A comparison of various estimators of a treatment difference for a multi-centre clinical trial

When a clinical trial is conducted at more than one centre it is likely that the true treatment effect will not be identical at each centre. In other words there will be some degree of treatment-by-centre interaction. A number of alternative approaches for dealing with this have been suggested in the literature. These include frequentist approaches with a fixed or random effects model for the observed data and Bayesian approaches. In the fixed effects model, there are two common competing estimators of the treatment difference, based on weighted or unweighted estimates from individual centres. Which one of these should be used is the subject of some controversy and we do not intend to take a particular methodological position in this paper. Our intention is to provide some insight into the relative merits of the indicated range of possible estimators of the treatment effect. For the fixed effects model, we also look at the merits of using a preliminary test for interaction assuming a 10 per cent significance level for the test. In order to make comparisons we have simulated a 'typical' trial which compares an active drug with a placebo in the treatment of hypertension, using systolic blood pressure as the primary variable. As well as allowing the treatment effect to vary between centres, we have concentrated on the particular case where one centre is out of line with the others in terms of its true treatment difference. The various estimators that result from the different approaches are compared in terms of mean squared error and power to reject the null hypothesis of no treatment difference. Overall, the approach that uses the fixed effects weighted estimator of overall treatment difference is recommended as one that has much to offer.