Exploring Dose Scenarios

Use simulation to compare doses and dosing schedules and understand exposure changes.
Tip

Big picture: Simulation becomes powerful when we compare treatment strategies rather than describing a single outcome.

Learning Objectives

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

  • compare alternative dose scenarios
  • simulate different dosing schedules
  • interpret exposure changes
  • distinguish dose and schedule effects
  • connect simulation to decision making

Key Ideas

  • simulation supports scenario comparison
  • dose changes alter exposure
  • schedules alter timing
  • outcomes should be interpreted in context

Setup

library(tidyverse)
library(rxode2)

This lesson uses simulation only.

No estimation is performed.

Why Compare Dose Scenarios?

Once a model exists, we can ask:

  • what if dose increases?
  • what if dose decreases?
  • what if dosing becomes more frequent?
  • what if concentration accumulates?

Simulation helps answer these questions before collecting new data.

Conceptually:

Model

↓

Alternative Scenarios

↓

Compare Outcomes

Worked Example 1: Define the Base PK Model

Use the same simple 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

  })

Worked Example 2: Compare Dose Levels

Create two scenarios.

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

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

Simulate.

sim_100 <-
  rxSolve(pk_model, ev_100) %>%
  as_tibble() %>%
  mutate(DOSE = "100 mg")

sim_200 <-
  rxSolve(pk_model, ev_200) %>%
  as_tibble() %>%
  mutate(DOSE = "200 mg")

Combine.

dose_compare <-
  bind_rows(
    sim_100,
    sim_200
  )

Plot.

ggplot(
  dose_compare,
  aes(
    time,
    cp,
    linetype = DOSE
  )
) +
geom_line() +
labs(
    title = "Effect of Dose",
    x = "Time",
    y = "Concentration"
)

Interpretation:

Ask:

Does doubling dose double exposure?

For this simple linear PK model, exposure is expected to increase approximately in proportion to dose.

More complex models may not behave this way.

Notice:

  • peak concentration changes
  • overall exposure changes
  • profile shape may remain similar

Worked Example 3: Compare Dosing Schedules

In the previous example we changed dose.

Now we keep overall daily dose similar and change only the dosing schedule.

100 mg every 24 hours
=
50 mg every 12 hours
=
100 mg/day

Create scenarios.

ev_q24 <-
  et(
    amt = 100,
    ii = 24,
    addl = 4,
    cmt = "depot"
  ) %>%
  et(
    seq(0, 120, by = 0.5)
  )

ev_q24
── EventTable with 242 records ──
1 dosing records (see x$get.dosing(); add with add.dosing or et)
241 observation times (see x$get.sampling(); add with add.sampling or et)
multiple doses in `addl` columns, expand with x$expand(); or etExpand(x)
── First part of x: ──
# A tibble: 242 × 6
    time cmt     amt    ii  addl evid         
   <dbl> <chr> <dbl> <dbl> <int> <evid>       
 1   0   depot   100    24     4 1:Dose (Add) 
 2   0   <NA>     NA    NA    NA 0:Observation
 3   0.5 <NA>     NA    NA    NA 0:Observation
 4   1   <NA>     NA    NA    NA 0:Observation
 5   1.5 <NA>     NA    NA    NA 0:Observation
 6   2   <NA>     NA    NA    NA 0:Observation
 7   2.5 <NA>     NA    NA    NA 0:Observation
 8   3   <NA>     NA    NA    NA 0:Observation
 9   3.5 <NA>     NA    NA    NA 0:Observation
10   4   <NA>     NA    NA    NA 0:Observation
# ℹ 232 more rows

The event table now includes additional dosing instructions.

