The design of multicentre trials.

The analysis of data collected in multicentre trials offers challenges because the data from the individual centres must be combined in some way to give an overall evaluation of the differences between the treatments in the trial. We propose that the combined response to treatment (CRT) be used as this overall measure. The definition and estimation of the CRT can be derived from either a fixed-effects or a random-effects model. For the latter we introduce the ECRT--the expected combined response to treatment. We describe and compare both types of model and express our preference for the random-effects model. We stress that the number of patients enrolled at a centre is a random variable and show that this source of randomness inflates the variance of the estimated ECRT. Variability in enrolment rates over the centres further inflates this variance. A simple conclusion from our results is that if variability in the treatment and centre effects, in the enrolment time, in the number of patients enrolled at a centre and in the enrolment rates is not properly accounted for, then an underpowered trial may result. Using properties of estimators generated by the random-effects model we propose methods for determining the optimal number of centres and total number of patients to enrol in a trial to minimize a loss function that accounts for centre and patient costs and loss of revenue. We discuss variants of the loss function and corresponding optimization problems for different types of enrolment. We end the paper with brief generalizations of the developed techniques to the case where the response is binary.