Factorial clinical trials in the presence and absence of plausible statistical interactions between treatment factors. A historical review of the methodological literature

Abstract

Factorial trials can be conducted when statistical interactions between two or more treatment factors are not anticipated, but also when they are. A k-in-1 factorial trial answers k single-factor questions with the same number of units as one parallel-group trial if there are no interactions. Literature on k-in-1 factorial trials has dominated trialists understanding of factorial trials in the UK. However, factorial experiments originated from the Design of Experiments field to enable interactions to be robustly estimated. Seemingly conflicting guidance from these literatures poses a source of confusion and misunderstanding for trialists. We bring these literatures together to provide clarity on the arguments that have been used to recommend use of factorial trials in the presence and absence of interactions. We outline motivating examples. We summarise the rationales for using factorial trials, the treatment contrasts of interest, and the properties of their estimators, for the two schools of thought. We describe the debate, going back to 1935, and use an empirical example to illustrate the impact of different analysis approaches. We conclude that it is vital that trialists carefully and clearly specify their objectives. Estimands of interest and treatment contrasts follow, with properties of estimators dictated by this choice.