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 epidemiologic indices to quantify the effect of a suspected risk factor on the probability of developing a disease. When we employ cluster sampling to collect data, an interval estimator that does not account for the intraclass correlation between subjects within clusters is likely inappropriate. In application of the beta-binomial model to account for the intraclass correlation, we develop four asymptotic interval estimators of the RR, which are direct extensions of some recently developed estimators for independent binomial sampling. We then use Monte Carlo simulation to evaluate the finite-sample performance of these four interval estimators in a variety of situations. We find that the estimator using the logarithmic transformation generally 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 illustrate the use of the estimators developed in this paper.