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Interval Estimation of Some Measures of Association for Epidemiological Data Sampled from Clusters: a Review and an Extension
Sudhir Paul, Universtiy of Windsor 
*Tasneem Zaihra, university of new brunswick 

Keywords: Clustered Binary Data, Epidemiological indices, Intra class correlation, Risk Difference, Risk ratio, Relative difference and Relative risk

In epidemiological cohort studies probability of developing a disease for individuals in an exposed group, for example, is compared with that in an unexposed group. The groups involve varying cluster sizes and the binary responses within each cluster cannot be assumed independent. Three risk measures, the risk difference (RD), the risk ratio (RR), the relative risk (RED), have been proposed in the literature. Lui (2004) discusses a number of methods of constructing confidence interval for each of these measures. Specifically, Lui (2004) discusses four methods for RD, four methods for RR and three methods for RED. For the construction of confidence interval for RD Paul and Zaihra (2008) compare the four methods discussed by Lui (2004), using extensive simulations, with a method based on an estimator of the variance of a ratio estimator by Cochran (1977) and a method based on a sandwich estimator of the variance of the regression estimator using the generalized estimating equations approach of Zeger and Liang (1986). Paul and Zaihra (2008) conclude that the method based on an estimate of the variance of a ratio estimator performs best overall. In this paper we extend the two new methodologies introduced in Paul and Zaihra (2008) to confidence interval construction of the risk measures RR and RED. Extensive simulations show that the method based on an estimate of the variance of a ratio estimator performs best overall for constructing confidence interval for the other two risk measures RR and RED as well. This method involves a very simple variance expression which can be implemented with a very few computer codes. Therefore it can be considered as an easily implementable alternative for all the three epidemiological indices.