Asymptotic confidence interval construction for proportion ratio based on correlated paired data

In ophthalmological and otolaryngology studies, measurements obtained from both organs (e.g., eyes or ears) of an individual are often highly correlated. Ignoring the intraclass correlation between paired measurements may yield biased inferences. In this article, four different confidence interval (CI) construction methods (maximum likelihood estimates based Wald-type CI, profile likelihood CI, asymptotic score CI and an existing method adjusted for correlated bilateral data) are applied to this type of correlated bilateral data to construct CI for proportion ratio, taking the intraclass correlation into consideration. The coverage probabilities and widths of the resulting CIs are compared with each other in a Monte Carlo simulation study to evaluate their performances. A real dataset from an ophthalmologic study is used to illustrate our methodology.