Non-Inferiority and Equivalence
Derive a fixed non-inferiority margin from historical active-control evidence using the lower confidence limit of the control effect and a prespecified preservation fraction. Supports difference and ratio/odds-ratio effect scales and runs entirely in your browser.
This calculator implements the fixed-margin / 95-95 approach to developing a non-inferiority margin. The approach uses historical evidence for the effect of an established Standard treatment relative to placebo or another reference. First, a conservative lower confidence limit for that historical effect is obtained. A clinically justified fraction of that effect is then retained when defining the final non-inferiority margin.
Let θ be the historical estimate of the Standard treatment effect, SE its standard error, and z the standard-normal critical value corresponding to the requested two-sided confidence level.
For a ratio or odds-ratio scale, the calculation is performed on the natural-log scale and transformed back to the original scale:
If r is the fraction of the historical control effect that should be preserved, the final margin is formed from the lower confidence limit. On an additive difference scale, the preserved effect is rL. On a ratio or odds-ratio scale with the null value equal to 1, preserving a fraction r of the log-scale effect gives:
For example, preserving 50% of a lower confidence limit of 1.40 gives √1.40 = 1.1832. This is the construction illustrated for the bivalirudin example in Odem-Davis and Fleming, where a 95-95 margin of approximately 1.19 was obtained by preserving half of the control effect.
Historical odds ratio: 1.82
Historical log-OR SE: 0.1338593
Confidence level: 95%
Effect preserved: 50%
Historical lower 95% CI: approximately 1.40
Expected NI margin: 1.1832, reported as approximately 1.19 in the published example
The published bivalirudin example describes a historical lower confidence limit of 1.40 and a 50% preservation calculation yielding a 95-95 margin of 1.19. Using 1.82 as the historical point estimate and reconstructing the corresponding standard error from the reported 1.40 lower limit gives 0.1338593; the calculator returns 1.1832 before rounding, reproducing the published result.
The calculated margin is a statistical design quantity, not an automatic determination of clinical acceptability. FDA guidance states that the choice of the non-inferiority margin requires consideration of the historical evidence for the active control, uncertainty in that evidence, and the clinical importance of the effect being preserved. The margin should therefore be prospectively justified rather than selected solely because it produces a convenient sample size.
Odem-Davis, K. & Fleming, T. R. (2013). Adjusting for unknown bias in non-inferiority clinical trials. Statistics in Biopharmaceutical Research, 5(3), 248–258. DOI: 10.1080/19466315.2013.795910.
U.S. Food and Drug Administration (2016). Non-Inferiority Clinical Trials. Guidance for Industry. The guidance discusses the rationale for non-inferiority trials and considerations in choosing the non-inferiority margin.
Yu, B., Yang, H., & Sabin, A. (2019). A note on the determination of non-inferiority margins with application in oncology clinical trials. Contemporary Clinical Trials Communications, 14, 100454.