New Confidence Intervals for Relative Risk of Two Correlated Proportions

Biomedical studies, such as clinical trials, often require the comparison of measurements from two correlated tests in which each unit of observation is associated with a binary outcome of interest via relative risk. The associated confidence interval is crucial because it provides an appreciation of the spectrum of possible values, allowing for a more robust interpretation of relative risk. Of the available confidence interval methods for relative risk, the asymptotic score interval is the most widely recommended for practical use. We propose a modified score interval for relative risk and we also extend an existing nonparametric U-statistic-based confidence interval to relative risk. In addition, we theoretically prove that the original asymptotic score interval is equivalent to the constrained maximum likelihood-based interval proposed by Nam and Blackwelder. Two clinically relevant oncology trials are used to demonstrate the real-world performance of our methods. The finite sample properties of the new approaches, the current standard of practice, and other alternatives are studied via extensive simulation studies. We show that, as the strength of correlation increases, when the sample size is not too large the new score-based intervals outperform the existing intervals in terms of coverage probability. Moreover, our results indicate that the new nonparametric interval provides the coverage that most consistently meets or exceeds the nominal coverage probability.