Clinical Trials

❘❙❚■ Chapter 11 | Factorial Design(an old anti-angina drug), and intravenous magnesium (an old agent) in 58,043patients with suspected acute myocardial infarction. While captopril showed asmall but significant reduction in mortality at 5 weeks, neither of the older agentsshowed significant benefit. This trial was a 2 × 2 × 2 factorial design. [2].A further example was the HOPE (Heart Outcomes Prevention Evaluation) study,which compared ramipril and vitamin E supplementation, both against control;the latter agent proved ineffective as opposed to the considerable benefit seenwith ramipril, in patients with coronary disease [3].How do we randomize for a factorial design?For a factorial design, randomization can be performed using the same methodsas in a two-arm parallel study; however, individuals have to be randomizedmultiple times, depending on the number of interventions used. In a 2 × 2 factorialstudy, participants are first randomized to either intervention A or its control,and then to either intervention B or its control in a second randomization.Alternatively, individuals can be randomized to one of the following four arms toavoid the need to randomize twice: A, B, A + B, or placebo.How do we calculate sample size for a factorial study?The most common technique used to calculate the sample size for a 2 × 2 factorialstudy is to first think of the study as consisting of two individual two-arm trials.Sample size calculations are carried out for the target effect size of eachintervention separately, assuming the same power and level of statisticalsignificance. The final number of individuals that need to be recruited is takenfrom the comparison that provides the larger sample size – this will ensure enoughpower to assess the effect of the remaining comparison. Sample sizes are calculatedin the usual way for parallel-arm randomized controlled trials, so the power todetect a treatment difference is dependent on the number of individuals in thegroups being compared, not on the overall number of individuals in the study.The aforementioned calculations are based on the assumption that there is nointeraction between interventions A and B; however, this will not necessarily betrue. An interaction between interventions means that the effect of treatment Adepends on the presence or absence of treatment B (or vice versa). In this case,it is more appropriate to consider the study as a multiple-arm study and ensureenough power to detect the smallest treatment difference among all possible pairwisecomparisons. As a result, the trial can be viewed as a four parallel-arm study104