Clinical Trials

❘❙❚■ Chapter 11 | Factorial DesignWhat is a factorial study?The simplest factorial design takes a 2 × 2 format, and throughout this chapter wewill refer to 2 × 2 factorial studies unless otherwise specified. In a factorial designclinical trial with a 2 × 2 format, individuals are randomly assigned to two separateinterventions (eg, interventions A and B) and these interventions are eachcompared with their corresponding control(s).In a balanced 2 × 2 factorial design, this would mean that from a total ofN individuals, N / 2 are randomly allocated to receive intervention A and N / 2 arerandomly allocated not to receive intervention A. Correspondingly, N / 2 individualsare allocated to receive intervention B or to not receive intervention B. Overall:• N / 4 individuals are allocated to no treatment (control group).• N / 4 individuals are allocated to intervention A only.• N / 4 individuals are allocated to intervention B only.• N / 4 individuals are allocated to the combination of A + B simultaneously.The benefit in terms of sample size or power of the factorial trial becomesapparent in the analysis. The usual method is to compare individuals who arerandomized to intervention A (ie, those who receive A and those who receiveA + B) with those who are not randomized to A (ie, those receiving eitherintervention B or no treatment at all). Similarly, individuals who are randomizedto intervention B are compared with those who are not randomized to B. In afactorial design, it is usual to assume A and B to have independent effects fromeach other, ie, that there is no interaction between treatment A and B.ExampleIn a 2 × 2 factorial trial set up to investigate the effects of multivitamins excludingvitamin A (factor 1) and including vitamin A (factor 2) on birth outcomes ofHIV-1 infected women, each woman was allocated once to each treatment [1].Therefore, every mother was randomized twice overall, resulting in the followingfour treatment groups:• Women who received vitamin A only.• Women who received multivitamins but no vitamin A.• Women who received both multivitamins and vitamin A.• Women who received neither.By using a factorial trial, it is possible to perform two comparisons simultaneouslyat the cost of one experiment. In this example, it is possible to compare birthoutcomes for mothers who received vitamin A with those who did not by102