Why Inspect One Subject at a Time?
A concentration-versus-time plot places each measured drug concentration at its sampling time. Displaying one subject at a time makes it easier to follow that subject’s observed profile: its broad rise or decline, its observed concentration range, and any unusually separated measurements. These are descriptive features of the recorded data, not estimates of an individual’s pharmacokinetic parameters.
A linear vertical axis is often the most direct place to begin. Equal vertical distances then represent equal absolute concentration differences in the stated units. This makes the scale straightforward to read when the goal is to describe concentrations in those units. It also means that observations at the high end can occupy much more of the visible range than observations at the low end. The scale is useful, but its visual emphasis needs to be understood.
Set Up the Axes and the Profile
Before plotting, establish what each record represents. Use the subject identifier to separate observations into subject-level profiles. Put time on the horizontal axis and measured concentration on the vertical axis. Label both axes with units, such as “Time since dose (h)” and “Concentration (mg/L).” A label such as “Time” is insufficient if the reader cannot tell whether it means time since the most recent dose, time since the first dose, or time since study entry.
Choose a time origin that matches the study question and the dosing history. For a single dose, elapsed time since that dose is often clear. With repeated doses, time since the most recent dose may help show where samples fall within a dosing interval, but it does not by itself show accumulation across successive doses. If time since first dose or study time is more appropriate, state that choice. Do not mix time definitions in a single profile without making the distinction explicit.
For a set of subject panels intended to be compared visually, use consistent units and, when practical, common axis limits. A shared scale helps readers see whether a difference is a real difference in displayed range rather than a consequence of different panel limits. If subjects have very different concentration ranges, a common scale may compress the lower profiles. Separate scales can improve visibility but make direct visual comparisons harder; identify that choice clearly.
Concentration has a physical lower bound of zero, so a vertical axis beginning at zero is usually an interpretable default. If a restricted range is needed to examine a narrow portion of a profile, show that the axis is truncated and retain enough context to avoid exaggerating small differences. Negative measured values should not be created by an axis choice or by replacing unavailable results with arbitrary numbers.
Worked Example: Reading a Single-Dose Profile
Suppose a hypothetical subject receives one dose, and the following concentrations are recorded. Time is measured in hours since dosing, and concentration in mg/L.
| Time (h) | 0.5 | 1 | 2 | 4 | 8 |
|---|---|---|---|---|---|
| Concentration (mg/L) | 2.0 | 5.0 | 8.0 | 4.0 | 1.0 |
Plot the five paired observations as points, with time on the horizontal axis and concentration on the vertical axis. The observed minimum is 1.0 mg/L and the observed maximum is 8.0 mg/L, so the observed range is:
The measured values rise from 2.0 mg/L at 0.5 h to the largest recorded value, 8.0 mg/L at 2 h, and then fall to 1.0 mg/L at 8 h. This supports the description “the observed concentrations rise and then decline, with the largest sampled value at 2 h.” It does not establish that the true peak occurred exactly at 2 h: the peak could fall between sampling times. A line connecting the points can help the eye follow their order, but it must not be mistaken for observed concentrations at every time along the line.
What the Linear Scale Shows—and Does Not Show
On a linear concentration axis, the vertical coordinate is proportional to concentration itself. For instance, the points at 2, 4, and 6 mg/L are evenly spaced vertically because each adjacent pair differs by 2 mg/L. Equal proportional changes do not have equal spacing: a change from 1 to 2 mg/L is a doubling, while a change from 4 to 5 mg/L is not, yet both are 1 mg/L increments and therefore have the same vertical distance.
This follows directly from the axis mapping. If \(y\) denotes vertical position and \(C\) concentration, a linear axis maps concentration to position by \(y=a+bC\), where \(a\) sets the origin on the page and \(b\) is a fixed scale factor. Thus:
A fixed concentration difference always produces the same vertical separation. Conversely, a fixed ratio, such as doubling concentration, produces a separation that depends on the starting concentration. This is why a linear plot makes absolute differences readily visible but may leave low concentrations crowded near the bottom when the range is wide.
Describe what is actually visible: the range of measured concentrations, the times at which they were sampled, and broad patterns across those observations. Avoid asserting an exact absorption peak, elimination rate, half-life, or continuous curve shape from a sparse set of points. Those quantities require assumptions and analyses beyond visual inspection.
Worked Example: Choosing a Common Vertical Range
Consider two hypothetical subjects measured at the same five times. Subject A has concentrations of 1, 2, 4, 3, and 1 mg/L; Subject B has concentrations of 2, 4, 8, 6, and 2 mg/L. The observed ranges are:
A common axis from 0 to 8 mg/L makes it clear that B’s observed values are twice A’s at each listed time. It also places A’s points in the lower half of the plotting region. Giving each panel a separate axis from 0 to its own maximum could make the profiles look more similar in height, although the absolute concentration ranges differ. For direct comparison, the shared 0-to-8 mg/L scale is more informative; if the purpose is instead to inspect detail within each subject, separate limits may be readable, but they must be stated and not used to imply equal concentrations.
