Estimating efficacy in clinical trials with clustered binary responses

When non-compliance occurs in a clinical trial, it may be of interest to supplement the intent-to-treat analysis with an analysis of the efficacy (or biological effect) of therapy. Sommer and Zeger (1991) developed a method for estimating efficacy applicable to the case of a binary response variable and all-or-none compliance that assumes independent subject responses. We extend this approach to accommodate within-cluster correlations as may be expected in a cluster-randomized design. The method is illustrated using data from a controlled village-randomized clinical trial conducted in Indonesia to investigate the effect of vitamin A supplementation on mortality in children. We find that within-cluster correlations for these data are very small and that taking into account the clustering does not substantially affect inferences in this case. Additional calculations show that small within-cluster correlations (though larger than those found in the vitamin A data) may have a large impact on efficacy inferences. We also present the results of a simulation study that demonstrates the validness of the proposed approach for finite sample sizes. Copyright (C) 2002 John Wiley Sons, Ltd.