Confidence intervals for the risk ratio under cluster sampling based on the beta-binomial model

In cohort studies, the risk ratio (RR) is one of the most commonly used epi demiologic indices to quantify the effect of a suspected risk factor on the probability of developing a disease. When we employ cluster sampling to co llect data, an interval estimator that does not account for the intraclass correlation between subjects within clusters is likely inappropriate. In ap plication of the beta-binomial model to account for the intraclass correlat ion, we develop four asymptotic interval estimators of the RR, which are di rect extensions of some recently developed estimators for independent binom ial sampling. We then use Monte Carlo simulation to evaluate the finite-sam ple performance of these four interval estimators in a variety of situation s. We find that the estimator using the logarithmic transformation generall y performs well and is preferable to the other three estimators in most of the situations considered here. Finally, we include an example from a study of an educational intervention with emphasis on behaviour change to illust rate the use of the estimators developed in this paper. Copyright (C) 2000 John Wiley & Sons, Ltd.