations?

Simulation asks:

Given a model, what outcomes might occur?

Conceptually:

Estimation: Data → Model Parameters

Simulation: Model Parameters → Predicted Outcomes

Both are essential.

They answer different questions.

Why Simulate?

Simulation lets us ask questions that may not be directly answered by the observed data.

Examples:

  • What if the dose changes?
  • What if dosing happens more often?
  • What if patients differ in clearance?
  • What response should we expect later?
  • What variability should we expect?

Simulation turns a fitted model into a prediction engine.

Worked Example 1: Define a Simple PK Model

Use a one-compartment oral PK model.

pk_model <-
  rxode2({
    ka <- 1
    cl <- 3
    v <- 30

    d/dt(depot) = -ka * depot
    d/dt(center) = ka * depot - cl / v * center

    cp = center / v
  })

pk_model
rxode2 5.1.1 model named rx_f69a20fda9fa08656c71fb657d14e6dd model (✔ ready). 
x$state: depot, center
x$params: ka, cl, v
x$lhs: cp

The printed model summarizes the variables and parameters that define the system.

The differential equations describe how drug amount changes in the depot and center compartments over time.

Notice that the output lists:

x$state: depot, center
x$params: ka, cl, v
x$lhs: cp

The states are quantities that change over time according to the differential equations.

The parameters are fixed values used by those equations.

The quantity cp appears under x$lhs because it is a calculated model output:

cp = center / v

Unlike depot and center, cp is not a compartment. It is a derived quantity that represents concentration.

Later, when we simulate the model, cp will appear in the simulation output as the predicted concentration.

This model describes:

Dose
↓
Absorption
↓
Central Amount
↓
Concentration

Worked Example 2: Define a Dosing Scenario

Simulation requires a scenario.

Here we simulate a single oral dose.

ev_100 <-
  et(amt = 100, cmt = "depot") %>%
  et(seq(0, 24, by = 0.25)) # add sampling

ev_100
── EventTable with 98 records ──
1 dosing records (see x$get.dosing(); add with add.dosing or et)
97 observation times (see x$get.sampling(); add with add.sampling or et)
── First part of x: ──
# A tibble: 98 × 4
    time cmt     amt evid         
   <dbl> <chr> <dbl> <evid>       
 1  0    depot   100 1:Dose (Add) 
 2  0    <NA>     NA 0:Observation
 3  0.25 <NA>     NA 0:Observation
 4  0.5  <NA>     NA 0:Observation
 5  0.75 <NA>     NA 0:Observation
 6  1    <NA>     NA 0:Observation
 7  1.25 <NA>     NA 0:Observation
 8  1.5  <NA>     NA 0:Observation
 9  1.75 <NA>     NA 0:Observation
10  2    <NA>     NA 0:Observation
# ℹ 88 more rows

The printed event table summarizes the simulation scenario.

Notice that it contains:

  • one dosing record
  • multiple observation times

The dosing record specifies what happens to the virtual subject:

100 mg dose into the depot compartment at time 0

The observation records specify when model predictions should be returned.

In this example, predictions are requested every 0.25 hours from 0 to 24 hours.

Because cp was defined as a model output, concentration predictions for cp will be returned at each observation time.

Interpretation:

100 mg dose → predict concentration over 24 hours

The event table defines what happens to the virtual subject and when model predictions are requested.

Worked Example 3: Simulate Concentration

Run the simulation.

sim_100 <-
  rxSolve(pk_model, ev_100) %>%
  as_tibble()

Inspect the output.

sim_100 %>% head()
# A tibble: 6 × 4
   time    cp depot center
  <dbl> <dbl> <dbl>  <dbl>
1  0    0     100      0  
2  0.25 0.728  77.9   21.8
3  0.5  1.28   60.7   38.3
4  0.75 1.69   47.2   50.6
5  1    1.99   36.8   59.7
6  1.25 2.21   28.7   66.2

The simulation output is a dataset.

Each row corresponds to a time point from the event table.

The column cp appears because we defined it in the model as:

cp = center / v

So cp is the predicted concentration returned by the simulation.

Plot the concentration profile.

ggplot(sim_100, aes(time, cp)) +
    geom_line() +
    labs(
        title = "Simulated Concentration After 100 mg",
        x = "Time",
        y = "Concentration"
    )

Interpretation:

The model generates concentration values over time.

These are predictions, not observations.

Worked Example 4: Ask a What-If Question

Now ask:

What if the dose were higher?

Simulate 200 mg.

ev_200 <-
  et(amt = 200, cmt = "depot") %>%
  et(seq(0, 24, by = 0.25))

sim_200 <-
  rxSolve(pk_model, ev_200) %>%
  as_tibble()

This uses the same model and the same sampling schedule.

Only the dose amount has changed.

This is what makes the example a clean what-if comparison.

Combine scenarios.

sim_compare <-
  bind_rows(
    sim_100 %>% mutate(DOSE = "100 mg"),
    sim_200 %>% mutate(DOSE = "200 mg")
  )

The DOSE column labels each simulated scenario so they can be compared in one plot.

Plot.

ggplot(sim_compare, aes(time, cp, linetype = DOSE)) +
    geom_line() +
    labs(
        title = "Dose Scenario Comparison",
        x = "Time",
        y = "Concentration"
    )

Interpretation:

Simulation lets us compare scenarios before observing them directly.

In this simple linear PK model, increasing the dose increases predicted concentration while keeping the overall profile shape similar.

Worked Example 5: Simulation Supports Decisions

Simulation does not make decisions automatically.

It provides evidence.

Conceptually:

Model

↓

Scenario

↓

Simulation

↓

Interpretation

↓

Decision

Examples:

Question Simulation Output
Does exposure increase? concentration-time profiles
Is accumulation expected? repeated-dose profiles
Do patients differ? population simulations
Which strategy looks better? scenario comparison

A simulation is only as useful as the model and assumptions behind it.

What Simulation Does Not Prove

Simulation does not prove the future.

It depends on:

  • model structure
  • parameter estimates
  • assumptions
  • variability
  • scenario definition

Simulation is best interpreted as:

Model-based expectation

not guaranteed truth.

Looking Ahead

This lesson used a simple typical-subject simulation.

Next, we add variability.

We will compare:

Typical Individual
↓
Population of Individuals

Strategies

  • define the question first
  • simulate simple scenarios before complex ones
  • interpret outputs in context

Common Mistakes

  • treating simulation as proof
  • forgetting variability
  • changing too many assumptions at once

Practice Problems

  1. What question does estimation answer?

  2. What question does simulation answer?

  3. Why do simulations need a scenario?

  4. What is the difference between prediction and observation?

  5. Why should simulation results be interpreted cautiously?

Problem 1

Estimation asks:

Given data, what parameters explain the observations?

Problem 2

Simulation asks:

Given a model, what outcomes might occur?

Problem 3

A scenario defines what is being simulated.

Examples include dose, timing, patient characteristics, and sampling times.

Problem 4

A prediction is generated by a model.

An observation is measured from real data.

Problem 5

Simulation depends on assumptions.

If the model or scenario is unrealistic, the simulation may be misleading.

Summary

  • estimation learns from data
  • simulation explores scenarios
  • simulation generates model-based predictions
  • interpretation depends on assumptions
  • Estimate first
  • Simulate scenarios
  • Interpret cautiously
  • Models support decisions