Non-inferiority trial sample size calculator for means and proportions

In a superiority trial the null hypothesis is "no difference" and you hope to reject it. In a non-inferiority trial the null hypothesis is that the new treatment is worse than the active control by at least the margin: with higher values better, H0 is (experimental minus control) ≤ -M. Rejecting it shows the new treatment is not unacceptably worse. It does not show the two are equal, and it does not show the new treatment is better.

Because the question is one-directional, alpha is one-sided. A one-sided alpha of 0.025 is the usual choice, and it is the same as requiring the lower limit of a two-sided 95% confidence interval for the difference to sit above -M. Using a one-sided 0.05 halves the evidence standard, which regulators generally do not accept for a confirmatory trial.

The design only makes sense with an active control of established effect. FDA's guidance "Non-Inferiority Clinical Trials to Establish Effectiveness" (final, November 2016) describes M1, the effect of the active control over placebo that can be assumed in the new trial, and M2, the largest loss of that effect that is clinically acceptable. M2 is usually the margin you test. In the EU, the "Guideline on the choice of the non-inferiority margin" (EMEA/CPMP/EWP/2158/99, effective January 2006) still applies; EMA published a draft replacement, "Non-inferiority and equivalence comparisons in clinical trials" (EMA/301654/2025), whose consultation closed on 31 May 2026. Check its status before you finalise a protocol. This page is not regulatory advice.

Continuous outcome. With σ = 10, M = 4, an expected true difference Δ = 0, one-sided alpha 0.025 (z = 1.960) and 90% power (z = 1.282), the sum of the z values squared is 10.51. n = 2 x 100 x 10.51 / 4² = 131.3, so 132 evaluable participants per group, 264 in total. This follows Julious (Statistics in Medicine, 2004). At 80% power the same inputs need 99 per group.

The expected true difference matters as much as the margin. If you expect the new treatment to be slightly better (Δ = +1), the denominator becomes 5² and n falls to 85 per group. If you expect it to be slightly worse (Δ = -1), the denominator is 3² and n rises to 234. Assuming "no difference" when the honest expectation is a small deficit is one of the commonest ways to underpower a non-inferiority trial.

Binary outcome. With success in 85% of both arms, M = 10 percentage points, one-sided alpha 0.025 and 90% power: n = 10.51 x (0.85 x 0.15 + 0.85 x 0.15) / 0.10² = 267.9, so 268 per group. This is the normal-approximation formula with unpooled variances, as in Blackwelder (Controlled Clinical Trials, 1982). If the experimental arm is expected to reach only 82%, n rises to 590 per group; with a 5-point margin and equal rates, it is 1,072.

Sloppy conduct biases a non-inferiority trial toward success. Missing data, poor adherence, misclassified outcomes and protocol deviations all tend to make the two arms look alike, and looking alike is what a non-inferiority trial is trying to show. That is the opposite of a superiority trial, where the same problems usually hide an effect. Regulators therefore look at both the full analysis set and the per-protocol set, and expect consistent conclusions.

The margin must be justified from historical evidence and clinical judgement before unblinding, never chosen to fit the sample size you can afford. The trial also relies on assay sensitivity and the constancy assumption: the active control must work in your trial as well as it did in the historical placebo-controlled trials. If standards of care have changed, that assumption weakens.

Because poor conduct pushes a non-inferiority result toward success, the data system is part of the design. In Capture, edit checks with range high, range low or custom rules raise a query automatically when a site enters a value that breaks a rule, and the field-level audit trail records the old value, new value, user, time and reason for every change. Source data verification can be set per field, so monitors focus on the primary endpoint and the variables that define the per-protocol set. Protocol deviation tracking describes how teams log the deviations that decide who is in that set.

Randomisation runs in the same system, blinded roles never receive treatment-arm values, and at database lock you can export CSV or Excel with a data dictionary, or SDTM datasets as SAS XPT files with Define-XML, for both analysis sets. Phase 3 confirmatory trials are a normal use case; see EDC for Phase 3 clinical trials. For a superiority comparison of two proportions, use the sample size calculator instead.