Cluster-Randomised and Crossover Trials

Overview

Cluster-randomised trials allocate groups such as clinics or schools.

Crossover trials allocate sequences so each participant receives more than one treatment.

Both designs violate the simple independent parallel-group model.

Their analyses must represent the unit and timing of randomisation.

Why this matters

In a cluster trial, 480 participants in 30 clinics do not provide 480 independent treatment assignments.

In a crossover trial, two periods from one participant are paired, and treatment can be confounded with period or carryover.

Ignoring these structures produces incorrect standard errors and potentially biased effects.

When to use these designs

Cluster randomisation is useful when:

• intervention is delivered at group level;
• contamination is likely;
• service organisation is the target;
• individual allocation is impractical.

Crossover is useful when:

• condition is stable;
• treatment effect is reversible;
• outcome can be measured repeatedly;
• carryover can be prevented or modelled.

Research question and variables

Cluster trial variables:

• cluster;
• cluster treatment;
• participant outcome;
• participant and cluster covariates.

Crossover variables:

• participant;
• sequence;
• period;
• treatment;
• outcome.

Data structure

Design-specific data structures

simulated data

Design	Independent unit	Repeated structure
Cluster trial	Cluster	Participants within cluster
Crossover	Participant	Periods within participant

Statistical assumptions

Cluster-randomised trials

A random-intercept model is:

The ICC is:

$$ICC= \frac{\sigma_u^2} {\sigma_u^2+\sigma_\varepsilon^2}$$

The approximate design effect is:

$$1+(\bar m-1)ICC$$

Few clusters require small-sample corrections.

Crossover trials

For two periods:

where $\tau$ is treatment effect, $\pi$ period effect and $s_i$ participant effect.

Sequence can be included as a between-participant factor.

Worked example

Worked analysis in R

cluster_trial <- read.csv(
  "data/part-13-cluster-trial-data.csv"
)

crossover <- read.csv(
  "data/part-13-crossover-data.csv"
)

library(lme4)

cluster_fit <- lmer(
  outcome ~ group +
    (1 | cluster),
  data = cluster_trial,
  REML = TRUE
)

summary(cluster_fit)

crossover_fit <- lmer(
  outcome ~ treatment +
    period +
    sequence +
    (1 | id),
  data = crossover,
  REML = TRUE
)

summary(crossover_fit)

Selected analysis output

Cluster trial: intervention increases the outcome by approximately 4 units.

Crossover trial: Treatment A increases the outcome by approximately 2.5 units after accounting for period, sequence and participant.

Visualising cluster allocation

Visualising crossover periods

Carryover

Carryover occurs when a period-1 treatment affects period 2.

Prevention is preferable:

• sufficient washout;
• stable disease;
• short-lived treatment effect.

Testing carryover and discarding period 2 after a non-significant or significant result is problematic.

If carryover is expected, a parallel design may be more appropriate.

Recruitment bias in cluster trials

When clusters are randomised before participant recruitment, recruiters may know allocation.

This can change who enters each arm.

Blinded or standardised recruitment and clear eligibility criteria are important.

Interpreting the output

Presenting the results

Suggested reporting

Use the CONSORT cluster extension [1] and crossover extension principles [2].

Report allocation unit, cluster count, ICC, sequence, periods, washout, carryover assumptions and missing clusters or periods.

Design and analysis principles for cluster-randomised and crossover trials are developed in specialised texts [3], [4].

Common mistakes

Knowledge check

What is the independent treatment unit in a cluster trial?

Answer and reasoning

The randomised cluster.

Why include participant random effects in crossover analysis?

Answer and reasoning

Repeated period outcomes from one participant are correlated.

What does the period effect represent?

Answer and reasoning

Systematic outcome difference between periods unrelated to treatment.

Why can few clusters be problematic?

Answer and reasoning

Treatment inference depends on the number of independent clusters.

When should crossover be avoided?

Answer and reasoning

When effects are irreversible, disease is unstable or carryover cannot be controlled.

Key take-home messages

References

1. Campbell MK, Piaggio G, Elbourne DR, Altman DG. CONSORT extension to cluster randomised trials. BMJ. 2012;345:e5661. https://doi.org/10.1136/bmj.e5661
2. Dwan K, Li T, Altman DG, Elbourne D. CONSORT 2010 statement: extension to randomised crossover trials. BMJ. 2019;366:l4378. https://doi.org/10.1136/bmj.l4378
3. Donner A, Klar N. Design and analysis of cluster randomization trials. London: Arnold; 2000.
4. Senn S. Cross-over trials in clinical research. 2nd ed. Chichester: Wiley; 2002.