Clinical Trial Designs · Cluster-Randomized Trials

Cluster-Randomized Equivalence Trial — Binary Outcome

Plan a two-arm parallel cluster-randomized trial in which the confidence interval for an experimental-minus-reference event-risk difference must lie entirely inside prespecified equivalence limits.

How this calculator works

The calculator evaluates both one-sided tests jointly using anticipated arm-specific Bernoulli variances and a finite-cluster variance-factor approximation. Limits are entered in percentage points; the contrast always remains experimental minus reference.

The calculator does not choose or justify the equivalence limits. A nonsignificant superiority test does not establish equivalence. The estimand, limits, analysis population, missing-data strategy, and sensitivity analyses require protocol-specific justification.

1. Outcome and equivalence hypotheses

Primary outcome label

Optional reporting label.

Event label

Describe what an event value of 1 means.

Expected reference event probability

Expected experimental event probability

Equal anticipated probabilities are valid for equivalence planning.

Equivalence-limit mode

SymmetricAsymmetric

Symmetric mode derives −M and +M. Asymmetric mode accepts signed limits.

Symmetric equivalence margin

Enter a positive absolute risk-difference magnitude.

2. Clustering assumptions

Intracluster correlation coefficient

Use evidence for a comparable outcome and cluster unit.

Analyzable mean participants per retained cluster

Expected analyzable size before recruitment inflation.

Cluster-size assumption

EqualVariable

Variable mode applies a common CV design-effect approximation.

3. Operating characteristics and recruitment

One-sided alpha for each TOST component

5% corresponds to a 90% two-sided confidence interval.

Target joint equivalence power

Experimental:reference cluster ratio

The realized integer ratio may differ slightly.

Participant attrition

Inflates participants per recruited cluster.

Whole-cluster attrition

Inflates clusters independently by arm.

4. Results

Review the TOST hypotheses, enter the assumptions, and select Calculate.

Analyzable design and recruitment target

Arm	Analyzable clusters	Analyzable participants	Expected events	Recruit clusters	Recruit participants

ICC sensitivity analysis

ICC	Design effect	Experimental clusters	Reference clusters	Total

Suggested sample-size wording

Formula, assumptions, limitations, and methodological note

Example clinical scenario

Community clinics are randomized to two implementation programmes. Investigators want to establish that six-month clinical-response probabilities are equivalent within prespecified absolute risk-difference limits.

Formula and methodological note

Equivalence requires both one-sided tests to reject. For each candidate allocation, the calculator integrates the shared confidence-interval containment event over a finite-cluster chi-square variance factor. The standard error uses arm-specific Bernoulli variances inflated by the common cluster design effect.

Equal-size DE = 1 + (m − 1)ρ. Variable-size DE = 1 + ([(1 + CV²)m] − 1)ρ. This is a planning approximation, not an exact clustered-binary mixed-model, GEE, score, beta-binomial, matched, or stepped-wedge method.

Technical results

References

European Medicines Agency. Guideline on the choice of the non-inferiority margin. EMEA/CPMP/EWP/2158/99.
Campbell MK, et al. CONSORT extension to cluster randomised trials. BMJ. 2012;345:e5661.
Eldridge SM, Ashby D, Kerry S. Sample size for cluster randomized trials and cluster-size variation. Int J Epidemiol. 2006;35:1292–1300.

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

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

Suggested citation

Yaacob, Najib Majdi. “Cluster-Randomized Equivalence Trial — Binary Outcome.” Web calculator. NajibMY, 2026. Accessed August 19, 2026. http://127.0.0.1:4321/tools/sample-size/clinical-complex-study-designs/cluster-randomized-equivalence-binary-outcome/.