Testing the Equality of Proportions for Combined Unilateral and Bilateral Data Under Equal Intraclass Correlation Model

In clinical studies, data can be collected either unilaterally or bilaterally in each subject. Especially in bilateral cases, the correlation between responses of a paired organs is non-negligible if we would like to formulate a homogeneity test among groups. In this article, we investigated and derived three test methods based on an equal intraclass correlation model aiming to exploit such combined data samples. The performance of each test method is examined by simulation under various parameter configurations, which suggests the Score test usually has the properties of satisfactory Type I error control and great power performance, and therefore, is recommended among these three proposed and existing methods. A real work example in the otolaryngologic study is analyzed to illustrate the practical application of our proposed test.