From Competing-Risk Output to a Clinical Display
A results table and a cumulative incidence figure do different jobs. A table gives precise estimates at selected horizons; a figure shows how estimated event probabilities change over follow-up. Their labels, population, time scale, event definitions, and estimates must agree. A small mismatch—such as calling an event “relapse” in one place and “progression” in another—can change how readers understand the result.
This tutorial assembles both displays from hypothetical competing-risk output. It assumes the analysis has already chosen and estimated the relevant cumulative incidence functions. The focus is on selecting, formatting, and checking the reported results, not on fitting a competing-risk model.
Before preparing a display, confirm that the analysis concerns a clearly defined cohort; that causes are defined as mutually exclusive first events; and that censoring has been handled under the assumptions of the estimator used. In particular, censoring must not systematically conceal event risk in a way unaccounted for by the analysis. The table and figure inherit the analysis’s limitations: careful formatting cannot repair a poorly defined estimand or unsupported assumptions.
Plan the Table and Figure Together
Choose the display contents before polishing either one. For a concise clinical report, a common arrangement is a table of the primary event probability at one or more prespecified horizons, with a figure showing the time course for the primary and competing events. A competing event should not disappear merely because the primary outcome is the focus: its occurrence affects the interpretation of the primary-event probability.
Use one set of names throughout. State the time unit explicitly, and distinguish percentages from proportions. If the table reports pointwise 95% confidence intervals, label them as such; a confidence interval at a horizon describes uncertainty in that horizon-specific estimate, not a probability that the fixed parameter lies in the realized interval. If intervals appear in the figure, identify whether they are pointwise intervals or simultaneous bands. These are not interchangeable.
Write down the population, event causes, and time origin used in the analysis. Use the same event names in the table, legend, and caption.
Report clinically meaningful, prespecified times and state the unit. Do not imply that a selected horizon was prespecified if it was chosen after inspecting results.
Use the same unrounded estimates to prepare the table and plotting data, then round consistently for display.
Compare labels, times, values, intervals, and curve behavior across the table, figure, and captions before reporting.
Worked Example: A Table and Two-Panel Figure
Worked Example: A Table and Two-Panel Figure
Hypothetical setting. A randomized study follows adults for up to 36 months after treatment. The mutually exclusive first events are relapse and non-relapse death; death before relapse competes with relapse. The clinical team wants a concise comparison of the cumulative incidence of each event in the two treatment groups. Suppose a valid competing-risk analysis has produced the following estimates and pointwise 95% confidence intervals. All values are proportions.
| Group | Cause | 12 months | 24 months | 36 months |
|---|---|---|---|---|
| Control | Relapse | 0.12 (0.08, 0.18) | 0.24 (0.18, 0.31) | 0.31 (0.24, 0.39) |
| Control | Non-relapse death | 0.05 (0.03, 0.09) | 0.11 (0.07, 0.17) | 0.17 (0.12, 0.24) |
| Treatment | Relapse | 0.09 (0.05, 0.14) | 0.16 (0.11, 0.23) | 0.22 (0.16, 0.30) |
| Treatment | Non-relapse death | 0.04 (0.02, 0.08) | 0.08 (0.05, 0.13) | 0.13 (0.08, 0.20) |
For a table focused on the primary event at 24 months, convert the relapse estimates and their limits to percentages. For control, \(100(0.24)=24\%\), and the limits are \(100(0.18)=18\%\) and \(100(0.31)=31\%\). For treatment, \(100(0.16)=16\%\), with limits \(100(0.11)=11\%\) and \(100(0.23)=23\%\). Thus the concise table can report 24% (95% CI 18% to 31%) and 16% (95% CI 11% to 23%). The arithmetic is just a change of scale; it does not create a new estimate.
| Group | Estimated cumulative incidence of relapse by 24 months |
|---|---|
| Control | 24% (95% CI 18% to 31%) |
| Treatment | 16% (95% CI 11% to 23%) |
For the figure, use time in months on the horizontal axis and cumulative incidence on the vertical axis, with the vertical scale from 0% to 100%. A clear choice is a two-panel figure: one panel for relapse and one for non-relapse death. Within each panel, draw one step curve for each group, using the same colors or line styles in both panels. If uncertainty is displayed, use bands or bars constructed from the analysis output and label them as pointwise 95% confidence intervals. The following table gives the plotted horizon coordinates after conversion to percentages; the curves themselves should use the full time-to-event output, not straight lines between these selected horizons.
| Panel and curve | 12 months | 24 months | 36 months |
|---|---|---|---|
| Relapse, control | 12% (8% to 18%) | 24% (18% to 31%) | 31% (24% to 39%) |
| Relapse, treatment | 9% (5% to 14%) | 16% (11% to 23%) | 22% (16% to 30%) |
| Non-relapse death, control | 5% (3% to 9%) | 11% (7% to 17%) | 17% (12% to 24%) |
| Non-relapse death, treatment | 4% (2% to 8%) | 8% (5% to 13%) | 13% (8% to 20%) |
A suitable caption is: “Cumulative incidence of first relapse (left) and non-relapse death (right) through 36 months by randomized group. Curves show estimated probabilities in the presence of the competing event; shaded regions show pointwise 95% confidence intervals. The 24-month relapse estimates are 24% (95% CI 18% to 31%) for control and 16% (95% CI 11% to 23%) for treatment.” This describes the estimand, groups, horizon, competing-event context, and uncertainty. It does not imply that the treatment caused the difference or that the groups differ statistically.
