Dose–Response Visualization

Visualize dose–response relationships using the PBG dataset from nlme: grouping, log-dose scaling, stratification, and nonlinear intuition.
Tip

Core idea of this lesson: Dose–response plots reveal functional relationships.
Unlike concentration–time data, dose–response visualization focuses on shape, saturation, and group differences.

Learning Objectives

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

  • Construct grouped dose–response plots correctly.
  • Connect repeated measurements within subject.
  • Use log-dose scaling appropriately.
  • Stratify by treatment.
  • Recognize visual signs of nonlinear response behavior.

Key Ideas

  • Dose–response plots focus on functional relationships (shape, curvature, saturation), not time dynamics.
  • Repeated measurements must be connected by subject (group = ID) to preserve structure.
  • Log-dose scaling helps reveal nonlinear behavior, especially at low doses.
  • Stratification (e.g., by treatment) allows comparison of shifts in response patterns.
  • Individual-level structure should be inspected before adding summary trends.
  • Visual patterns suggest hypotheses about nonlinearity and group differences — they do not confirm them.

Why Dose–Response Is Different from PK Profiles

Concentration–time plots show how drug levels evolve over time.

Dose–response plots answer a different question:

How does response change as dose increases?

This shifts interpretation toward:

  • Curvature
  • Saturation
  • Relative shifts between groups
  • Within-subject consistency
Note

Dose–response visualization prepares you to think about nonlinear models — but here we focus strictly on visual structure, not model fitting.

Setup

library(tidyverse)
library(nlme)

data(PBG, package = "nlme")

pbg <- as_tibble(PBG) %>%
  rename(
    DV   = deltaBP,
    DOSE = dose,
    ID   = Rabbit,
    TRT  = Treatment
  )

Worked Example 1: Basic Dose–Response Plot

ggplot(pbg, aes(DOSE, DV, group = ID)) +
  geom_point() +
  labs(
    title = "Dose–Response",
    x = "Dose",
    y = "Change in Blood Pressure"
  ) +
  theme_minimal()

Questions to ask:

  • Do curves increase monotonically?
  • Do responses plateau?
  • Is variability consistent across dose levels?

Worked Example 2: Log-Dose Scale

ggplot(pbg, aes(DOSE, DV, group = ID)) +
  geom_point() +
  scale_x_log10() +
  labs(
    title = "Dose–Response (Log Dose Scale)",
    x = "Dose (log scale)",
    y = "Change in Blood Pressure"
  ) +
  theme_minimal()

Note

Log scaling often linearizes the lower-dose region and spreads out low-dose values, making curvature easier to see.

Worked Example 3: Stratify by Treatment (Facet)

ggplot(pbg, aes(DOSE, DV, group = ID)) +
  geom_line(alpha = 0.5, color = "grey40") +
  geom_point() +
  facet_wrap(~ TRT) +
  scale_x_log10() +
  labs(
    title = "Dose–Response by Treatment Group",
    x = "Dose (log scale)",
    y = "Change in Blood Pressure"
  ) +
  theme_minimal()

Ask:

  • Does one treatment shift the curve?
  • Is maximal response reduced in one group?
  • Is curvature different?

Worked Example 4: Add a Mean Trend Overlay (Cautiously)

ggplot(pbg, aes(DOSE, DV)) +
  geom_point(alpha = 0.4) +
  stat_summary(fun = mean, geom = "line", linewidth = 1) +
  scale_x_log10() +
  labs(
    title = "Mean Dose–Response Trend",
    x = "Dose (log scale)",
    y = "Mean Change in Blood Pressure"
  ) +
  theme_minimal()

Warning

Always inspect individual curves before trusting the mean.
Summary lines can hide heterogeneous responses.

Interpretation Discipline

When reading dose–response plots, ask:

  • Is there evidence of saturation?
  • Is the relationship linear or curved?
  • Are differences between treatments vertical (magnitude) or horizontal (potency shift)?
  • Is variability increasing with dose?

These visual cues guide modeling decisions later.

Strategies

  • Always start with individual lines.
  • Try log-dose scale when dose spacing is multiplicative.
  • Compare treatment groups using faceting.
  • Use summaries only after structural inspection.
  • Describe patterns before speculating about mechanisms.

Practice Problems

  1. Recreate the dose–response plot without grouping. What happens?
  2. Compare linear vs log-dose scale visually.
  3. Add color by treatment instead of faceting.
  4. Overlay mean trends by treatment.
  5. Write one sentence describing the apparent nonlinear pattern.
# 3) Color by treatment
ggplot(pbg, aes(DOSE, DV, group = ID, color = TRT)) +
  geom_point() +
  scale_x_log10() +
  theme_minimal()

# 4) Mean by treatment
ggplot(pbg, aes(DOSE, DV, color = TRT)) +
  stat_summary(fun = mean, geom = "line", linewidth = 1) +
  scale_x_log10() +
  theme_minimal()

Summary

In this lesson, you:

  • Built grouped dose–response plots.
  • Used log-dose scaling to clarify nonlinear patterns.
  • Stratified by treatment.
  • Added cautious summary overlays.
  • Practiced disciplined interpretation without modeling.

Dose–response visualization builds intuition for nonlinear behavior —
but visual structure must be understood before modeling begins.

  • Are lines grouped correctly?
  • Does log-dose scaling improve clarity?
  • Are treatment differences consistent?
  • Are summaries hiding variability?
  • What hypothesis would you test next?