Why the Layout of a Scenario Table Matters
A sensitivity analysis can produce several treatment-effect estimates from the same trial data because each estimate is conditional on a different assumption about unobserved outcomes. A scenario table puts these results side by side. Its value is not merely compactness: the layout can make clear which assumptions produced each estimate and whether the conclusion changes across the prespecified scenarios. If assumptions are hidden, intervals are mismatched, or only a favorable row is shown, readers cannot make that comparison reliably.
This tutorial concerns how to design and read that table. It does not determine which assumptions are scientifically plausible; those should be justified in the analysis. Instead, it sets out what a table needs to show so a reader can connect each assumption to its estimate, uncertainty, and clinical interpretation.
For consistent interpretation, state the direction of benefit and the clinical threshold in the table or its note. In the examples below, \(\hat\theta_s\) is the estimated treatment benefit under scenario \(s\), measured in points on a symptom scale. Larger positive values favor treatment, and \(\Delta=3\) points is the hypothetical threshold for a clinically important benefit. The threshold is an interpretive benchmark, not a claim that every value above it has the same clinical consequences.
What Each Row Must Connect
A reader should be able to move across a row without guessing which assumptions, estimate, or interval belong together. At minimum, include a scenario identifier, a concise statement of its assumptions, the estimate, an uncertainty interval, and an interpretation tied to the endpoint's direction and clinical threshold. If the analysis uses different assumptions in the two treatment arms, identify them separately rather than compressing them into an ambiguous label such as “strict.”
| Table element | What it should make explicit |
|---|---|
| Scenario label | A unique, stable name or number for the prespecified scenario |
| Assumptions | The assumptions defining the row, including arm-specific assumptions when relevant |
| Estimate and units | The assumption-conditional estimate and the outcome scale |
| Uncertainty | The interval and confidence level, calculated under the same scenario as the estimate |
| Interpretation | How the estimate and interval compare with the null and the clinical threshold |
The assumptions should be specific enough to distinguish scenarios. If the row relies on an arm-specific departure from a reference assumption, give its value and units, or define a label in a table note. A table note can clarify a shared estimation method, the interval level, the benefit direction, and the meaning of \(\Delta\). It should not make the reader search elsewhere to discover what the scenario labels mean.
The uncertainty interval must match the estimate in its row. If \(\hat\theta_s\) has standard error \(SE_s\), a large-sample, two-sided 95% Wald interval is \(\hat\theta_s \pm 1.96SE_s\), provided the normal approximation and standard-error calculation are appropriate for that analysis. This is an interval conditional on scenario \(s\), not an interval that includes uncertainty about which scenario is correct.
The comparison to \(\Delta\) should be explicit. A point estimate above \(\Delta\) is an estimated benefit at least as large as the threshold; it does not, by itself, show that the entire uncertainty interval exceeds the threshold. An interval wholly above zero supports a positive effect at the stated confidence level under that scenario, while an interval wholly above \(\Delta\) supports an effect greater than the chosen clinical threshold at that level. These are different claims.
Worked Example: Reading Every Row Against the Same Benchmarks
Hypothetical results. A trial compares a treatment with control on a symptom score, for which a reduction is favorable. The analysis reports benefit as control minus treatment, so positive values favor treatment. The clinical threshold is \(\Delta=3\) points. The following three scenarios were prespecified; their missing-outcome assumptions are stated in the table.
| Scenario | Missing-outcome assumption | \(\hat\theta_s\) (points) | SE (points) | 95% CI (points) |
|---|---|---|---|---|
| A | Missing outcomes follow the reference model in both arms | 5.2 | 1.0 | [3.24, 7.16] |
| B | Unobserved treatment-arm outcomes are 1 point less favorable than the reference model; control follows the reference model | 3.8 | 1.1 | [1.64, 5.96] |
| C | Unobserved treatment-arm outcomes are 2 points less favorable than the reference model; control follows the reference model | 2.1 | 1.2 | [-0.25, 4.45] |
For Scenario B, for example, the interval is \(3.8 \pm 1.96(1.1)\). The margin is \(2.156\) points, so the interval is \([3.8-2.156,\ 3.8+2.156]=[1.644,\ 5.956]\), or \([1.64,\ 5.96]\) after rounding. The same calculation gives Scenario A as \(5.2 \pm 1.96(1.0)=[3.24,\ 7.16]\), and Scenario C as \(2.1 \pm 1.96(1.2)=[-0.252,\ 4.452]\), or \([-0.25,\ 4.45]\).
Under A, the entire interval is above both zero and the 3-point threshold. Under B, the interval is above zero but includes values below 3; the estimate exceeds the threshold, but the interval does not establish that the benefit exceeds it. Under C, the interval includes zero and values above 3, so it is compatible with no benefit as well as a clinically important benefit. Each statement is conditional on its row's assumptions. Taken together, the rows show that the point estimate declines as the assumed treatment-arm outcomes become less favorable; they do not identify which assumption is true.
Why the Interval Must Stay With Its Scenario
The row-specific interval follows directly from using the estimate and its standard error under the same assumptions. For a two-sided 95% Wald interval, the normal approximation places about 95% of the standard normal distribution between \(-1.96\) and \(1.96\). If the estimate's sampling distribution is approximately normal around the scenario-specific target, standardizing by \(SE_s\) gives the interval formula above. The approximation concerns repeated-sampling uncertainty with the scenario held fixed.
This justification depends on an appropriate standard error and an adequate normal approximation (or another justified interval method). It does not validate the missing-outcome assumptions. Nor does it make the 95% interval a 95% probability statement about a fixed parameter. It describes the long-run coverage of the interval procedure when the scenario's assumptions and the statistical model hold.
