Testing the homogeneity of proportions for combined unilateral and bilateral data

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 the bilateral data, recent literatures have shown some test procedures that take into account the intraclass correlation between paired organs of the same person. Ma et al. investigated three test 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 the 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 homogeneity of proportions. We illustrate the application of the proposed methods with two real world examples.