Interval estimation of some epidemiological measures of association

In epidemiological cohort studies, the probability of developing a disease for individuals in a treatment/intervention group is compared with that of a control group. The groups involve varying cluster sizes, and the binary responses within each cluster cannot be assumed independently. Three major measures of association used to report the efficacy of treatments or effectiveness of public health intervention programs in case of prospective studies are Risk Difference (RD), Risk Ratio (RR) and Relative Risk Difference (RED). The preference of one measure of association over the other in drawing statistical inference depends on design of study. Lui (2004) discusses a number of methods of constructing confidence intervals 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 intervals 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 measures of association.