  Measurements are generally collected as unilateral or bilateral data in
clinical trials or observational studies. For example, in ophthalmology
studies, the primary outcome is often obtained from one eye or both eyes of an
individual. In medical studies, the relative risk is usually the parameter of
interest and is commonly used. In this article, we develop three confidence
intervals for the relative risk for combined unilateral and bilateral
correlated data under the equal dependence assumption. The proposed confidence
intervals are based on maximum likelihood estimates of parameters derived using
the Fisher scoring method. Simulation studies are conducted to evaluate the
performance of proposed confidence intervals with respect to the empirical
coverage probability, the mean interval width, and the ratio of mesial
non-coverage probability to the distal non-coverage probability. We also
compare the proposed methods with the confidence interval based on the method
of variance estimates recovery and the confidence interval obtained from the
modified Poisson regression model with correlated binary data. We recommend the
score confidence interval for general applications because it best controls
converge probabilities at the 95% level with reasonable mean interval width. We
illustrate the methods with a real-world example.
