Non-Inferiority and Equivalence
Assess how a treatment-effect confidence interval relates to both a superiority boundary of 0 and a prespecified non-inferiority margin. The calculator shows whether the result supports superiority, non-inferiority only, inferiority, or an indeterminate result.
This calculator evaluates a treatment effect defined as new treatment minus control, with positive values favoring the new treatment. It uses the normal-approximation confidence interval estimate ± z1−α/2 × SE.
For a two-sided confidence level of 1−α, statistical superiority in the prespecified favorable direction is supported when the entire confidence interval is above zero. Equivalently, the lower confidence limit is greater than 0.
With a non-inferiority margin Δ > 0, the null boundary is −Δ on the treatment-effect scale. Non-inferiority is supported when the lower confidence limit is above −Δ. A confidence interval that crosses −Δ does not establish non-inferiority.
If a non-inferiority trial produces a confidence interval entirely above zero, the result also supports statistical superiority. Conversely, a superiority trial that does not establish superiority can support non-inferiority only when an acceptable non-inferiority margin was defined prospectively and the trial satisfies the relevant design and conduct requirements. A post hoc choice of a margin should not be used to manufacture a non-inferiority conclusion.
The regulatory guidance emphasizes that switching the objective is more than a mechanical comparison of p-values. The comparator, endpoint, population, trial conduct, analysis populations, sensitivity, and justification of the non-inferiority margin all matter. This calculator therefore reports the statistical CI relationship but does not by itself certify that a regulatory switch is appropriate.
Committee for Proprietary Medicinal Products (CPMP). (2001). Points to consider on switching between superiority and non-inferiority. British Journal of Clinical Pharmacology, 52, 223–228. DOI: 10.1046/j.1365-2125.2001.01397-3.x.
Lewis, J. A. (2001). Switching between superiority and non-inferiority: an introductory note. British Journal of Clinical Pharmacology, 52(3), 221. DOI: 10.1046/j.0306-5251.2001.01424.x-i1.
Althunian, T. A., de Boer, A., Klungel, O. H., & Stolk, P. (2017). Defining the noninferiority margin and analysing noninferiority: An overview. British Journal of Clinical Pharmacology, 83, 1636–1642. DOI: 10.1111/bcp.13280.
this method is a commercial power and sample-size package from the software. the relevant methodological literature describes separate non-inferiority and superiority-by-a-margin procedures and notes that its procedures can solve for power, sample size, and effect size depending on the procedure.