Factorial Clinical Trial Designs

INTRODUCTION

This JAMA Guide to Statistics and Methods article discusses clinical trials using factorial designs in which participants receive several randomized interventions simultaneously to allow efficient evaluation of multiple therapies and their combinations.

Clinical trials using factorial designs in which participants receive several randomized interventions simultaneously allow efficient evaluation of multiple therapies and their combinations.¹ Assuming each intervention does not influence the effects of the others, the information obtained from a factorial trial is akin to that from 2 or more separate trials but requires the resources for only 1 trial. If a treatment does alter the effects of others, factorial designs also enable evaluation of these interactions.

The BaSICS randomized trial reported by Zampieri et al^2,3 involved 11 052 critically ill patients and evaluated 2 characteristics of intravenous fluid infusion by using a factorial design: solution composition (balanced vs 0.9% saline) and infusion rate (slow [333 mL/h] vs rapid [999 mL/h]). The design allowed investigators to obtain 2 separate estimates of treatment effects—1 for each infusion choice—from 1 clinical trial.^2,3

EXPLANATION OF THE CONCEPT

What Is a Factorial Design?

Factorial designs randomize participants to combinations of treatments within a single trial to make more than 1 comparison and estimate multiple treatment effects.¹ They often involve 2 comparisons, each with 2 treatment options, as shown in Figure 1. This design is termed a 2 × 2 factorial, indicating 2 comparisons, each with 2 treatment options. A factorial design with 3 comparisons, each with 2 treatment options, is denoted a 2 × 2 × 2 factorial, with participants randomized to 8 possible treatment groups.

The trial illustrated in Figure 1 would randomize participants to 1 of 4 treatment combinations or groups, labeled A, B, C, or D. This design permits estimation of several different target treatment effects, termed estimands,⁴ for each experimental treatment compared with its corresponding control; for example, by comparing outcomes for study participants in groups A and B with those in C and D for the first comparison, and by comparing the outcomes in groups A and C with those in B and D for the second comparison. These effects are traditionally called “main” or “marginal” effects because the numbers summarizing them are customarily written on the margins of the table. The statistical analyses ...