Why Stratify Concentration-Time Profiles by Dose?
Concentration-time plots show how measured concentrations vary over time. Stratifying them by dose or regimen makes it easier to inspect whether the observed profiles differ across the treatment groups represented in a dataset. A display may reveal higher or lower concentrations, different apparent rates of decline, or different amounts of between-subject spread. These are descriptive patterns: the plot alone does not establish that dose caused a difference.
A useful display starts with clearly defined groups and a defensible time axis. A dose group might be defined by the administered amount for a specific occasion, or by a planned regimen. Those definitions are not interchangeable. A person whose dose changes during follow-up may contribute observations under more than one dose category if the analysis records dose at each observation. Alternatively, a display may classify each person by an assigned regimen. The plot’s labels and caption should say which approach was used.
Prepare the Comparison Before Plotting
For each concentration record, identify the subject, concentration value and unit, sampling time, dose or regimen category, and the time origin used for the horizontal axis. When the question concerns a profile following a dose, time is commonly expressed relative to that dose administration. If records include multiple administrations, ensure that the time origin and the relevant dose are matched consistently. Otherwise, points with the same plotted time may refer to different stages of treatment.
Define dose groups in a way that corresponds to the scientific question. For example, separate panels for planned regimens answer a different descriptive question from classifying every sample by the most recent administered dose. In either case, state how dose changes, missed administrations, and records with unclear dose assignment were handled. Use consistent concentration units and explicit dose units in group labels, such as 50 mg and 100 mg.
When comparing groups, use the same horizontal and vertical scales wherever practical. Common scales make visual differences interpretable; independently scaled panels can make similar profiles appear different, or conceal substantial differences. If the concentration range is broad, a logarithmic vertical scale may help show lower concentrations, but it requires positive values and a clear account of how zero or below-quantification observations are represented. The linear and log-scale displays serve different visual purposes; the axis scale must be apparent to the reader.
Name the dose group or regimen, its units, and whether classification applies to a subject or to an individual observation.
Confirm that the time origin has the same meaning across groups and that the displayed window is comparable.
Use an overlay for direct comparison when it remains readable; use aligned panels when traces overlap heavily.
Indicate individual profiles or add group summaries, and report the number of subjects and observations represented.
State visible differences in levels or shape, and note design or composition differences that limit interpretation.
Display Choices and What They Show
An overlay places profiles from multiple dose groups on common axes. It is compact and supports direct comparison, but can become difficult to read when many subjects or groups are present. Use distinct, color-blind-accessible colors and line types, and avoid relying on color alone. A legend should identify the group and, where relevant, the regimen. If the traces obscure one another, aligned panels with identical axes can preserve comparability while improving legibility.
Individual traces show the spread and irregularity of the observed data, but do not make group-level patterns easy to summarize. A group summary at selected times can complement them. For example, a median concentration and lower and upper quantiles at each time bin show the central observed level and its spread. Always display the number of contributing subjects or samples at each time or bin: a summary based on a few observations should not look equally well-supported as one based on many. A time-bin summary is descriptive and can conceal variation within the bin, so retain the bin definition and sampling coverage in the display or caption.
A mean can be useful when it answers the intended descriptive question, but it can be strongly influenced by a few high concentrations. Medians are less sensitive to extreme values, though neither a median curve nor a mean curve represents every subject’s trajectory. It is often informative to combine a summary with faint individual traces, provided the plot remains readable.
Worked Example: Summarizing Observations at a Shared Time
Suppose a hypothetical dataset has concentration measurements at 2 hours after dosing for two dose groups. In the 50 mg group, the values are 18, 20, 22, 24, and 26 ng/mL. In the 100 mg group, they are 30, 34, 36, 38, and 42 ng/mL. Assume each value comes from a different subject and all measurements use the same time origin and units.
For the 50 mg group, the ordered values are already \(18, 20, 22, 24, 26\). The median is the middle value, \(22\) ng/mL. For the 100 mg group, the median of \(30, 34, 36, 38, 42\) is \(36\) ng/mL. The observed median difference at 2 hours is \(36 - 22 = 14\) ng/mL.
A plot could show the two medians at 2 hours, accompanied by the individual points or the observed ranges. The defensible description is that the hypothetical 100 mg group has a higher sample median at this sampled time. Five subjects per group provide limited coverage, and one time point does not establish how the full profiles differ. The arithmetic describes these data; it is not a causal dose-effect estimate.
Compare Shapes Without Overstating Them
A profile’s level refers to the observed concentration magnitude at a given time or over part of the displayed window. Its shape refers to how concentration changes over time—for example, whether the displayed points rise, decline, or appear to decline at different rates. Shape comparisons require adequate observations across comparable portions of time. If one group is sampled mostly early and another mostly late, their plotted curves may look different simply because they are supported by different parts of the time course.
Consider a summary formed from several subjects. At a particular time, the group mean is the total of the observed concentrations divided by the number of observations. If the number of observations from each subject differs, subjects with more records contribute more weight. In general, with subject \(i\) contributing \(m_i\) observations \(C_{ij}\), the pooled mean is
This follows directly from adding all recorded values and dividing by their total count. It is not generally the same as giving each subject equal weight: the latter would average each subject’s mean, \(\frac{1}{n}\sum_{i=1}^{n}\bar{C}_i\). Therefore, when sampling intensity differs by subject or group, report the unit being summarized—observations or subjects—and consider showing individual profiles alongside summaries.
