Factorial trial
- Study design
One trial answers two questions: two interventions are randomised at once, alone, together or neither.
What it is
In a 2×2 factorial trial participants are randomised to four groups: intervention A, intervention B, both or neither. If A and B do not interact, each intervention is assessed with all participants (the half who got it versus the half who did not), so two questions are answered with roughly the sample size of one. If they interact, each combination must be analysed separately and power falls.
How it is built
- Two interventions that can be safely combined are defined.
- Random allocation to the four cells, usually of equal size.
- The outcome is measured in every group.
- Analysis: effect of A (margins), effect of B (margins) and a test of the A×B interaction.
Worked example
- 800 older adults; 200 per cell. A = pharmacist medication review; B = balance exercise. Outcome: falls in 1 year.
- Falls: neither 60/200 (30 %); A only 50/200 (25 %); B only 44/200 (22 %); A + B 34/200 (17 %).
- Effect of A: with A (50 + 34) / 400 = 21 %; without A (60 + 44) / 400 = 26 %; difference −5 points.
- Effect of B: with B (44 + 34) / 400 = 19.5 %; without B (60 + 50) / 400 = 27.5 %; difference −8 points.
- Interaction: A without B 25 − 30 = −5; A with B 17 − 22 = −5. Same effect: no interaction on the difference scale.
- Reading: 800 people answer two questions; each intervention reduces falls on its own and the effects add up.
Factorial trial versus other options
| Aspect | 2×2 factorial | Two separate parallel trials | Three-arm trial (A, B, control) |
|---|---|---|---|
| Questions | A, B and their interaction | A and B separately | A and B versus control |
| Sample size | About that of one trial (no interaction) | Double | Larger than a two-arm trial |
| Studies the combination | Yes | No | No |
| Main risk | Unexpected interaction | Cost and time | Less power per comparison |
Markers
- 2×2
- Interaction
- Analysis at the margins
When to use it
- Cardiovascular or cancer prevention with two independent measures.
- Comparing two aspects of care (anaesthesia and post-operative analgesia) in the same operation.
- Studying whether two treatments boost or cancel each other.
Common pitfalls
- Analysing only the margins when there is interaction: the average effect represents nobody.
- Sizing the trial assuming no interaction and then wanting to test it: power is usually too low.
- Combining interventions that interfere with each other or add up adverse effects.
Test yourself
Think of the answer, then tap the question to see it.
How many groups does a 2×2 factorial trial have, and which are they?
Four: neither intervention, A only, B only and A + B.
Which assumption lets you answer two questions with about the same sample size?
No interaction: the effect of A is the same with or without B, so everyone who got A is compared with everyone who did not.
If A lowers risk by 10 points without B and by 0 points with B, what do you conclude?
There is interaction: the effect of A depends on B, and the effect in each cell must be reported, not the average.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Chapter 23: Including variants on randomized trials (Cochrane, 2024); CONSORT 2025 Statement: updated guideline for reporting randomised trials (EQUATOR Network, 2025).
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Representative model, for educational purposes only.