Enter Trial Assumptions
Formula Used
For a continuous outcome, the calculator first estimates the individually randomized control arm sample size:
nC = (Zα + Zβ)² × SD² × (1 + 1/r) / Δ².
For a binary outcome, it uses a normal approximation:
nC = [Zα√((1 + 1/r)p̄(1 - p̄)) + Zβ√(pC(1 - pC) + pT(1 - pT)/r)]² / Δ².
The cluster inflation factor is:
DE = 1 + [((1 + CV²) × m) - 1] × ICC.
Here, m is average cluster size, CV is cluster size variation,
and ICC is intracluster correlation.
Final enrollment adjusts for loss:
required participants = ceiling(individual sample × DE / retention).
Required clusters equal:
ceiling(required participants / average cluster size).
How to Use This Calculator
- Select a continuous or binary outcome.
- Enter alpha, power, and hypothesis direction.
- Add the expected effect size values.
- Enter ICC, average cluster size, and cluster size CV.
- Add expected attrition or loss to follow-up.
- Press calculate to view clusters, participants, design effect, and chart.
- Download the CSV or PDF report for study planning notes.
Example Data Table
| Scenario | Outcome | Effect | ICC | Cluster Size | CV | Attrition |
|---|---|---|---|---|---|---|
| Clinic blood pressure study | Continuous | 120 vs 115, SD 15 | 0.02 | 25 | 0.20 | 10% |
| School nutrition program | Binary | 40% vs 52% | 0.04 | 35 | 0.25 | 8% |
| Village prevention trial | Binary | 22% vs 15% | 0.03 | 50 | 0.30 | 12% |
| Ward recovery study | Continuous | 70 vs 76, SD 18 | 0.015 | 20 | 0.10 | 5% |
Article: Planning Sample Size for Cluster Randomized Trials
Why Cluster Trials Need Special Planning
Cluster randomized trials randomize groups, not single people. The group may be a clinic, class, ward, village, or work site. This design is useful when an intervention affects a whole setting. It also helps avoid contamination between participants. Yet it changes sample size planning. People inside the same cluster often behave more alike than people in different clusters.
Role of Intracluster Correlation
The intracluster correlation measures this similarity. A small ICC can still inflate the required sample size. Large clusters make this effect stronger. The calculator applies a design effect. This converts an individually randomized sample size into a cluster trial sample size. It also supports unequal cluster sizes through the coefficient of variation.
Continuous and Binary Outcomes
The tool supports continuous and binary outcomes. For continuous outcomes, enter the expected means and standard deviation. For binary outcomes, enter the control and treatment percentages. The calculator estimates the effect, applies the selected alpha and power, then inflates the sample for clustering.
Attrition and Allocation
Attrition can reduce the final analyzed sample. Add a realistic loss percentage before recruitment starts. Unequal allocation is also available. This helps when treatment clusters are easier to recruit, more important, or less costly. The output shows clusters by arm and total enrollment.
Reading the Output
The design effect shows how much clustering increases the sample size. The effective sample size shows the approximate independent information left after clustering. Rounded cluster counts may slightly increase achieved power. Use the chart, table, CSV file, and PDF file to compare assumptions. Always review final assumptions with a statistician before funding or ethics submission.
FAQs
1. What is a cluster randomized trial?
A cluster randomized trial assigns groups instead of individuals. Common clusters include clinics, schools, wards, villages, or workplaces. Outcomes are still measured on participants.
2. Why is the sample size larger?
Participants inside the same cluster may be similar. This reduces independent information. The design effect inflates the sample size to handle that correlation.
3. What is ICC?
ICC means intracluster correlation. It measures how strongly participants within a cluster resemble each other. Higher ICC values usually require more clusters or participants.
4. What does cluster size CV mean?
Cluster size CV measures variation in cluster sizes. A higher value means cluster sizes are more unequal. Unequal clusters can increase the design effect.
5. Should I use one-sided or two-sided alpha?
Most confirmatory trials use two-sided alpha. One-sided testing should be justified before the study starts. It should match the protocol and analysis plan.
6. Can this calculator handle binary outcomes?
Yes. Select binary outcome and enter control and treatment percentages. The calculator uses a normal approximation for comparing two proportions.
7. Why adjust for attrition?
Attrition reduces the number of analyzed participants. Planning for it helps protect statistical power when follow-up loss, missing data, or exclusions occur.
8. Is this a final protocol tool?
It is a planning calculator. Use it for early design, assumption checks, and reports. Confirm final sample size with a qualified trial statistician.