Why These Checks Matter
A cumulative incidence function is nondecreasing in time: the probability of having experienced a particular cause by a later time cannot be smaller than the probability by an earlier time. In the example, the control relapse estimates increase from 12% to 24% to 31%, and the treatment estimates increase from 9% to 16% to 22%. These ordered values are consistent with cumulative probabilities. If a table shows a decrease, first check for a transcription, labeling, or time-order error; do not silently adjust the numbers.
For mutually exclusive first-event causes, their cumulative incidences at a common time cannot sum to more than one, because a participant cannot have experienced two different first causes by that time. At 36 months in the control group, the two estimates sum to \(0.31+0.17=0.48\); in the treatment group they sum to \(0.22+0.13=0.35\). Both are at most one. This is a useful consistency check, not a requirement that the sum equal one: some participants remain event-free at that horizon, and censoring means their later outcomes are not thereby known.
The figure should show step curves for event-time estimates, not smooth curves that suggest unsupported precision between observed event times. Selected-horizon table values are useful checks on the plotted curves, but are not a substitute for the full estimated curve. Also verify that the table and figure use the same analysis population, time origin, group names, event definitions, and censoring rules. A visually polished graph with a mismatched population or endpoint is still misleading.
Worked Example: Rounding Without Losing Agreement
Worked Example: Rounding Without Losing Agreement
Suppose a hypothetical software output gives a treatment-group 24-month relapse estimate of 0.1637, with pointwise 95% confidence limits 0.1092 and 0.2314. The table and figure are to report percentages to one decimal place.
Convert to percentages. Multiply each value by 100: the estimate is 16.37%, and the limits are 10.92% and 23.14%. Rounding all three to one decimal place gives 16.4% (95% CI 10.9% to 23.1%).
Carry the same rounded result across displays. Use 16.4% as the 24-month table entry and make the figure’s 24-month point agree with the same underlying value, 0.1637. If the plotting software uses proportions on the vertical axis, the coordinate is 0.1637, not 16.37; if the axis is in percentages, it is 16.37 before display rounding. A table value of 17% paired with a plotted value of 16% would signal inconsistent rounding or a copied value, not a meaningful difference.
Check the interval label. The interval should be identified as a 95% confidence interval for the 24-month relapse cumulative incidence estimate. It is not a 95% prediction interval for an individual patient’s outcome, and it does not state that 95% of patients experience relapse between 10.9% and 23.1%.
Worked Example: Writing a Caption That Stays Within the Evidence
Worked Example: Writing a Caption That Stays Within the Evidence
Consider the hypothetical 24-month estimates from the first example: relapse cumulative incidence is 24% (95% CI 18% to 31%) in control and 16% (95% CI 11% to 23%) in treatment. A caption saying “Treatment reduced relapse by eight percentage points” turns a descriptive contrast into a causal conclusion. The difference between the displayed point estimates is \(24\%-16\%=8\) percentage points, but whether this supports a treatment effect depends on the study design and the relevant inferential analysis.
A more limited caption is: “At 24 months, estimated relapse cumulative incidence was 24% (95% CI 18% to 31%) in control and 16% (95% CI 11% to 23%) in treatment; non-relapse death was treated as a competing event.” This identifies the estimates and event context without asserting a causal effect or a statistically significant difference. Overlap or non-overlap of the two confidence intervals alone is not a substitute for a formal comparison.
Common Mistakes and Limitations
- Changing the event name mid-report. The correction is to use the methods-defined cause label consistently in the table, legend, and caption.
- Plotting only the primary cause and omitting the competing event without explanation. Readers may miss that the primary cumulative incidence is defined in the presence of competing events. Show the competing cause when clinically relevant, or explain the scope of a deliberately focused figure.
- Connecting selected horizon estimates with straight lines. These are only selected coordinates; the estimated cumulative incidence curve is a step function based on event times. Use the full curve output for plotting.
- Reporting confidence intervals without identifying their type or horizon. State which estimate they quantify and whether they are pointwise. Avoid presenting pointwise intervals as if they jointly cover the entire curve with 95% confidence.
- Using the display to imply more than the analysis supports. A table or figure alone does not establish causality, statistical significance, or individual prognosis. Interpret it in light of the design, estimand, uncertainty, and analysis assumptions.
Displays also have practical limits. Too many causes, groups, horizons, or overlapping intervals can make a figure unreadable. In that situation, retain the clinically central comparisons, use clearly labeled panels, and provide the remaining estimates in a table or supplement. Do not remove a competing cause merely to make a primary-event estimate look larger or simpler.
Check Your Understanding
For each item, decide what should be reported or checked. Brief solutions follow the questions.
- A hypothetical estimate of 0.287 has a 95% confidence interval from 0.201 to 0.361. Express the estimate and interval as percentages to one decimal place.
- At 12 and 24 months, a cause-specific cumulative incidence is reported as 18% and 15%. What should be checked before publication?
- At 24 months, two mutually exclusive competing causes have estimated cumulative incidences of 0.42 and 0.19. Is their total permissible, and what does the remainder represent?
- A figure plots only 12- and 24-month table estimates and joins them with a straight line. What is the problem, and what should be plotted instead?
Solutions. (1) Multiply each value by 100: 28.7% (95% CI 20.1% to 36.1%). (2) A cumulative incidence cannot decrease over time; check time ordering, labels, data transfer, and whether the entries are estimates of the same cause in the same population. Do not silently alter a value. (3) Yes. The sum is \(0.42+0.19=0.61\), which is at most one. The remaining 0.39 is the probability not yet experiencing either first event by 24 months, subject to the interpretation of the estimated event probabilities; it is not necessarily known to be event-free indefinitely. (4) The straight segment can misrepresent the step-shaped estimated curve and implies unsupported interpolation. Plot the full cumulative incidence curve from the event-time output, using the horizon estimates as cross-checks.