Free Non-Inferiority Sample Size Calculator

This calculator covers two designs: a non-inferiority comparison of two independent proportions (e.g. a response rate for a new treatment vs. an active comparator) and a non-inferiority comparison of two independent means (e.g. a continuous outcome against a pre-specified margin), each for a one-sided test.

How a non-inferiority trial differs from a superiority trial

A superiority trial (see the standard sample size calculator) asks whether a treatment is better than a comparator. A non-inferiority trial asks a narrower question: is the treatment not unacceptably worse than an active comparator, by more than a margin the investigators defined in advance? This design is common when the new treatment offers some other advantage - lower cost, fewer side effects, easier administration - and does not need to beat the comparator on the primary efficacy outcome, only avoid being meaningfully worse on it.

Two consequences follow for the sample size calculation: the test is one-sided (you only care about ruling out "worse by more than the margin," not detecting "better than"), and the non-inferiority margin - not a clinically meaningful difference to detect - drives the calculation.

Choosing the non-inferiority margin

The margin is the largest loss of effect, relative to the active comparator, that would still be considered clinically acceptable. It must be pre-specified, clinically justified, and is typically set well inside the comparator’s own established effect over placebo - not chosen after seeing the data, and not simply copied from another trial's margin without justification. Regulatory guidance (FDA and EMA both publish non-inferiority guidance documents) generally expects the margin to be justified by historical evidence of the active comparator’s effect, often using a fraction of that historical effect.

Formula

For two proportions: n = (z_α+z_β)²(p_T(1−p_T)+p_C(1−p_C)) / (margin − |p_C−p_T|)², where z_α is the one-sided critical value (not divided by 2, unlike a two-sided superiority test). For two means: n = 2σ²(z_α+z_β)² / (margin − |μ_C−μ_T|)². Both reduce to the simplest, most conservative case when the treatment and comparator are assumed equal (difference = 0), which is the standard assumption unless prior data suggests otherwise.

Why the default alpha is 0.025, not 0.05

A one-sided test at α = 0.025 uses the same critical value (z = 1.96) as a two-sided test at α = 0.05 - which is exactly why regulatory guidance for non-inferiority trials conventionally specifies one-sided 0.025 rather than one-sided 0.05. It keeps the evidentiary bar consistent with a standard superiority trial rather than making it easier to pass by halving the apparent stringency.

Worked example: two proportions

A new treatment is expected to match an active comparator's 80% response rate exactly, with a non-inferiority margin of 10 percentage points, one-sided α = 0.025, and 90% power.

• Result: 337 participants per group, 674 in total.

Enter 0.80 for both proportions, 0.10 for the margin, 0.025 for α, and 0.90 for power in Two Proportions mode to reproduce this - a commonly cited textbook example for this exact design.

Worked example: two means

A continuous outcome has a common standard deviation of 5, the treatment and comparator are assumed equal, the non-inferiority margin is set at 2 units, one-sided α = 0.025, and 90% power. Enter 10 for both means, 5 for the SD, and 2 for the margin in Two Means mode to compute the required sample size for this scenario.

When not to use this calculator

It also does not build in a dropout adjustment - inflate the per-group result by your expected dropout rate (divide by 1 minus the dropout rate) when planning actual recruitment, the same as for a superiority trial.

References

Chow S-C, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Chapman & Hall/CRC; 2017. Julious SA. Sample sizes for clinical trials with Normal data. Statistics in Medicine. 2004;23(12):1921-1986. FDA Guidance for Industry: Non-Inferiority Clinical Trials to Establish Effectiveness (2016).