Factorial trial
Why this level?
Participants or clusters are randomly allocated to concurrent comparison groups. NHMRC 2009 sourceRandom allocation of the intervention combinations determines the design category. Interaction assumptions, multiplicity and prespecification affect interpretation and study quality, which need separate appraisal.
What question does this help answer?
It answers two or more questions for close to the price of one, and it is the only design that lets you ask whether the interventions INTERACT: whether the benefit of one depends on receiving the other.
When to use it
Use it when two interventions are both worth testing, can be given together safely, and are not expected to interfere strongly. The efficiency is real: a 2x2 factorial can test both main effects at roughly the sample size of a single two-arm trial.
When not to use it
Avoid it when the interventions plausibly interact strongly, because the efficiency argument depends on their effects being roughly additive. Avoid it also when giving both together is unsafe or implausible in practice.
How it works in plain language
In a 2x2 design each participant is randomized twice: to intervention A or not, and independently to intervention B or not. Four groups result. The main effect of A compares everyone who got A with everyone who did not, averaging over B, and vice versa.
What the four groups look like
Why Mallard may recommend it
Mallard may recommend a factorial design when the investigator describes two distinct interventions that could be delivered independently to the same participants.
Key assumptions and design requirements
- Effects are assumed roughly additive; this is what the efficiency rests on and it should be stated.
- The trial is usually POWERED FOR MAIN EFFECTS, so a null interaction test is not evidence of no interaction.
- If an interaction is expected and important, the sample size must be calculated for it, which is far larger.
- Results are presented so main effects and the interaction are distinguishable, with all four cells shown.
- The analysis plan states in advance whether main effects will still be reported if an interaction appears.
What to watch out for
A factorial trial is usually powered for the MAIN EFFECTS, not for the interaction, so a study that finds no interaction has usually not excluded one. If the two interventions do interact, the main effects become hard to interpret and the efficiency the design was chosen for disappears.
Clinical example
Question: Do a nurse-led education session and a text-message reminder each improve medication adherence? Design: Randomize each participant independently to education or not, and to texts or not, giving four groups, and report both main effects with the interaction shown rather than assumed absent.
How to report it
CONSORT extension for factorial trials is the guideline for this design. It asks you to state which treatment groups form each main comparison, how interaction between the interventions was evaluated and on what scale, and the estimated interaction for each primary outcome, with outcome data for every treatment group as well as for the main comparisons. A reporting guideline is not a design manual: use it to make the study transparent, not as a substitute for careful design. Check the target journal's own requirements as well, which this page cannot know.
- Design, analysis and presentation of factorial randomised controlled trials (opens in a new tab) · BMC Med Res Methodol · doi 10.1186/1471-2288-3-26
- Overview of clinical study designs (opens in a new tab) · Clin Exp Emerg Med · doi 10.15441/ceem.23.036
- Reporting of Factorial Randomized Trials: Extension of the CONSORT 2010 Statement (opens in a new tab) · JAMA · doi 10.1001/jama.2023.19793