Factorial Randomised Controlled Trials

Abstract

The cost effectiveness of a trial can be improved through the use of a factorial design, where we can evaluate two interventions for the ‘price’ (in terms of sample size) of evaluating a single intervention. A factorial design can also reveal whether or not there is an interaction between two interventions. We can test if intervention A is better than no intervention and whether intervention B is better than no intervention. We can also test if interventions A + B work together in synergy, or are additive, or do not work as well in the presence of each other. However, if we are intent on observing an intervention-by-intervention interaction we need to boost our sample size by a factor of about 4, and consequently reduce the appeal of evaluating ‘two interventions for the price of one’. Few factorial trials are powered a priori to detect interactions, and whilst interactions are commonly held as an important reason for using a factorial design, they are not usually justified in sample size calculations.