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.