Analyzing the influence of binary data clustering on relative risk within the context of inferential methods

Abstract

In epidemiological cohort studies, the relative risk is a key measure to gauge the connection between two treatments or exposures. It quantifies the proportional change in the risk of disease due to the application of a specific treatment. However, the conventional methods for calculating relative risk, available in widely-used software, might yield inaccurate results when applied to correlated binary data from studies conducted over time or in clusters. Recently, various techniques have been proposed to estimate the risk ratio for correlated binary data. However, some methods exhibit a tradeoff between maintaining accurate coverage probability (CP) and ensuring an appropriate interval width or location. This paper introduces a new approach to confidently estimating the risk ratio using a hybrid method. This hybrid method combines two distinct confidence intervals (CIs) derived from single risk rates to establish a unified confidence interval for their ratio. Furthermore, we present a methodology to construct a confidence interval for the risk ratio, which builds upon established methods for correlated binary data. This extension incorporates principles such as the design effect and adequate sample sizes commonly used in representative sample surveys. An extensive simulation study is conducted to evaluate the effectiveness of these proposed methods. The performance of the methods is thoroughly examined in various scenarios. Additionally, the practicality of the proposed methods is showcased through three real-life examples. These examples involve comparing the side effects of low-dose tricyclic antidepressants with a placebo, assessing the efficacy of a treatment group in a teratological experiment, and evaluating the efficiency of active drugs in curing infections during clinical trials.

Keywords:

• Confidence interval
• Correlated binary data
• Coverage probability
• Distal noncoverage
• Expected length
• Intraclass correlation
• Mesial noncoverage
• Risk ratio

Acknowledgments

The authors are grateful to the referees for their constructive comments and suggestions that have led to improvement in this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by a CSU-AAUP University research grant and by the Simons Foundation Mathematics and Physical Sciences - Grant for Collaboration among Mathematicians #499650.