Clinical Trials

❘❙❚■ Chapter 11 | Factorial DesignTable 2. Number of strokes or deaths / number of individuals in the Canadian Trial in Threatened Stroke [4].SulfinpyrazoneYesAspirinNoYes 20 / 146 38 / 156No 26 / 144 30 / 139The odds of stroke or death for individuals on aspirin was (20 + 26) / ([144 + 146] – [20 + 26]) = 46 / 244.The odds of stroke or death for individuals not on aspirin was (38 + 30) / ([139 + 156] – [38 + 30]) = 68 / 227.an interaction between treatments exists and the study results must be presentedseparately for each treatment combination.For example, in the GISSI (Gruppo Italiano per lo Studio della Streptochinasinell’Infarto Miocardico) trial, the data were initially analyzed using a two-waymethod and then by a four-way method, looking at the outcome in individualcells compared with the control [5]. The interaction effect was found to benonsignificant and the results from the main effects model were thereforepresented as the main study result. Difficulties arise if the interaction testresults in a low, but nonsignificant, P-value (eg, between 0.05 and 0.10) – thiscan indicate that the study is underpowered to detect an interaction, rather thanestablishing the absence of an interaction effect.Different types of factorial designsThe notation of a factorial study is rather mathematical; the number ofinterventions in a factorial study is represented by a product term, which alsocontains the number of levels of that intervention. Each number refers to thedifferent levels of each intervention; for example, treatment ‘yes’ / ‘no’ representstwo levels, whereas treatment ‘none’ / ‘dose 1’ / ‘dose 2’ corresponds to threelevels. In an investigation of two treatments an I × J factorial study is required,where the first treatment has I levels and the second has J levels.An I × J × K factorial study refers to an evaluation of three treatments, with thethird treatment having K levels. A 2 × 2 × 2 notation would be suitable for anevaluation of three drugs given at a single dose for each drug; that is, the levelswould correspond to the dose and the control. If two dosages of two drugs areto be simultaneously evaluated and compared with their baseline value, a 3 × 3notation would be used where each drug is given at three different levels (control,dose 1, and dose 2). The number of treatment arms can be deduced by solving theproduct of the notation: eg, a 2 × 2 factorial study results in four treatment groups,a 2 × 3 design in six groups, a 2 × 2 × 2 notation in eight groups, and so on.106