[The center effect in multicenter studies: fixed or random?]

The multiplication of multicentric clinical studies leads to a generalization of the use of a center effect in statistical analyses. In the simple situation where the dependent variable is quantitative and there is only a simple factor of interest, the formalisation of such a protocol corresponds to a two way ANOVA (with the factor of interest and the center factor) with generally a term of interaction. Even such a simple situation leads to interrogations, one of them being to determine whether the centre effect is fixed or random. In the first situation, the conclusion of the study will concern only the centres evaluated in the study, while in the second, the conclusion will concern the whole population from which the centers have been randomly selected. Such a generalizability has a cost: a loss of power in determining the effect of the factor of interest (the loss being as important as the interaction factor of interest x centre factor is large) and the necessity of sophisticated statistical software. This paper will focus on successively: the notion of ANOVA, of fixed or random effect (with the conceptual, formal and numerical differences that distinguish these two approaches). A numerical example is proposed.