8. Parallel, Factorial, and Cluster Randomized Trials Explained
After this lesson you can
- Explain why the parallel-group design is the default
- Read the two main effects of a factorial and check the no-interaction assumption
- Describe what a large simple trial keeps and gives up
- Compute a design effect from cluster size and intraclass correlation
- Choose among four designs with a four-question decision tree
Video coming soon
Lessons publish daily from November 17, 2026.
This lesson compares the parallel-group, two-by-two factorial, large simple and cluster randomized designs. It reads factorial main effects under the no-interaction assumption and shows how the intraclass correlation and design effect inflate a cluster trial.
Questions and answers
Questions a learner would ask about this lesson. Think through your own answer before you open each one.
- Why is the parallel-group design the default?
Show answer
Each participant is in exactly one arm for the whole trial, and the arms are followed side by side. It is the simplest to explain and run, has no carryover between periods, works for any endpoint including death, and the standard sample-size formulas assume it. A protocol uses it unless there is a reason not to.
- How does a two-by-two factorial answer two questions at once?
Show answer
Two factors, each at two levels, make four cells. In the fictional Oakhaven version, 400 participants sit in four cells of 100, and each main effect compares 200 with 200, so all 400 are used twice. The saving depends on the no-interaction assumption: the effect of one factor must not depend on the level of the other.
- What is a large simple trial, and what does it give up?
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It is still a parallel-group randomized trial, built on broad eligibility, minimal data and one hard endpoint, so it can enroll thousands. That size lets it detect small effects. It gives up mechanism, subgroups and fine safety data.
- When should clinics be randomized instead of people?
Show answer
When contamination between arms in the same place is likely, when the intervention acts on the whole clinic, or when delivery is only practical by site. Convenience alone is not a reason. Contamination means the control arm receives part of the intervention, which shrinks the observed difference.
- What is the design effect, and why does it matter?
Show answer
People inside a clinic resemble one another, so their outcomes are correlated. The design effect is 1 plus (m minus 1) times the intraclass correlation; with 50 per clinic and 0.02 it is 1 plus 49 times 0.02, which is 1.98, about 2. The individual sample size is multiplied by it, and the analysis must respect the clusters or confidence intervals come out too narrow.
Practice quiz
- Question 1In the Oakhaven factorial version with 400 participants in four cells of 100, each main effect compares:
- Question 2The factorial's efficiency depends on:
- Question 3In a plot of the four factorial cells, what pattern suggests no interaction?
- Question 4With 50 participants per cluster and an intraclass correlation of 0.02, the design effect is about:
- Question 5With a design effect of about 2, 400 clustered participants carry about as much information as how many independent participants?
- Question 6Cluster randomization is chosen mainly to:
- Question 7A cluster trial randomizes clinics but analyzes all participants as if they were independent. What goes wrong?
- Question 8For a fixed total of 400 people in a cluster trial, which arrangement is almost always better?
- Question 9A large simple trial trades away:
- Question 10Why did the Oakhaven unit decline the factorial with reminder messages?
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Design of Clinical Studies is education only. Every lesson follows the fictional Oakhaven Adherence Trial with invented numbers; the course uses no real data and cites no real studies.