The pointwise ratios in this particular example are all 2, but this visual pattern alone does not establish why the subjects differ. Dose, sampling, and other study information would be needed before making a causal or pharmacokinetic interpretation.
Repeated Doses, Sparse Samples, and Unquantifiable Results
Repeated-dose records need particular care because the meaning of time affects the visual story. A plot against time since the first dose displays the overall study chronology; a plot against time since the most recent dose displays position relative to a dose. Neither view answers every question. If the plot uses time since the most recent dose, observations from different dosing intervals can share the same horizontal coordinate. They should not be connected as if they were consecutive points on a single uninterrupted time course unless the display clearly distinguishes the intervals. Dose times can be marked when they help orient the reader, while keeping the actual sampling times visible.
Sparse data limit interpretation regardless of how attractive the plot looks. Widely spaced observations cannot reveal short-lived changes between samples. A smooth-looking line drawn between two points is only a visual guide, not evidence of the path taken. When sampling times are irregular, use the actual recorded times rather than equally spacing points for visual convenience.
A concentration below the assay’s quantification limit is not a known zero. Do not silently replace it with zero or another single value and then present that value as measured. If below-quantification observations are included in the display, use a distinct symbol or annotation and state how they are represented. Their exact concentration is unknown within the relevant range; the symbol should not suggest a precise numerical measurement.
Worked Example: Handling Below-Quantification Observations
In a hypothetical profile, the assay’s lower limit of quantification is 0.5 mg/L. A subject has measured concentrations of 1.8 mg/L at 2 h, 0.7 mg/L at 8 h, and a result reported below the quantification limit at 12 h.
Plot the quantified observations at their measured values: (2 h, 1.8 mg/L) and (8 h, 0.7 mg/L). Mark the 12 h observation with a distinct symbol and a note such as “below 0.5 mg/L,” rather than placing it at 0 mg/L. The result indicates that the concentration was not quantified at or above the stated limit; it does not provide an exact concentration of zero or a precise location below 0.5 mg/L.
The quantified observations decline by 1.1 mg/L from 2 h to 8 h:
That difference describes the two measured values only. The later below-quantification result is consistent with a low concentration, but it cannot be used as an exact third value to calculate an additional numerical decline.
Diagnostics, Alternatives, and Limitations
Review the finished plot as a data display, not only as a picture of a profile. Check that subject identifiers are correct, time units and origin are consistent, axes are labelled, and concentrations match the records. Look for points that are out of sequence, duplicated, or unexpectedly distant from neighboring observations. Such features may reflect a real observation, a timing or data-processing issue, or a mismatch in units; the plot flags questions but does not determine their cause. Reconcile concerns with the underlying records before changing data.
Individual panels are useful for tracing one subject’s observations, but they use screen space and can make population-wide comparisons slow. An overlay of many subjects can provide a compact view of multiple profiles, although overlapping symbols may obscure individuals. A population summary can be more concise, but it does not show each person’s complete trajectory. A log-scale plot can make a wide concentration range easier to inspect in relative terms, while changing how differences appear; use the scale suited to the question rather than treating either scale as universally preferable.
The linear individual plot is descriptive. It does not account for differing doses, quantify uncertainty, or separate within-subject from between-subject variability. Differences in profile height or shape are not, on their own, evidence that a particular covariate caused a difference or that a model is adequate. Its value is to expose the data structure and identify patterns or irregularities that merit follow-up.
Specify the time origin and units, especially when repeated doses or visits are involved.
Plot each subject’s records in an individual panel, with consistent concentration units.
Use a readable linear scale, state any truncated or subject-specific limits, and preserve zero as the meaningful lower bound when feasible.
Describe observed ranges and sampled patterns; distinguish measured values from below-quantification results and avoid claims about unsampled behavior.
Check Your Understanding
Answer each question, then compare with the brief solutions below.
- A subject has measurements of 3, 7, and 4 mg/L at 1, 3, and 6 h after a dose. What is the observed range, and what can be said about the largest observation?
- Why can separate vertical limits make two individual profiles appear more alike than they are in absolute concentration?
- A result is reported below a quantification limit of 0.2 mg/L. Why should it not be plotted as an exact zero?
- For repeated-dose data, what information is needed to interpret a horizontal axis labelled “time since dose”?
Solutions. 1. The observed range is \(7-3=4\) mg/L; 7 mg/L is the largest sampled concentration, at 3 h, not necessarily the true peak. 2. Each panel can fill a similar fraction of its own plotting area despite having different concentration limits, so apparent heights are not directly comparable. 3. The actual concentration is unknown below the stated quantification limit; zero asserts an exact value the assay did not provide. 4. State whether the time is since the first dose or the most recent dose, and explain how samples from different dosing intervals are represented.