Clinical Trial Designs · Cluster-Randomized Trials

Cluster-Randomized Equivalence Trial — Continuous Outcome

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

How this calculator works

The calculator evaluates the two one-sided tests jointly under a pooled-variance cluster-level t model. Symmetric or asymmetric limits are supported, but the contrast always remains experimental minus reference.

The calculator does not choose or justify the equivalence limits. The estimand, limits, analysis population, missing-data strategy, and sensitivity analyses require protocol-specific clinical and statistical justification.

1. Outcome and equivalence hypotheses

Primary outcome label

Optional reporting label.

Outcome unit

All differences, limits, and the SD must use this scale.

Expected mean difference: experimental − reference

Enter a signed value strictly inside the equivalence limits.

Equivalence-limit mode

SymmetricAsymmetric

Symmetric mode derives −Δ and +Δ. Asymmetric mode accepts two signed limits.

Symmetric equivalence margin Δ

Enter a positive magnitude; the calculator derives [−Δ,+Δ].

2. Outcome and clustering assumptions

Expected common individual-level outcome SD

Use relevant external evidence.

Intracluster correlation coefficient

Use an outcome- and setting-specific estimate.

Analyzable mean participants per retained cluster

This is the analyzable size before recruitment inflation.

Cluster-size assumption

EqualVariable

Variable mode uses 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	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 health centres are randomized to two service-delivery programmes. Investigators want to establish that mean patient experience scores are equivalent within prespecified lower and upper clinical limits.

Formula and methodological note

Equivalence requires both one-sided tests to reject. For each candidate cluster allocation, the calculator integrates the joint confidence-interval containment event over the pooled-variance chi-square distribution. This avoids treating the two component failures as independent.

Equal-size DE = 1 + (m − 1)ρ. Variable-size DE = 1 + ([(1 + CV²)m] − 1)ρ. The method is a cluster-level pooled-variance t planning approximation and does not represent every mixed-model, GEE, matched, stepped-wedge, multilevel, or informative-cluster-size design.

Technical results

References

Schuirmann DJ. A comparison of the two one-sided tests procedure and the power approach for assessing equivalence. J Pharmacokinet Biopharm. 1987;15:657–680.
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 — Continuous 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-continuous-outcome/.