non inferiority sample size calculator - Aaron Graves, PhDude Replica

Calculator: Two-Arm Non-Inferiority Trial (Binary Outcome)

Estimate required sample size per group for a one-sided non-inferiority test comparing two proportions with equal allocation.

Control group success rate Enter as percent (e.g., 70) or decimal (e.g., 0.70).

Expected treatment group success rate Expected observed success rate under the alternative hypothesis.

Non-inferiority margin (absolute difference) Maximum acceptable drop in success rate (e.g., 10 or 0.10).

One-sided alpha Common choices: 2.5% or 5% (enter 2.5 or 0.025).

Power Typical target: 80% or 90% (enter 80 or 0.80).

Expected dropout / non-evaluable rate Enter 0 if no inflation needed.

How this non-inferiority sample size calculator works

This tool estimates how many participants you need in each arm of a two-group, parallel, non-inferiority trial when your endpoint is binary (success/failure). It assumes equal randomization (1:1) and a one-sided hypothesis.

In a non-inferiority design, the goal is to show that a new treatment is not unacceptably worse than control by more than a pre-specified margin. That margin is usually denoted by Δ (delta).

Statistical setup used

Outcome: two independent proportions (treatment vs control)
Design: parallel groups, equal sample size per arm
Hypothesis direction: one-sided non-inferiority
Approximation: large-sample normal (Wald-style) calculation

The implemented equation is:

n per group = ((Z(1-α) + Z(power))² × [pC(1-pC) + pT(1-pT)]) / (pT - pC + Δ)²

Where pC is the control success rate, pT is the expected treatment success rate, and Δ is the non-inferiority margin in absolute proportion units.

Input guidance and interpretation

1) Control success rate

Use the best estimate from prior RCTs, registries, or a pilot. Overly optimistic control rates can underpower your trial.

2) Expected treatment success rate

This should reflect your best planning assumption for the experimental arm under realistic implementation conditions.

3) Non-inferiority margin (Δ)

The margin is the most important design choice and should be clinically justified, not only statistically convenient. A margin that is too wide may produce a trial that is statistically positive but clinically unconvincing.

4) Alpha and power

One-sided alpha: often 0.025 in regulatory settings
Power: often 0.80 or 0.90

5) Dropout inflation

The calculator reports both base sample size and dropout-adjusted sample size. The adjusted figure should usually drive your enrollment target.

Quick example

Suppose your control success rate is 70%, treatment is expected at 68%, and non-inferiority margin is 10%. With one-sided alpha of 2.5% and 80% power, the tool computes the required sample per group and then inflates for dropout.

Common mistakes in non-inferiority planning

Choosing a non-inferiority margin without clinical and historical evidence.
Using two-sided alpha in planning when the primary test is one-sided.
Ignoring dropout, protocol deviations, and non-adherence.
Planning with a single uncertain control rate and no sensitivity checks.
Forgetting that analysis population strategy (ITT vs PP) matters more in NI trials.

Important limitations

This calculator is intended for fast protocol planning and educational use. It does not replace a full statistical analysis plan. For pivotal trials, consult a biostatistician and consider method-specific approaches (e.g., Farrington-Manning, continuity correction, unequal allocation, stratification, event-driven design, or time-to-event methods when relevant).

Practical checklist before finalizing sample size

Document the clinical rationale for Δ.
Run sensitivity analyses over plausible pC and pT values.
Validate assumptions with historical data and feasibility constraints.
Define primary and supportive analysis populations early.
Confirm one-sided alpha and multiplicity rules with your regulatory strategy.