🤖 AI Summary
This study addresses the long-standing methodological confusion surrounding factorial clinical trials, particularly regarding the presence or absence of treatment interactions. By systematically integrating theoretical frameworks from both clinical trials and experimental design literatures, the work clarifies the appropriate conditions for applying factorial designs and outlines corresponding analytical strategies across different scenarios. Through comprehensive literature review, theoretical derivation, and empirical case studies, the research emphasizes the logical coherence among study objectives, estimable parameters, and treatment contrasts. It resolves conceptual ambiguities and explicitly delineates how interaction effects influence estimation properties, thereby offering clinical researchers a clear and rigorous methodological guide for designing and analyzing factorial trials.
📝 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.