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Factorial designs for clinical trials are often encountered in medical, dental, and orthodontic research. Factorial designs assess two or more interventions simultaneously and the main advantage of this design is its efficiency in terms of sample size as more than one intervention may be assessed on the same participants. However, the factorial design is efficient only under the assumption of no interaction (no effect modification) between the treatments under investigation and, therefore, this should be considered at the design stage. Conversely, the factorial study design may also be used for the purpose of detecting an interaction between two interventions if the study is powered accordingly. However, a factorial design powered to detect an interaction has no advantage in terms of the required sample size compared to a multi-arm parallel trial for assessing more than one intervention. It is the purpose of this article to highlight the methodological issues that should be considered when planning, analysing, and reporting the simplest form of this design, which is the 2 × 2 factorial design. An example from the field of orthodontics using two parameters (bracket type and wire type) on maxillary incisor torque loss will be utilized in order to explain the design requirements, the advantages and disadvantages of this design, and its application in orthodontic research.

Factorial designs: an overview with applications to orthodontic clinical trials