Choose Displays to Support the Report’s Argument
A population pharmacokinetic report can contain many possible tables and figures: participant summaries, parameter estimates, covariate effects, diagnostic plots, and sensitivity analyses. The challenge is not to include every output. It is to select a manageable set that lets readers follow the analysis and inspect the evidence relevant to its objectives.
Start with the question each display should answer. A table is usually effective when readers need exact values, units, and labels. A figure is often more effective when the main message concerns a pattern, comparison, or relationship that is difficult to see across many rows. Some results need both: a concise figure can reveal an overall pattern, while a table provides the values needed to verify or reuse it. Include both only when each adds information.
This selection is part of the report’s reasoning, not a formatting task at the end. The architecture of a population PK analysis report and its analysis objectives determine which results are essential. The main report should provide enough evidence to understand the study data, the final model, important effects, and model evaluation. It should not make readers sift through every run, parameterization, or diagnostic panel to find those results.
Match the Display to the Information
Before making a table or figure, write down its purpose in one sentence. For example: “Show how observations are distributed across the study population” or “Compare the estimated covariate effects and their uncertainty.” If the purpose is unclear, the display is likely to be redundant, overly broad, or difficult to interpret.
| Reporting need | Often useful in the main report | Detail that may belong in an appendix |
|---|---|---|
| Study participants and observations | A compact participant summary and, where needed, a figure showing the sampling or concentration-time pattern | Expanded summaries by site, visit, or additional subgroups |
| Final model estimates | A parameter table with units and uncertainty measures | Full covariance output, alternative parameterizations, and optimizer output |
| Covariate effects | A concise table or effect plot, chosen to make size and uncertainty easy to compare | Detailed model-development comparisons or additional subgroup results |
| Model evaluation | A small set of displays that addresses the principal evaluation questions | Expanded diagnostic panels, extra stratifications, and secondary checks |
These are starting points, not fixed rules. A figure may be more informative than a table for one report and less informative for another. Consider the number of results, the precision readers need, the scale of the quantities, and the report’s objectives. A display is not useful merely because software produced it.
Worked Example: Showing the Analysis Population and Data Coverage
Suppose a hypothetical study enrolled 120 participants. Twelve were excluded from the analysis population under the prespecified criteria, leaving 108 analyzed participants. The analyzed participants contributed 864 drug-concentration observations. The report must make both the analysis population and the amount of concentration data clear.
Choose a compact table for exact counts. A short table can state that 120 participants were enrolled, 12 were excluded, and 108 were analyzed. A separate row or concise accompanying text can report 864 concentration observations. These are exact counts, so a table or direct text is more precise than a bar chart.
Consider a figure for the pattern of observations. If the timing and spread of concentration measurements across the dosing interval are relevant to the analysis, a concentration-versus-time figure can show that pattern. Its axes should identify time and concentration units, and the display should state what observations or summaries are plotted. It does not replace the exact participant and observation counts.
Keep the two purposes distinct. The count display answers “how many?” The concentration-time figure answers “when, and with what pattern?” If the figure adds no information needed for the report’s objectives, the count table may be sufficient. If the timing pattern matters, include both and explain their different roles.
Present Estimates and Covariate Effects Clearly
A parameter-estimate table is generally the main place for exact final-model estimates. It should identify each parameter, give an estimate and its units, and include uncertainty information appropriate to the analysis. Random-effects and residual-error results should be labelled so readers can distinguish them from typical values of structural parameters. The table should be internally consistent with the final model equations and the reporting choices already documented in the report.
Use a figure when visual comparison is the priority. For example, a plot can make it easier to compare the sizes and uncertainty of several covariate effects on a common scale. But a plot should not force readers to estimate exact values from positions on an axis when those values matter. A table may still be needed for exact estimates; if both are included, the figure should reveal a comparison that is not already obvious from the table.
Worked Example: Choosing a Table for Final-Model Estimates
Suppose a hypothetical final model reports typical clearance \(CL\) of 4.20 L/h, typical central volume \(V\) of 35.0 L, and an absorption-rate parameter \(k_a\) of 1.10 h\(^{-1}\). It also reports relative standard errors of 12%, 18%, and 25%, respectively. The report’s objective requires readers to retrieve estimates, units, and uncertainty measures.
Choose a table. The reader needs exact values and distinct units. A suitable compact presentation is:
| Parameter | Estimate | Unit | Relative standard error |
|---|---|---|---|
| \(CL\) | 4.20 | L/h | 12% |
| \(V\) | 35.0 | L | 18% |
| \(k_a\) | 1.10 | h\(^{-1}\) | 25% |
The table keeps each estimate attached to its unit and uncertainty measure. A plot could show which estimate has the largest relative standard error, but with only three differently scaled parameters it may add little: the reader can compare 12%, 18%, and 25% directly. The table also avoids placing parameters with different units on one numerical axis.
This does not mean a table alone is always sufficient. If the report needs to compare many effects or show their direction and uncertainty visually, a plot may add value. The decision follows the question, rather than a general preference for tables or figures.
For a covariate effect represented on the log scale, the report should make its clinical or model scale understandable. For example, if a coefficient \(\beta\) multiplies a parameter through \(\exp(\beta)\), the multiplier is often easier to compare across effects than the raw coefficient alone. When uncertainty is reported as an interval on the coefficient scale, transform both endpoints rather than treating the interval as symmetric after transformation.
Worked Example: Choosing a Plot for Covariate Effects
Suppose a hypothetical model estimates a sex-associated clearance coefficient of \(\beta=0.262\), with a 95% interval from 0.095 to 0.429 on the log scale. The model defines the clearance multiplier for the compared group as \(\exp(\beta)\). The report needs readers to compare this effect with effects for other covariates.