A common table error is to calculate an estimate under one scenario but attach the standard error or interval from another. The displayed endpoints may still look plausible, but the row no longer represents the uncertainty calculation for its stated assumptions. Check the estimate, standard error, interval method, and scenario together. If the method is not the Wald formula, label or describe the method rather than implying that the formula above was used.
Worked Example: Checking an Interval Before Interpreting It
Hypothetical results. A table gives a benefit estimate of 4.0 points and a standard error of 1.5 points under Scenario D. The interval is labelled “95% CI,” and the analysis states that a two-sided Wald interval is appropriate. The clinical threshold is 3 points.
Calculate the interval from the values in that row:
The interval includes only positive values, so it is above zero, but its lower endpoint is below 3. The point estimate is 4.0 points, greater than the clinical threshold; however, the interval does not show that the benefit exceeds 3 points at the stated confidence level. If the table instead displayed \([2.04,\ 5.96]\), it would not agree with the reported estimate and standard error under this method. A reader should flag the inconsistency and seek clarification, not interpret the more favorable interval as though it were verified.
Keeping the Prespecified Scenario Set Visible
A fair comparison requires showing the full set of prespecified scenarios, not only the row with the largest estimate, the narrowest interval, or the most favorable interpretation. Use a stable ordering, such as the order in which scenarios were defined or an order that makes the assumption changes easy to follow. If a scenario is omitted because a computation failed, identify the omission and its reason; do not let the table imply that the displayed rows are the entire planned set.
This does not require treating every conceivable assumption as equally plausible. It requires a clear account of the scenarios actually specified and the results under each. Keep the scenario definition visible, and do not present a row as the primary result merely because its estimate is most attractive. A table can include a reference scenario, but should label it as such and retain the other prespecified rows for comparison.
Worked Example: Auditing a Favorable-Only Summary
Hypothetical report. An analyst prespecified Scenarios A, B, and C as in the first example, but a summary table reports only Scenario A and says, “The estimated benefit was 5.2 points, with a 95% CI of 3.24 to 7.16 points.” The report does not say that two other scenarios were prespecified.
The arithmetic and the conditional interpretation for A are correct: the interval is above the 3-point threshold. The problem is that this result alone does not describe the prespecified sensitivity analysis. B has an estimate of 3.8 points and an interval from 1.64 to 5.96; C has an estimate of 2.1 points and an interval from -0.25 to 4.45. Those rows give materially different interpretations.
A complete summary would display all three rows, name the assumptions, retain the common units and interval level, and apply the same benchmark to every row. It could then state that the evidence is more favorable under A, while B and C have intervals that do not lie wholly above the clinical threshold, and C also includes zero. This description does not choose a preferred assumption; it lets readers see what changes across the prespecified scenarios.
Diagnostics, Alternatives, and Limits
Before interpreting a scenario table, check for the following warning signs:
- Unclear scenario labels: a label such as “conservative” is not enough unless its assumptions are defined.
- Unmatched quantities: the standard error or interval may not correspond to the estimate in that row.
- Inconsistent directions or units: a sign convention or scale change can make apparently comparable estimates point in opposite directions.
- Missing prespecified rows: a table may give an incomplete picture if exclusions are not disclosed.
- Overstated clinical claims: an estimate above \(\Delta\) is not the same as an interval entirely above \(\Delta\).
A scenario table is useful when exact assumptions and row-by-row intervals are important. A treatment-effect surface can show how estimates vary continuously across two sensitivity parameters, while a table is often easier to audit for a finite set of prespecified cases. A confidence envelope over a sensitivity set answers a different summary question by displaying a range that covers results across that set; it does not replace the need to identify which assumptions generate particular row-specific results. These summaries are complementary, not interchangeable.
A table also has limits. Its intervals quantify sampling uncertainty conditional on each scenario; the spread of estimates across rows reflects sensitivity to the chosen assumptions, not a probability distribution over those assumptions. A finite list cannot show every possible assumption, and a neat table cannot establish that its assumptions are plausible or that the underlying model is correct. Interpretation therefore depends on both transparent presentation and substantive justification of the scenarios.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A benefit estimate is 2.5 points, its 95% interval is \([0.4,\ 4.6]\), and the clinical threshold is 3 points. What can be said about benefit and the threshold under that scenario?
- Why should a scenario table state arm-specific assumptions separately when they differ by treatment arm?
- A table shows an estimate of 6.0 points, \(SE=2.0\) points, and a 95% Wald interval of \([3.0,\ 9.0]\). Check the interval and interpret it when \(\Delta=3\) points.
- What is lost if only the scenario with the largest estimated benefit is shown, even when its estimate and interval are calculated correctly?
Solutions. (1) The interval is entirely above zero, so it supports positive benefit under this scenario at the stated confidence level. Its lower endpoint is below 3, so it does not establish that benefit exceeds the clinical threshold, even though the point estimate is below that threshold as well. (2) Separate statements show exactly what is assumed for each arm and prevent a reader from mistaking a joint or arm-specific departure for a shared assumption. (3) The Wald interval is \(6.0 \pm 1.96(2.0)=6.0\pm3.92=[2.08,\ 9.92]\) points, not \([3.0,\ 9.0]\). The displayed interval is inconsistent with the stated estimate and standard error under the stated method. Using the recalculated interval, the interval is above zero but not wholly above \(\Delta=3\); the table should be corrected or its interval method clarified. (4) The reader cannot assess how results depend on the other prespecified assumptions. The favorable row alone does not represent the full sensitivity analysis or show whether its interpretation holds across the planned scenarios.