A trial reports that a shorter rehabilitation programme is “noninferior” to its comparator. That conclusion does not mean the programmes produce identical results. It means the analysis has ruled out a specified degree of disadvantage, subject to the design and analysis assumptions.
To read the result, you need three items together: the direction of the outcome, the order of subtraction, and the prespecified margin. A confidence interval without those items is an unfinished comparison.
All programmes, scales, margins and results below are fictional teaching examples. They do not establish an acceptable loss for any real rehabilitation intervention.
Put the unacceptable loss on the correct side
Imagine a Canadian research team comparing a reduced-visit programme with a standard programme. The outcome is a fictional ability score from 0 to 100, with higher scores indicating better ability. Define the effect as:
difference = mean score with new programme − mean score with standard programme
A negative difference therefore favours the standard programme. The protocol specifies a noninferiority margin of −5 points. For this exercise, its statistical rule requires the lower limit of a two-sided 95% confidence interval to be strictly above −5. This corresponds to a one-sided test at the 2.5% level under the matching procedure.
The FDA guidance explains the distinction between excluding an unacceptable loss and demonstrating equivalence. Its regulatory scope is US drugs and biologics; we use its statistical principles here, not as a Canadian physiotherapy requirement. Non-Inferiority Clinical Trials to Establish Effectiveness.
Four fictional results, four different conclusions
Each row is an alternative result from the same imagined design, not a set of outcomes from one actual trial.
| Estimated difference | Two-sided 95% interval | What the specified rule permits |
|---|---|---|
| −1 point | −4 to +2 | Supports noninferiority; does not establish superiority |
| −1 point | −7 to +5 | Does not establish noninferiority; does not establish inferiority |
| −3 points | −4 to −2 | Supports noninferiority and indicates a lower mean score with the new programme |
| −7 points | −8 to −6 | Indicates a disadvantage exceeding the margin |
The first row excludes losses of five or more points, but includes zero. “The new programme is equally effective” would claim more than the interval supports.
The second row has exactly the same point estimate. Its uncertainty is wider, encompassing both an unacceptable loss and a benefit. A failed noninferiority test is not automatically proof that the new programme is inferior. It can be an inconclusive result.
The third row is the useful boundary case. Every value in the interval is below zero, yet every value is above −5. The new programme can be statistically worse on this outcome and still satisfy the chosen noninferiority criterion. Whether that trade-off is worthwhile requires evidence about the other benefits, harms and burdens, alongside a defensible margin.
The fourth row lies entirely beyond the unacceptable-loss boundary. It provides a very different message from the inconclusive second row.
An interval that ends exactly at −5 does not satisfy the strict rule specified here. In practice, consult unrounded values and the prespecified testing procedure; rounded display values may conceal which side of a boundary the analysis actually reached.
A margin needs an argument before it needs a number
Our example stipulates −5 to teach interval reading. A real reviewer should not accept that number merely because it appears in a methods section.
Ask what loss patients and clinicians would consider unacceptable, what evidence supports the comparator’s benefit, and whether the new study could detect meaningful differences under its actual conditions. A comparison in which both programmes are delivered ineffectively can produce similar outcomes without preserving an established benefit. These issues underpin the guidance’s discussion of margin justification and assay sensitivity. FDA guidance.
A within-person threshold for important change is not automatically the correct between-group noninferiority margin. Those quantities answer different questions. Nor should investigators select a convenient margin after seeing the interval. Moving the boundary from −5 to −8 would make the second result pass, but it would change the question after the answer was visible.
In this fictional study, “fewer visits” is a proposed advantage, not proof of lower total burden. Travel, home practice, support needs and adverse outcomes would need their own evidence. Noninferiority on one ability score cannot establish every claimed advantage of a service model.
Read the question behind ITT and per-protocol analyses
An intention-to-treat comparison addresses assignment to programmes, retaining participants in their randomized groups. That can be the right question for a service decision. If many participants receive similar care despite different assignments, however, a small assignment effect does not establish that the programmes would have similar effects if followed as intended.
A simple per-protocol comparison that deletes nonadherent participants does not automatically solve this problem. Adherence occurs after randomization and can relate to prognosis. A methodological analysis explains why both approaches need careful interpretation and why the direction of problems depends on the pattern of nonadherence. Non-adherence in non-inferiority trials: pitfalls and recommendations.
Consider a fictional imbalance: participants with early difficulty are more likely to leave the reduced-visit programme, while participants who improve quickly are more likely to leave the standard programme. Removing both sets can make the retained groups differ in prognosis. Labelling the remaining comparison “per protocol” does not restore the original balance created by randomization.
For a paper review, write down the intended effect first: assignment under the trial’s delivery conditions, or following a specified programme. Then inspect the analysis population, deviations, missing outcomes and assumptions. Consistent ITT and per-protocol results are informative, but two analyses can agree while sharing a problem. Estimating an adherence effect credibly may require methods beyond deleting participants.
Transfer exercise: reverse the direction carefully
A second fictional study measures an undesirable event by twelve weeks. It defines the effect as new minus standard event risk, in percentage points. Its prespecified unacceptable excess is +3 percentage points. The rule requires the upper bound of the two-sided 95% interval to be strictly below +3.
Result A is −1 to +2 percentage points. Result B is −1 to +4. Which supports noninferiority, and does either establish superiority?
Reasoned solution: A satisfies the specified noninferiority rule because its upper limit is below +3. B does not: the interval still includes an unacceptable excess. Neither establishes superiority on this outcome because both intervals include zero. For this undesirable event, superiority would require the relevant interval to lie below zero under the planned procedure.
The direction changed because higher values now indicate a worse outcome. Memorizing “look at the lower bound” would therefore produce the wrong answer. Start with the outcome and subtraction order every time.
A useful sentence for your next appraisal
Write: “For [outcome and time], the [new minus standard] interval [did/did not] exclude the prespecified unacceptable loss of [margin], under [analysis and assumptions].” Then add whether the margin and design were credible. That wording keeps the numerical decision and the scientific justification visible together.
Sources and further reading
- FDA: Non-Inferiority Clinical Trials to Establish Effectiveness, 2016 — statistical framing, margin justification and trial quality; selected full-text sections reviewed.
- Mo et al.: Non-adherence in non-inferiority trials: pitfalls and recommendations, 2020 — analysis questions and adherence-related bias; indexed excerpts reviewed because direct publisher access was unavailable.