<p> Stats Moment Factorial Trials: two (or more) for one</p><p>The paper by Williamson et al. is an example of a factorial trial. As the article states factorial trials are the “most efficient way of testing more than 1 hypothesis…” without having to increase the number of patients. </p><p>In this trial there were four groups, as below:</p><p>Steroids Abx n Effect</p><p>1 Yes Yes 46 XSA</p><p>2 Yes No 56 XS0</p><p>3 No Yes 54 X0A</p><p>4 No No 51 X00 Total 207</p><p>Thus, approximately half of the sample population received steroids (1&2) and another half received antibiotics (1&3). To delineate the effect of each intervention, the effect of each treatment group can be combined as follows:</p><p>Steroid effects = 0.5 x [(XS0 – X00) + (XSA – X0A)]</p><p>Likewise, the Antibiotic effects = 0.5 x [(X0A – X00) + (XSA – XS0)]</p><p>An inherent assumption is that the treatments do not interact with each other to increase or decrease their individual effects. </p><p>To test for interaction: Xi = [(XS0 – X00) – (XSA – X0A)] </p><p>Xi should be close to 0 if there is no interaction.</p><p>Other practical considerations to consider when designing factorial trials are whether the selected treatments can safely be administered together and whether it is ethically acceptable to have one group without any treatment (placebo).</p><p>In the trial, sample size calculations for the antibiotic treatment revealed that ~200 pts would have to be recruited to discern a difference with adequate power. Assuming the same sample size is needed to detect a difference in the steroid groups, a total of 400 patients would have to be recruited to perform 2 separate studies. </p><p>A second important use of factorial trials is the analysis of interactions between co- administered interventions (i.e. where treatment A affects B and vice versa). However, instead of requiring fewer patients to answer more questions, these trials require a larger study population to answer one question. Another good example of a factorial study is the ISIS-4 trial that compared 3 interventions in 56,000 patients with suspected MI. They assessed the efficacy of oral captopril, oral mononitrate and IV magnesium. </p><p>1. Construct a similar table that would be used in the ISIS-4 trial (omit the effect column).</p><p>2. If a new power calculation determined that 1000 pts were required for each of the three interventions (if tested separately), how many pts would be required in a new combined factorial trial?</p><p>3. In a study of the prevention of post-operative nausea and vomiting, 6 interventions were combined into a factorial trial. How many different groups would be required?</p>