Transform the estimate and interval. The multiplier is
The transformed interval endpoints are
Thus the estimated clearance multiplier is 1.30, with an interval from 1.10 to 1.54, for the stated group comparison. The interval is not symmetric around 1.30 on the multiplier scale: its lower and upper distances are 0.200 and 0.236. This follows because the exponential transformation is increasing, so it preserves endpoint order, but it does not preserve equal distances.
A plot of covariate multipliers with intervals can support visual comparison across several effects, provided the effects are defined consistently and the axis is labelled with the multiplier scale. A concise table may be preferable when only one effect is central or readers need exact values. Whichever display is chosen, state the reference group and define the direction of the comparison; a multiplier without that context is incomplete.
Select Model-Evaluation Displays Without Overloading the Main Report
Model evaluation often produces a large number of figures. The main report should include a purposeful subset that addresses the principal evaluation questions, not every available panel. A typical selection may include a general observed-versus-predicted view, a residual display against a relevant quantity such as time or prediction, and a predictive-check display when it is central to the evaluation. These names identify possible display types; the appropriate set depends on the model, data, and analysis objectives.
The role of this tutorial is to help choose and organize displays, not to interpret their patterns. A later, dedicated discussion of goodness-of-fit figures addresses their interpretation; predictive-check results also warrant their own focused treatment. Here, the practical selection questions are: Which evaluation question does this figure address? Does it add a distinct view? Is it readable at the size used in the report? Does the main text state where expanded versions can be found?
A figure that overlays many groups can become unreadable. Rather than shrinking the labels or stacking every possible stratification into one panel, choose a small set of views that serves the main evaluation purpose. Put additional panels in an appendix and point to them specifically. “See Appendix Figure A4 for site-stratified displays” is more useful than a general statement that supplementary diagnostics are available.
Identify the evidence readers need to see for the study data, final estimates, covariate effects, and model evaluation.
Use tables for exact values and labels; use figures when comparisons or patterns are more readily seen visually.
If two displays communicate the same result, retain the clearer one unless the second provides a distinct verification purpose.
Move useful but nonessential expansions to an appendix and give readers a precise cross-reference.
Design for Verification and Readability
A well-chosen display can still fail if its contents are ambiguous. Tables need clear row and column labels, units, definitions of abbreviations, and enough information to identify the analysis population or model version where relevant. Figures need legible axes, units, symbols, and legends. Captions should explain what is shown, identify key groupings, and define uncommon abbreviations; they should not merely repeat the figure number.
Keep precision consistent with the evidence. Report numerical results to a sensible number of significant figures and avoid implying more precision than the analysis supports. In a figure, the axis range should permit the intended comparison without concealing relevant variation. In a table, avoid excessive decimal places and unnecessary columns. If a table spans multiple pages or a figure requires a long legend to decode, consider whether the display can be simplified or split.
Separate results that are easily confused. For example, distinguish typical parameter estimates from variability and residual-error estimates through headings or table sections. Label confidence or uncertainty intervals clearly, and do not let a graphic imply a scale or comparison that the model did not estimate. When a quantity is transformed for presentation, retain enough explanation for a reviewer to see how it relates to the model parameter.
Main Report, Appendix, and Common Pitfalls
The main report and appendix serve different but connected purposes. The main report prioritizes the evidence needed to understand and evaluate the stated objectives. The appendix preserves traceability and detail: expanded tables, secondary displays, and supporting output can be located there without interrupting the main narrative. Moving a result to an appendix does not make it irrelevant; it changes how prominently it is presented. Important conclusions should not depend on an appendix result that the main text never identifies.
A common mistake is to include every generated plot in the main report because completeness is mistaken for transparency. That reasoning can make key evidence harder to find and reduce figure legibility. The correction is to select displays by purpose, retain the essential evidence in the main report, and use precise cross-references for additional detail. The opposite mistake is to provide only a polished summary while omitting the information readers need to verify it. A concise main report still needs clear definitions, units, uncertainty, and a route to supporting output.
Another pitfall is treating a table and a figure as automatically complementary. If the figure simply reproduces the same three values shown in a table, with no clearer comparison or additional pattern, it may be redundant. Conversely, a figure cannot substitute for exact values when readers need to report or compare those values precisely. Ask what each display contributes, and remove it if the answer is “nothing beyond the other display.”
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A report needs to present four final parameter estimates, each with a different unit, and their uncertainty measures. Which display is usually the clearest starting point, and why?
- A covariate effect is estimated as a log-scale coefficient with an interval. The model uses \(\exp(\beta)\) as the multiplier. Which values should be plotted if the intended display is on the multiplier scale?
- A report has one main model-evaluation figure and 18 additional stratified versions. Give one defensible way to organize these displays.
- When is it useful to include both a table and a figure for the same set of results?
- Why is “all software-generated figures are in the main report” not a sufficient display-selection rule?
Solutions. (1) Begin with a table: it can place each exact estimate beside its own unit and uncertainty measure without forcing different scales onto one axis. (2) Transform the estimate and both interval endpoints using the exponential function; because it is increasing, the transformed lower endpoint remains lower than the transformed upper endpoint. (3) Include the main evaluation view or a small objective-driven subset in the report, place the additional stratified versions in an appendix, and cite their location specifically. (4) Include both when they contribute distinct information—for example, a figure makes a pattern or comparison easy to see while the table gives exact values needed for verification. (5) Software output is not selected according to the report’s questions; including everything can obscure essential results and make displays unreadable. Select by purpose and preserve supporting detail through clear appendix references.