Superiority, equivalence and non-inferiority trials
- Study design
A better treatment is not always the goal: sometimes it is enough to show that a simpler or cheaper one is not worse than the standard beyond a set margin.
What it is
A superiority trial aims to show that one treatment is better than another. A non-inferiority trial aims to show that a new treatment with other advantages (shorter, cheaper, less toxic) is not worse than the standard by more than a margin set in advance. An equivalence trial aims to show that the difference lies within a margin on both sides. The conclusion comes from reading where the confidence interval of the difference falls relative to zero and to the margin.
How it is built
- A comparator of proven efficacy is chosen and the margin is set (for example, −10 percentage points).
- A sample size is calculated for that margin.
- Patients are randomised and the outcome is measured in both groups.
- The difference and its 95% CI are calculated and compared with 0 and the margin.
Worked example
- A 5-day antibiotic course is compared with the standard 10 days in pneumonia: 400 patients per group; margin set at −10 points.
- Cure: 352 of 400 (88%) with the short course and 360 of 400 (90%) with the standard.
- Difference: 88% − 90% = −2 percentage points.
- Standard error ≈ square root of (0.88 × 0.12 / 400 + 0.90 × 0.10 / 400) ≈ 0.022, about 2.2 points.
- 95% CI ≈ −2 ± 1.96 × 2.2 ≈ −6.3 to +2.3 points (rounded to one decimal).
- The lower limit (−6.3) does not reach −10: non-inferiority is shown.
- The CI includes 0: superiority is not shown. Reading: the short course is not worse by more than 10 points.
Reading the 95% CI of the difference (new − standard), margin −10 points
| 95% CI of the difference | Conclusion |
|---|---|
| +1 to +8 | Superior (and also non-inferior) |
| −6 to +2 | Non-inferior; not superior |
| −13 to +1 | Inconclusive: crosses the margin |
| −18 to −11 | Inferior: the whole CI lies beyond the margin |
Markers
- 95% CI
- Margin
- ITT
When to use it
- Used when a new treatment promises practical advantages: fewer days, oral route, fewer side effects or lower cost.
- A margin that is too wide can label a clearly worse treatment ‘non-inferior’: judge whether it is clinically acceptable.
Common pitfalls
- Concluding equivalence because a superiority trial found no significant difference: absence of evidence is not evidence of absence.
- Setting or changing the margin after seeing the data.
- Using a weak or poorly delivered comparator, which makes it easier to look non-inferior.
Test yourself
Think of the answer, then tap the question to see it.
What is the non-inferiority margin?
The largest loss of efficacy against the standard that is judged clinically acceptable; it is set before the trial starts.
With a margin of −10 points, the difference has a 95% CI of −12 to +3. What is the conclusion?
The result is inconclusive: the interval crosses the margin, so a loss larger than 10 points cannot be ruled out.
Does a superiority trial with no significant difference show equivalence?
No. It may lack power; claiming equivalence or non-inferiority needs a design with a pre-set margin.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Non-Inferiority Clinical Trials (U.S. Food and Drug Administration, 2016); Chapter 15: Interpreting results and drawing conclusions (Cochrane, 2024).
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Representative model, for educational purposes only.