In models including treatment-centre effects balance will only be achieved in the unlikely situation where there are an equal number of patients per treatment per centre (this condition is also required to achieve balance across random effects). Treatment mean estimates from either a fixed or random effects model will then equal the raw treatment means. In the more usual situations where there are unequal numbers of patients per treatment per centre, treatment means will differ between fixed effects and random effects models.

In models omitting centre-treatment effects, balance across random effects is achieved when treatments are allocated in equal proportions at each centre (even if the overall centre sizes vary). Treatment estimates are then the same regardless of whether centre effects are taken as fixed or random. However, if treatments are not allocated in equal proportions at each centre, treatment estimates will differ between the models because information is combined from both the centre and residual error strata in the random effects model.

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