Correlated binary data often arise in epidemiological cohort studies. The risk ratio (RR) is one of three major useful measures of association for summarizing the results from such epidemiological cohort studies. In applications, the RR and its complement, the percentage reduction in risk, have a direct interpretation. This usually measures the relative change in the epidemiological risk due to the application of the treatment. Standard approaches for estimating RR available in software packages may lead to biased inferences when applied to a correlated binary data. In this paper, we develop some simple and efficient inference procedures for estimating RR based on a hybrid method introduced by Zou (2008) using four existing interval methods for a single proportion for correlated binary data. A simulation study is conducted to investigate the performance of the proposed methods, and an application to a toxicological study is used to illustrate the proposed methods.