Analysis of binary data from a multicentre clinical trial

SUMMARY We develop several methods for estimating the treatment effect difference defined as the overall log-odds ratio of favourable response in a multicentre clinical trial comparing two treatments with binary response. A simulation study compares the bias and mean squared error of the point estimates and the exact coverage probabilities of confidence intervals obtained distributions. Multicentre randomized clinical trials are frequently used to test the efficacy of new medical regimens. These trials are attractive due to the ease of getting the desired sample size in a short period of time and the broad coverage of the patient population and medical practitioners. The analysis of data from such trials requires combining information from the centres in a way that properly accounts for the variation due to the centres and the differential efficacy of treatments between the centres. In this paper we investigate several approaches to pooling the data across centres and for handling the effects associated with the centres. Chakravarthi & Grizzle (1975) and Beitler & Landis (1985) argue for treating these effects as random, and Fleiss (1986) argues against because the centres are seldom chosen at random from a well-defined population of clinics and therefore the effects cannot be associated with any population. We prefer the random effect model approach for the following reasons. The goal of a trial is to extend the results of the study to the general population, duly accounting for variation in the patient population and the medical skills of practitioners. Hence, if we believe that the variability between centres as estimated by the data is typical of the variability in the population of centres, then the inference based on the random effects model is more appropriate than the one based on the fixed effects model. Furthermore, the variation among the centres may be more than that predicted from samples from a binomial distribution. Treating the centre effects as random introduces this intra-class correlation into our model assumptions. Let the outcome variable from each centre be a pair of binomial random variables XAj