Factorial randomized trial
Can two or more intervention factors be evaluated together?
When to use this project
Randomize combinations of intervention factors when the joint design can answer the planned factor-specific or interaction questions efficiently.
How it differs
A factorial trial crosses factors, rather than merely adding unrelated parallel arms. Effects depend on the contrast and scale; absence of a significant interaction test does not establish no interaction.
Decisions before you start
- Define all factor levels, permissible combinations and separate randomization constraints.
- State whether claims concern marginal effects, simple effects at another factor level or interactions.
- Power the intended contrasts and multiplicity plan; consider adherence and intercurrent events separately for each factor.
How the flows work together
Each flow below links to its diagram, steps and tables. Flow order organizes the project; it does not imply that all work is strictly sequential. Data assessment, analysis planning and protocol refinement may inform one another.
1. Factorial trial overview
Overview · Question through combined intervention evaluation
Use this overview to state the purpose and link to detailed decisions. Keep a versioned protocol and decision register, and add evidence references for the rationale.
2. Recruitment and combination allocation
Selection · Assign participants across factor combinations
Specify eligible combinations and the randomization of each factor. Restrictions, differing eligibility or nonindependent assignments can change which contrasts are estimable.
3. Factor definitions and estimands
Design · Define main effects and interactions
Distinguish marginal effects averaged over the other factor, simple effects at a specific factor level and interactions. Name the outcome scale; absence of significant interaction is not evidence that effects are identical.
4. Sample size and multiplicity
Statistics · Plan effect precision and testing
Plan power or precision for priority factor and interaction claims, including multiplicity. A design adequate for a marginal effect may be inadequate for an interaction.
5. Follow-up and safety
Conduct · Track adherence assessments and harms
Stopping treatment need not end outcome follow-up. Distinguish adverse-event seriousness from severity, define ascertainment windows and keep clinical safety review separate from statistical efficacy monitoring.
6. Data and analysis populations
Data · Derive combination-specific and pooled populations
Keep assignment, receipt, adherence and intercurrent events for each factor separately. The four combinations should remain reconstructable from the released dataset.
7. Factorial analysis plan
Statistics · Specify interactions contrasts and sensitivity
Derive the intended contrast from the fitted model rather than interpreting every coefficient as a marginal effect. Report combination outcomes and intervals for the planned effects and interactions.
Equations and statistical interpretation
These explanations describe notation and assumptions. Flow does not calculate these values.
Interaction on an additive outcome scale
μ_ab is the mean outcome under factor A level a and factor B level b in a 2 × 2 design.
This defines additive interaction; interaction on a relative scale is different. A regression coefficient for one factor in a model with interaction is generally a simple effect, not automatically its marginal effect.
Published example
Identify the two factors and four randomized combinations. Distinguish an effect averaged over the other factor from evidence about interaction.
This publication illustrates a study design, not an endorsement of every method or a reproduction of its results. Follow its protocol, supplement and update history when studying the example.
Hypothetical scenario
A prevention team wants to evaluate reminder messages and nurse follow-up, separately and in combination.
- Factorial trial overview: Define the two factors and justify testing their combinations in one protocol.
- Recruitment and combination allocation: Randomize participants to four eligible combinations with concealed allocation.
- Factor definitions and estimands: Specify marginal, simple and interaction contrasts and their outcome scale.
- Sample size and multiplicity: Plan sample size for the priority claims and plausible interaction scenarios.
- Follow-up and safety: Track delivery, adherence and safety for both factors.
- Data and analysis populations: Construct factor-specific assignment and receipt variables and analysis populations.
- Factorial analysis plan: Estimate the prespecified contrasts, with intervals and a transparent multiplicity strategy.
Deliver a populated protocol, decision log, data specification, and planned outputs. Enter numerical findings only after analysis and verification. Keep decisions made before seeing results distinguishable from later amendments.
Sources
- CONSORT 2025: reporting randomized trials
- SPIRIT 2025: randomized trial protocols
- CONSORT extension for factorial randomized trials (2023)
- ICH E9(R1): estimands and sensitivity analysis (2019)
- WHO: clinical trials and prospective registration
- ISRCTN: what the clinical study registry records
- ClinicalTrials.gov: about the registry
Source check: 2026-09-17. Record the version of each reporting or appraisal tool used in your actual protocol.
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