The impact of clustering binary data on relative risk towards a study of inferential methods

In epidemiological cohort studies, the relative risk (also known as risk ratio) is a major measure of association to summarize the results of two treatments or exposures. Generally, it measures the relative change in disease risk as a result of treatment application. Standard approaches to estimating relative risk available in common software packages may produce biased inference when applied to correlated binary data collected from longitudinal or clustered studies. In recent years, several methods for estimating the risk ratio for correlated binary data have been published, some of which maintain a well-controlled coverage probability but do not maintain an appropriate interval width or the interval location to measure the balance between distal and mesial noncoverage probabilities accurately or, vice versa. This paper develops efficient and straightforward inference procedures for estimating a confidence interval for risk ratio based on a hybrid method. In general, the hybrid method combines two separate confidence intervals for two single risk rates to form a hybrid confidence interval for their ratio. Additionally, we propose the procedures for constructing a confidence interval for risk ratio that directly extends recently recommended methods for correlated binary data by building on the concepts of the design effect and effective sample sizes typically used in representative sample surveys. In order to investigate the performance of these proposed methods, we conduct an extensive simulation study. To demonstrate the utility of our proposed methods, we present three examples from real-life applications, comparing the side effects of low-dose tricyclic antidepressants with a placebo, the efficacy of the treatment group in a teratological experiment, and the efficiency of the active drugs in curing infection for clinical trials.