Cluster randomized trial

Concepts and reasoning

Randomizing a clinic changes the unit of information

Imagine testing a prescribing intervention by assigning entire clinics to training or usual care. Patients at the same clinic share clinicians, referral patterns, and organizational practices. Their outcomes may therefore resemble one another even before the intervention. Recording another patient at the same clinic adds information, but usually less than recruiting an otherwise comparable patient from a new clinic.

The intraclass correlation coefficient, or ICC, measures the correlation between two observations in the same cluster under a simple exchangeable model. An ICC of 0.05 can look small. Its impact becomes substantial when dozens of patients share each randomized clinic: many correlated pairs accumulate. Treating all patient records as independent then exaggerates the effective sample size and can produce overly narrow confidence intervals.

Participants and clusters solve different problems

More patients within each clinic improve estimation of that clinic’s mean. More randomized clinics improve the treatment comparison across independently assigned units. These are not interchangeable resources. A trial with two large clinics in each arm still has very little independent replication of its treatment assignment, even if it contains thousands of patients.

Cluster randomization may be appropriate when an intervention is delivered collectively or individual randomization would create contamination. It also changes recruitment and analysis. Identifying patients after a clinic’s allocation becomes known can create differential selection. Repeated observations of the same patient introduce another correlation level. The basic design-effect calculation below addresses a simpler parallel design with equal-sized independent clusters. The cluster-design tutorial provides the planning context.

Mathematical foundations

On a small screen, scroll wide equations and tables horizontally.

Deriving the inflation factor

Suppose each cluster contains observations with common variance and pairwise correlation . The variance of the cluster mean includes individual variances and covariance terms:

The expression in braces is the design effect, . When , ordinary independent-sample planning is recovered. When approaches 1, additional observations within a cluster contribute almost no new independent information.

A simple planning approximation multiplies the independent participant requirement by , then rounds up to whole clusters within each arm. The approximate effective sample size is , but this is an information comparison, not a replacement dataset or a license to use an ordinary individual-level analysis. Unequal cluster sizes and a small number of clusters require further care; the equal-size formula can be optimistic. Eldridge and colleagues’ unequal-size study examines that issue.

Worked example

Hypothetical data for learning; independent of your analysis inputs.

From individual enrollment to clinic recruitment

Suppose an individually randomized design would require 200 analyzable participants per arm. Each clinic can provide 20 analyzable participants, and the planning ICC is 0.05. The design effect is . Multiplying 200 by 1.95 gives 390 participants per arm. Because clinics cannot be fractionally randomized, is rounded to 20 clinics per arm. The final design has 40 clinics and 800 analyzable participants.

The table shows why an ICC sensitivity analysis belongs in planning:

These are hypothetical approximations, not guarantees of achieved power. If 20 is a recruitment target rather than an analyzable cluster size, individual attrition changes the calculation. Losing an entire clinic is a separate event: enrolling extra patients in other clinics does not fully replace that independent randomized unit.

For another comparison, a clinic of 20 patients at ICC 0.05 contributes roughly independent-patient equivalents. Doubling its size to 40 gives , not 20.52. The diminishing information gain explains why adding clinics can be more valuable than repeatedly enlarging the same clinics.

Interpreting the results

Read the number of independent units

The main recruitment decision is the number of clusters in each arm, alongside the number of analyzable participants per cluster. Participants within one clinic or school share influences, so adding participants is not equivalent to adding independent clusters. A design with many participants but very few clusters can still have weak precision for the treatment comparison.

The design effect compares variance with that of an individually randomized design of similar total size. With cluster size 20 and intracluster correlation 0.05, it is 1.95; the correlated observations provide substantially less information than the same number of independent observations. This is a variance comparison, not a statement that 95% of participants are redundant.

Report cluster counts, planned cluster size, intracluster correlation, effect and standard deviation together. Achieved power is conditional on those assumptions and rounding. Participant dropout inflation changes recruitment within clusters; it does not replace clusters that withdraw entirely.

Assumptions and limitations

Preserve the unit of randomization

The treatment is assigned to clusters, and the eventual analysis must account for that assignment. Treating all individuals as independent generally understates uncertainty. Outcomes should be comparable across clusters, and interference between clusters should be absent or addressed in the design; a shared intervention across neighboring sites can weaken the intended comparison.

A simple planning model assumes equally sized clusters, a common within-cluster correlation, and a continuous outcome with an appropriate variance estimate. Unequal cluster sizes can change power, particularly when their variation is large or linked to outcomes. The intracluster correlation is population- and endpoint-specific, so an estimate from another setting is uncertain rather than a universal property of a measurement.

Individual dropout and whole-cluster loss are different mechanisms. Informative enrollment after allocation can also create selection bias. These issues require recruitment and analysis plans beyond multiplying a sample size by a design effect.

Diagnostics and sensitivity analysis

Stress-test cluster size and correlation

Make a small planning grid of plausible intracluster correlations and analyzable cluster sizes. Record the required cluster count in each scenario. Increasing cluster size has diminishing information gains when correlation is positive; compare the feasibility of recruiting more sites with recruiting more people at existing sites.

Review the origin of the standard deviation and correlation estimates, cluster-size variation, and plausible site withdrawals. If only a few clusters are feasible, assess whether the intended small-sample analysis and degrees of freedom are adequately represented. Do not assume that a large participant total compensates for inadequate cluster replication.

After recruitment, inspect cluster counts and sizes by arm, cluster-level missingness, and whether participant eligibility or enrollment changed after allocation. Present sensitivity to the uncertain correlation and to cluster loss. This cluster-trial planning paper discusses the importance of specifying the design and analysis together.

References and other material

Read the methodological references and supporting tutorials below. The examples in this lesson are original teaching calculations, not findings from these sources.

• Two questions about the design of cluster randomized trials — A free tutorial on clusters, correlation and sample size.

Related method guides

• Noninferiority & equivalence
• Survival trial sample size
• Browse all analysis families