The Design and Analysis of Multicentre Trials in the Random Effects Setting
The Design and Analysis of Multicentre Trials in the Random Effects Setting
Valerii Fedorov, Byron Jones and Frank Rockhold
ABSTRACT. Dragalin, et al. (2001) defined a combined response to treatment (CRT) in a multicentre trial and showed how it could be estimated using fixed effects models which are appropriate in the ”testground” setting. Here we extend the previous work to the situation where centres can be viewed as a sample from a population and the treatment and centre effects may be assumed random. We give iterative formulae for obtaining the maximum likelihood estimators of the treatment mean vector and its variance-covariance matrix, including the case with unknown components of variance and the case where the variance is different for the compared treatments or varies randomly over the centres. While most of these formulae have appeared in various forms in the statistical literature, we have attempted to unify and simplify them both in the general setting and in the simplest case of two treatments with no covariates. Most formulae allow singular centres where some centres have data from only one of the treatments. We show that the CRT estimators generated within the random effect model approach and the estimators for various fixed effect models can be described by the same formula if additional control parameters describing the variability between centres are introduced. That unified presentation allows us, for different settings, to derive the optimal number of centres and numbers of patients per centre to recruit, subject to (i) a total cost constraint and (ii) a maximum variance constraint. The effect on the variance of the CRT caused by random enrollment is illustrated using two simulated examples. The recruitment waiting time distribution is discussed under Poisson sampling assumptions and the implications of alternative recruitment strategies are considered. Finally, we give an illustrative example
using data based on a real multicentre trial for two treatments.
An important conclusion of the results presented in this report is that the total sample size of a multicentre trial needs to take into account inflationary effects due to a number of sources: treatment effects varying over centres, centre sizes deviating from those in a balanced design due to random recruitment and varying rates of recruitment over the centres.
