. Author manuscript; available in PMC: 2025 Jan 26.

Published in final edited form as: JAMA. 2023 Dec 5;330(21):2106–2114. doi: 10.1001/jama.2023.19793

Table 1. Example of a 2 × 2 Factorial Randomized Trial.

	Treatment B (high-dose)^a,b	Treatment B (low-dose)^a,b
Treatment A (active) ^a,b	Active A + high-dose B^c	Active A + low-dose B^c
Treatment A (placebo) ^a,b	Placebo A + high-dose B^c	Placebo A + low-dose B^c

A and B are factors.

Active A and placebo A are levels within factor A and high-dose B and low-dose B are levels within factor B. Low-dose B is taken as the control condition for factor B.

Active A plus high-dose B, active A plus low-dose B, placebo A plus high-dose B, and placebo A plus low-dose B are the treatment groups. In a “full” factorial trial all participants are eligible to be randomized between each of the 4 treatment groups; in a “partial” factorial trial, a subset of participants would only be randomized between high- and low-dose B and assigned to placebo A without randomization. In a “factorial” analysis, all participants allocated to intervention A (active A plus low-dose B and active A plus high-dose B) are compared against those not allocated to A (placebo A plus low-dose B and placebo A plus high-dose B), and similarly for the comparison for intervention B. In a “multiarm” analysis, each of the treatment groups are compared against control (eg, active A plus high-dose B, active A plus low-dose B, and placebo A plus high-dose B are all compared against placebo A plus low-dose B).