  Measurements are generally collected as unilateral or bilateral data in
clinical trials or observational studies. For example, in ophthalmologic
studies, statistical tests are often based on one or two eyes of an individual.
For bilateral data, recent literatures have shown some testing procedures that
take into account the intra-class correlation between two eyes of the same
person. Ma et al. (2015) investigated three testing procedures under Rosner's
model. In this paper, we extend Ma's work for bilateral data to combined
bilateral and unilateral data. The proposed procedures are based on the
likelihood estimate algorithm derived from the root of 4th order polynomial
equations and fisher scoring iterations. Simulation studies are performed to
compare the testing procedures under different parameter configurations. The
result shows that score test has satisfactory type I error rates and powers.
Therefore, we recommend score test for testing the equality of proportions. We
illustrate the application of the proposed methods with a double-blind
randomized clinical trial.
