Controversies concerning randomization and additivity in clinical trials

Abstract

'As ye randomise so shall ye analyse', is one way of describing Fisher's defence of randomization. Yet, when it comes to clinical trials we nearly always randomize but we rarely analyse the way we randomize and Fisher himself was no exception. Two controversies involving Fisher in the 1930s are discussed: one with Neyman concerning additivity and the other with Student concerning randomization. Their relevance today is considered, as is whether randomization inference in clinical trials is dead and whether modelling rules the day, whether minimization is an acceptable procedure and to what extent trialists confuse experiments with surveys. It will be maintained that a number of different possible purposes of clinical trials have been confused because in the case of the general linear model, under strong additivity, they can all be satisfied by a single analysis. More generally, however, this is not the case.