Clinical Trial Designs · Cluster-Randomized Trials

Cluster-Randomized Superiority Trial — Binary Outcome

Plan a one-sided superiority comparison between experimental and reference cluster-randomized arms with a binary primary endpoint.

How this calculator works

The treatment contrast is experimental minus reference. The calculator applies the prespecified one-sided superiority test using arm-specific Bernoulli variances, a cluster design effect, and a noncentral-t whole-cluster search.

Use this calculator only when the event interpretation and direction of benefit are justified before the trial begins.

Privacy: Calculations run locally in your browser. Values entered are not uploaded by this calculator.

Planning disclaimer: This tool supports research planning and does not replace protocol-specific statistical consultation.

1. Planning setup

Primary outcome name

Optional. Used only in protocol-ready wording.

Cluster-size assumption

EqualVariable

Choose variable when retained clusters are expected to contribute meaningfully different participant counts.

2. Information obtained from previous study / literature

Expected group 1 event probability

Expected group 2 event probability

Intracluster correlation coefficient ρ

Use evidence from a comparable outcome, population, and clustering unit.

Analysable mean participants per retained cluster m

3. Information decided by the researcher

Interpretation of event = 1

Favourable eventUnfavourable event

Test direction

Two-sidedOne-sided

Use one-sided testing only when justified before the trial begins.

Significance level α

Statistical power

Group 2:group 1 cluster allocation ratio

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

Participant-level attrition

Whole-cluster attrition

4. Results

Enter the cluster-trial assumptions and select Calculate.

Allocation and recruitment

Arm	Analysable clusters	Analysable participants	Expected events	Recruit clusters	Recruit participants

ICC sensitivity analysis

ICC	Design effect	Group 1 clusters	Group 2 clusters	Total

Suggested sample-size wording

Formula, assumptions, limitations, and methodological note

Example clinical scenario

Primary-care clinics are randomized to an implementation programme or usual care, and the proportion of patients achieving clinical response is compared between arms.

Formula and methodological note

The calculator combines arm-specific Bernoulli variances with the cluster design effect and evaluates candidate whole-cluster allocations using a noncentral-t planning approximation. It supports a common ICC and mean cluster size across arms. Variable-size mode applies the Eldridge common-CV approximation.

It excludes matched, stratified, multilevel, stepped-wedge, repeated-binary, non-inferiority, equivalence, covariate-adjusted, GEE-specific, and simulation-based designs. Sparse expected events or non-events within clusters can make this approximation unreliable. The final analysis must account for clustering and use an appropriate small-sample correction when clusters are few. This tool supports research planning and does not replace statistical consultation.

Technical results

Method references

Donner A, Klar N. Design and Analysis of Cluster Randomization Trials in Health Research. Arnold; 2000.
Eldridge SM, Ashby D, Kerry S. Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method. Int J Epidemiol. 2006;35:1292–1300.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for a Parallel Cluster-Randomized Trial — Binary Outcome (CRT-2A-B).” Web calculator. NajibMY, 2026. Accessed August 5, 2026. http://127.0.0.1:4321/tools/sample-size/clinical-complex-study-designs/parallel-cluster-randomized-binary-outcome/.