Interval estimation of risk difference for data sampled from clusters

Risk difference (RD) is an important measure in epidemiological studies where the probability of developing a disease for individuals in an exposed group, for example, is compared with that in a control group. There are varying cluster sizes in each group and the binary responses within each cluster cannot be assumed independent. Under the cluster sampling scenario, Lui ( Statistical Estimation of Epidemiological Risk . Wiley: CA, 2004; 7–27) discusses four methods for the construction of a confidence interval for the RD. In this paper we introduce two very simple methods. One method is based on an estimator of the variance of a ratio estimator ( Sampling Techniques (3rd edn). Wiley: New York, 1977; 30–67) and the other method is based on a sandwich estimator of the variance of the regression estimator using the generalized estimating equations approach of Zeger and Liang ( Biometrics 1986; 42 :121–130). These two methods are then compared, by simulation, in terms of maintaining nominal coverage probability and average coverage length, with the four methods discussed by Lui ( Statistical Estimation of Epidemiological Risk . Wiley: CA, 2004; 7–27). Simulations show at least as good properties of these two methods as those of the others. The method based on an estimate of the variance of a ratio estimator performs best overall. It involves a very simple variance expression and can be implemented with a very few computer codes. Therefore, it can be considered as an easily implementable alternative. Copyright © 2008 John Wiley & Sons, Ltd.