Key arguments:

ii   = interdose interval
addl = additional doses

For example:

amt = 100
ii = 24
addl = 4

means:

100 mg at time 0
100 mg at 24 h
100 mg at 48 h
100 mg at 72 h
100 mg at 96 h

for a total of five doses.

ev_q12 <-
  et(
    amt = 50,
    ii = 12,
    addl = 9,
    cmt = "depot"
  ) %>%
  et(
    seq(0, 120, by = 0.5)
  )

ev_q12
── EventTable with 242 records ──
1 dosing records (see x$get.dosing(); add with add.dosing or et)
241 observation times (see x$get.sampling(); add with add.sampling or et)
multiple doses in `addl` columns, expand with x$expand(); or etExpand(x)
── First part of x: ──
# A tibble: 242 × 6
    time cmt     amt    ii  addl evid         
   <dbl> <chr> <dbl> <dbl> <int> <evid>       
 1   0   depot    50    12     9 1:Dose (Add) 
 2   0   <NA>     NA    NA    NA 0:Observation
 3   0.5 <NA>     NA    NA    NA 0:Observation
 4   1   <NA>     NA    NA    NA 0:Observation
 5   1.5 <NA>     NA    NA    NA 0:Observation
 6   2   <NA>     NA    NA    NA 0:Observation
 7   2.5 <NA>     NA    NA    NA 0:Observation
 8   3   <NA>     NA    NA    NA 0:Observation
 9   3.5 <NA>     NA    NA    NA 0:Observation
10   4   <NA>     NA    NA    NA 0:Observation
# ℹ 232 more rows

These scenarios have the same total daily dose:

This allows us to isolate the effect of dosing schedule while keeping overall daily dose similar.

Simulate.

sim_q24 <-
  rxSolve(pk_model, ev_q24) %>%
  as_tibble() %>%
  mutate(SCHEDULE = "100 mg q24h")

sim_q12 <-
  rxSolve(pk_model, ev_q12) %>%
  as_tibble() %>%
  mutate(SCHEDULE = "50 mg q12h")

Combine.

schedule_compare <-
  bind_rows(
    sim_q24,
    sim_q12
  )

Because doses are repeated before the drug is fully eliminated, concentrations from successive doses may accumulate.

Accumulation is often easier to visualize than to calculate, making simulation particularly useful.

Plot.

ggplot(
  schedule_compare,
  aes(
    time,
    cp,
    linetype = SCHEDULE
  )
) +
geom_line() +
labs(
    title = "Effect of Schedule",
    x = "Time",
    y = "Concentration"
)

Interpretation:

Compare:

  • peak concentration
  • trough concentration
  • accumulation

Question:

Can the same total daily dose produce different profiles?

Yes.

Timing matters.

Worked Example 4: Quantify Exposure

Compute summary measures.

schedule_compare %>%
  group_by(SCHEDULE) %>%
  summarise(
    CMAX = max(cp),
    CMIN = min(cp),
    .groups = "drop"
  )
# A tibble: 2 × 3
  SCHEDULE     CMAX  CMIN
  <chr>       <dbl> <dbl>
1 100 mg q24h  2.87     0
2 50 mg q12h   1.92     0

For simplicity, we compute a few basic summary measures.

In practice, pharmacometric analyses often examine metrics such as:

Cmax

AUC

Trough

Time Above Threshold

Visualization and summaries often complement each other.

Worked Example 5: Scenario Thinking

Simulation does not identify the best treatment.

It compares assumptions.

Conceptually:

Scenario A

↓

Outcome A


Scenario B

↓

Outcome B

Decision making still requires:

  • objectives
  • safety
  • clinical interpretation

Simulation supports decisions.

It does not replace them.

Connecting to Practice

Scenario exploration is common in:

  • dose selection
  • schedule evaluation
  • pediatric extrapolation
  • clinical planning

Simulation allows exploration without new experiments.

Looking Ahead

So far we manually defined scenarios.

Next we simulate directly from fitted population models.

Strategies

  • compare one change at a time
  • visualize profiles
  • summarize outcomes

Common Mistakes

  • assuming more dose always improves outcomes
  • ignoring timing
  • overinterpreting simulations

Practice Problems

  1. Why compare scenarios?

  2. What changes when dose changes?

  3. What changes when schedule changes?

  4. Can equal daily dose produce different profiles?

  5. Why summarize simulations?

Problem 1

To compare possible outcomes.

Problem 2

Exposure changes.

Problem 3

Timing and accumulation.

Problem 4

Yes.

Schedule matters.

Problem 5

Summaries simplify interpretation.

Summary

  • simulation supports comparison
  • dose changes exposure
  • schedules change timing
  • interpretation guides decisions
  • Compare fairly
  • Change one thing at a time
  • Visualize before concluding