Visual QC for Profiles and Terminal Phase

Use profile plots and log-scale diagnostics to assess data integrity and terminal slope reliability.
Tip

Big idea: If a terminal phase looks wrong visually, half-life is unreliable no matter what the number says.

Learning Objectives

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

  • Generate individual PK profile plots.
  • Use log-scale plots to evaluate terminal-phase behavior.
  • Visually identify poor lambda_z regions.
  • Detect suspicious profiles before performing NCA.

Key Ideas

  • Visual inspection is one of the most powerful QC tools in PK analysis.
  • Linear-scale plots help reveal overall exposure patterns.
  • Log-scale plots reveal the terminal log-linear region used to estimate \(\lambda_z\).
  • Terminal slope diagnostics should always be confirmed visually.
  • Numerical outputs like half-life are only reliable if the terminal region is visually credible.

Setup: Prepare Example Data

library(tidyverse)

data(Theoph)

conc_df <- as_tibble(Theoph) %>%
  transmute(
    ID = Subject,
    TIME = Time,
    CONC = conc
  )

conc_df
# A tibble: 132 × 3
   ID     TIME  CONC
   <ord> <dbl> <dbl>
 1 1      0     0.74
 2 1      0.25  2.84
 3 1      0.57  6.57
 4 1      1.12 10.5 
 5 1      2.02  9.66
 6 1      3.82  8.58
 7 1      5.1   8.36
 8 1      7.03  7.47
 9 1      9.05  6.89
10 1     12.1   5.94
# ℹ 122 more rows

Strategies

When reviewing PK profiles visually:

  • Start with a linear-scale plot to understand the full profile.
  • Then inspect a log-scale plot to evaluate the terminal decline.
  • Look specifically at the last several time points.
  • Confirm that the terminal phase appears approximately log-linear.
  • Flag profiles that look inconsistent or noisy.

Worked Example 1: Linear Profile Plot

A linear-scale plot provides an overview of the full concentration-time profiles.

ggplot(conc_df, aes(TIME, CONC, group = ID)) +
  geom_line(alpha = 0.4) +
  labs(
    title = "Individual Profiles (Linear Scale)",
    x = "Time",
    y = "Concentration"
  )

This plot helps reveal:

  • overall exposure patterns
  • potential outliers
  • unusual spikes or dips

Worked Example 2: Log-Scale Profile Plot

Log-scale plots reveal the terminal phase used to estimate \(\lambda_z\).

ggplot(conc_df, aes(TIME, CONC, group = ID)) +
  geom_line(alpha = 0.4) +
  scale_y_log10() +
  labs(
    title = "Individual Profiles (Log Scale)",
    x = "Time",
    y = "Concentration (log scale)"
  )

On a log scale, a well-behaved terminal phase should appear approximately linear.

What to Look For in Log Plots

A reliable terminal phase typically shows:

  • A clear log-linear decline
  • Several points forming a consistent slope
  • No upward curvature at the end
  • Minimal noise in the last samples

These visual signals support a stable \(\lambda_z\) estimate.

Common Mistakes

Warning
  • Trusting half-life estimates without visually checking the terminal region.
  • Ignoring noisy or upward-trending final samples.
  • Using too few points to define the terminal phase.
  • Overlooking time unit errors that distort the curve shape.

Practice Problems

  1. Executable: Create a faceted log-scale plot with one panel per subject.
  2. Executable: Identify subjects with unusually noisy terminal regions.
  3. Conceptual: Why does an upward final point distort \(\lambda_z\) estimation?

1. Faceted log-scale plot

ggplot(conc_df, aes(TIME, CONC)) +
  geom_line() +
  scale_y_log10() +
  facet_wrap(~ID)

2. Identifying noisy terminal regions

Visual inspection is typically used. Look for:

  • jagged terminal segments
  • upward final points
  • inconsistent slopes

3. Conceptual explanation

An upward final point violates the assumption of log-linear elimination. When included in the terminal regression, it flattens the slope, which inflates the half-life estimate.

Summary

Visual QC is a non-negotiable step before trusting terminal-phase metrics.

Reliable half-life estimation requires:

  • a clear log-linear terminal phase
  • adequate terminal sampling
  • visually consistent concentration decline

Numbers should confirm what the plot already suggests, not replace visual judgment.

  • Always inspect log-scale plots before trusting half-life.
  • Terminal phases should appear approximately linear on a log scale.
  • Watch closely for noisy final samples.
  • Visual QC should always precede automated NCA reporting.