Worked Example: Unequal Numbers of Observations
In a hypothetical 2-hour bin, subject A in one dose group has concentrations of 10 and 14 ng/mL, while subject B has one concentration of 30 ng/mL. The observation-level mean is
Subject A’s mean is \((10 + 14)/2 = 12\) ng/mL, and subject B’s mean is \(30\) ng/mL. Giving the two subjects equal weight produces \((12 + 30)/2 = 21\) ng/mL. The results differ because the pooled mean gives subject A two-thirds of the observation weight, while the subject-average gives both subjects one-half of the weight.
Neither calculation is automatically the right display summary; they answer different descriptive questions. A plot that reports an observation-level mean should not be described as an equally weighted average subject profile. Here the small sample also makes either summary unstable, so showing the three measurements and the subject identities would clarify the data behind the number.
Worked Comparison Across Regimens
Worked Example: A Higher Profile Is Not Necessarily a Dose Effect
Suppose a hypothetical observational dataset compares a 50 mg regimen with a 100 mg regimen. At 1, 4, and 8 hours, the displayed group medians are 12, 8, and 4 ng/mL for the 50 mg group, and 24, 16, and 8 ng/mL for the 100 mg group. The plotted medians in the latter group are twice those in the former at each of these times: \(24/12=2\), \(16/8=2\), and \(8/4=2\).
The visual description is that the 100 mg group has higher median concentrations at each displayed time, while both sets of medians decline across the sampled window. The plot does not show whether dose alone explains the difference. Suppose the 100 mg group consists mainly of participants with a different body-size distribution and also received a different regimen schedule. Those group differences could contribute to the observed profiles. Without an appropriate study design and analysis, the display cannot separate these possibilities from a dose-related explanation.
A careful caption would identify the groups, time origin, summary and sample counts, and say that the curves are descriptive. It would not claim that increasing the dose caused the observed concentration difference. The numerical ratios above compare plotted medians; they are not a dose-normalized analysis or an estimate of an individual response.
Diagnostics, Alternatives, and Limitations
Before interpreting apparent group differences, inspect the data coverage and the construction of the plot. Check the number of subjects per group, the number of observations at each time, and whether observations cluster at different times across groups. Look for mislabeled dose units, inconsistent time origins, dose changes that are hidden by subject-level classification, and extreme values that dominate the axis. Where individual traces are shown, check whether a few subjects account for most of the apparent separation. If the group summary changes substantially when a single subject is removed, state that the display is sensitive to sparse data rather than presenting a smooth curve as a stable pattern.
The main display alternatives serve different purposes. A common-axis overlay emphasizes direct visual comparison but may suffer from overplotting. Aligned small panels improve readability while retaining shared scales. Individual traces emphasize subject-level variation, while time-binned summaries offer a compact view of group-level patterns but can mask irregular trajectories and uneven sampling. These are complementary displays, not competing inferential procedures. Choose based on the comparison of interest and show enough of the underlying data to make the summary credible.
Important limitations remain even when the display is carefully built. A dose group may differ from another in subject characteristics, study period, regimen, sampling schedule, or other design features. Sparse or irregular measurements may make curve shape uncertain. A visual separation is not a test of statistical significance, and apparent overlap does not prove equivalence. Descriptive plots are useful for identifying patterns and questions for subsequent analysis; they do not by themselves control confounding or quantify a causal effect.
- Pitfall: treating vertical separation as proof that dose caused the difference. A higher curve in one dose group is an observed association in the displayed data. The groups may differ in other ways, so describe the pattern and name plausible design differences rather than asserting causation.
- Pitfall: interpreting lines as observed continuous trajectories. A line connecting sparse samples is a visual guide between measurements, not evidence that concentrations were measured at every intervening time.
- Pitfall: comparing independently scaled panels as if their heights were directly comparable. Use common axes for magnitude comparisons, or clearly state when panel scales differ.
- Pitfall: omitting counts. A median based on two subjects and one based on twenty should not be presented as equally supported. Provide group sizes and, where possible, time-specific coverage.
Check Your Understanding
Answer each question, then compare with the brief solutions.
- A 75 mg group has a median of 15 ng/mL at 3 hours, and a 150 mg group has a median of 25 ng/mL. What can be concluded from this comparison, and what cannot?
- Why should subject counts or observation counts be shown with a time-binned summary?
- At one time, subject A contributes four measurements and subject B contributes one. Does a pooled observation mean give each subject equal weight?
- When might aligned panels be more useful than an overlay, and what should remain consistent across panels?
- Two dose groups are sampled at substantially different times. Why does this limit a comparison of profile shape?
Solutions. (1) The observed median is 10 ng/mL higher in the 150 mg group at that time; this alone does not show that dose caused the difference or describe the entire profile. (2) Counts reveal how much data support each summary and help identify sparse or uneven coverage. (3) No. Subject A contributes four-fifths of the pooled observations, so receives four-fifths of the observation weight. (4) Panels help when overplotting makes traces hard to read; use identical axes and scales for direct magnitude comparisons. (5) Apparent shape differences may reflect which portions of the time course were sampled rather than a genuine difference across comparable times.