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Clinical Trials · PAR-SUP-B

Sample Size for a Superiority Trial with a Binary Outcome

Use this calculator to plan a two-arm superiority trial with a binary outcome when superiority is defined on the absolute difference in event or response probabilities.

1. Planning setup

Outcome direction

Enter 1 for equal allocation, 2 for 2:1, or 0.5 for 1:2.

2. Information obtained from previous study / literature

3. Information decided by the researcher

Enter 0 for conventional superiority versus no difference. A value above 0 requires the anticipated benefit to exceed that additional threshold.

4. Results

Enter the trial assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A randomized vaccine trial compares seroconversion proportions between a new vaccine and the current vaccine and is designed to demonstrate superior response.

Formula and methodological note

This calculator uses the specified Chow et al. large-sample normal-approximation method for two independent parallel groups. It assumes the planned allocation ratio, no clustering or pairing, and no covariate adjustment. It does not implement exact, score-based, Farrington–Manning, crossover, repeated-measures, or cluster-trial methods.

For superiority, the planning gap is the anticipated benefit minus the required superiority threshold. Set the threshold to 0 for conventional superiority versus no difference; a positive threshold means the study is planned to demonstrate benefit greater than that threshold.

Method references

  1. Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. CRC Press; 2018. Eq. 4.8.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for a Superiority Trial with a Binary Outcome (PAR-SUP-B).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. http://127.0.0.1:4321/tools/sample-size/clinical-complex-study-designs/superiority-binary-outcome/.