Non-Inferiority and Equivalence
Sample-size planning for a two-arm parallel non-inferiority trial with a continuous outcome. Specify the expected treatment difference, non-inferiority margin, variability, allocation ratio, significance level, power, and anticipated dropout. The calculation uses the large-sample normal-approximation framework used for non-inferiority tests of two means.
This calculator implements the general two-arm parallel-group sample-size framework for a non-inferiority test of two means using a difference scale and a large-sample normal approximation. this method lists this method as Non-Inferiority Tests for Two Means using Differences, including an unequal-allocation version. likewise provides a one-sided non-inferiority test for the difference of two means.
The calculator expresses the non-inferiority margin as a positive amount of clinically unacceptable loss, M. The expected treatment effect is first put onto a favorable-effect scale: treatment minus control when higher values are better, or control minus treatment when lower values are better.
If the expected favorable treatment effect is d, the distance between the assumed alternative and the non-inferiority boundary is therefore d + M. A larger distance from the boundary requires fewer participants, while a smaller distance requires more participants.
Let r = nT/nC be the treatment-to-control allocation ratio, σT and σC the treatment and control standard deviations, z1−α the one-sided normal critical value, and z1−β the normal quantile corresponding to the desired power.
The continuous sample sizes are rounded up to whole participants. If dropout is specified, each arm is inflated by dividing by 1 minus the dropout proportion and rounded up again.
This is a planning calculation for a continuous endpoint under the stated normal-approximation assumptions. It is not a substitute for choosing and justifying the non-inferiority margin. In an actual clinical trial, the margin should be justified from historical evidence, preservation of an appropriate fraction of the comparator effect, clinical considerations, and the intended analysis population.
A published worked example from the Chinese University of Hong Kong considers a non-inferiority margin of 5%, an expected treatment-control mean difference of 0%, a standard deviation of 10%, 80% power, and a one-sided α of 0.05. With equal allocation, the normal-approximation calculation gives a continuous requirement of approximately 49.46 participants per group, which rounds to 50 participants per group. The calculator reproduces this result.
Chow, S.-C., Shao, J., & Wang, H. (2003). Sample Size Calculations in Clinical Research. Marcel Dekker / CRC Press. The book presents sample-size procedures for non-inferiority and superiority testing under parallel-group designs, including unequal treatment allocation.
Chinese University of Hong Kong, Centre for Clinical Trials. Sample Size Estimation — Two Parallel-Sample Means. The worked example specifies a 5% non-inferiority margin, 0% expected mean difference, SD = 10%, 80% power, α = 0.05, and reports n = 50 per group using the normal approximation.
this method (the software). this method 2026 Sample Size Procedures. The this method procedure list includes Non-Inferiority Tests for Two Means using Differences and the corresponding unequal-allocation procedure.
/ Statistical Solutions. Non-Inferiority t-test for Two Means. provides one-sided non-inferiority procedures for differences between two means; its documentation and worked examples describe the corresponding parallel-group design.