Clinical Trial Designs · Cluster-Randomized Trials

Cluster-Randomized Non-Inferiority Trial — Binary Outcome

Plan a two-arm parallel cluster-randomized trial in which an absolute event-risk difference must rule out a prespecified unacceptable loss relative to reference.

How this calculator works

The contrast is always experimental minus reference. Enter anticipated event probabilities, identify whether the event is favorable or unfavorable, and specify a positive maximum acceptable loss in percentage points. The calculator derives the signed boundary and searches cluster allocations using a finite-cluster noncentral-t risk-difference approximation.

The calculator does not choose or justify the margin. Margin selection, assay sensitivity, constancy, analysis population, missing data, and sensitivity analyses require protocol-specific clinical and statistical justification.

1. Outcome and non-inferiority hypothesis

Primary outcome label

Optional reporting label.

Event label

Describe what an event value of 1 means.

Interpretation of the event

FavorableUnfavorable

This orients the hypothesis without changing the experimental-minus-reference subtraction order.

Expected reference event probability

Expected experimental event probability

Equal anticipated arm probabilities are valid for non-inferiority planning.

Maximum acceptable loss relative to reference

Enter a positive absolute risk-difference magnitude—not a relative percentage or signed boundary.

2. Clustering assumptions

Intracluster correlation coefficient

Use evidence for a comparable binary outcome, population, 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 Type I error

2.5% corresponds to a 95% two-sided confidence interval.

Target power

Experimental:reference cluster ratio

The realized integer ratio may differ slightly.

Participant attrition

Inflates recruited participants per cluster.

Whole-cluster attrition

Inflates randomized clusters separately by arm.

4. Results

Review the signed 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

Choose the planning ICC from credible evidence, not because it produces a convenient design.

Suggested sample-size wording

Formula, assumptions, limitations, and methodological note

Example clinical scenario

Primary-care clinics are randomized to an experimental follow-up strategy or reference care. Investigators want to rule out an unacceptable increase in the six-month hospital-readmission probability using a prespecified absolute risk-difference margin.

Formula and methodological note

Let δ = pE − pR and let d be +1 for a favorable event and −1 for an unfavorable event. For positive margin M, the signed boundary is b = −dM and favorable gap is g = d(δ − b). The design requires g > 0 and a feasible implied boundary probability pR + b.

Arm variances are p(1 − p). Equal-size DE = 1 + (m − 1)ρ; variable-size DE = 1 + ([(1 + CV²)m] − 1)ρ. For candidate clusters, SE = √[(DE/m) × (pE(1−pE)/kE + pR(1−pR)/kR)], df = kE + kR − 2, and noncentrality = g/SE. Power is the noncentral-t upper tail beyond t_1−α,df.

This is a finite-cluster planning approximation, not an exact clustered-binary, GEE, or generalized linear mixed-model calculation. Sparse events, informative cluster sizes, repeated outcomes, matched or stepped-wedge designs, and arm-specific ICCs require another method.

Technical results

Method references

FDA. Non-Inferiority Clinical Trials to Establish Effectiveness. Final guidance; 2016.
Campbell MK, et al. CONSORT extension to cluster randomised trials. BMJ. 2012;345:e5661.
Eldridge SM, Ashby D, Kerry S. 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 Non-Inferiority 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-non-inferiority-binary-outcome/.