In clinical trials, data can be collected either unilaterally (response from one organ) or bilaterally (response from paired organs) in each subject and each stratum. Especially in bilateral cases, the correlation between responses of a paired organs is non-negligible if we would like to formulate a homogeneity test of relative risk among strata. In this article, we investigated and derived three test methods based on an equal intraclass correlation model aiming to deal with such a combined data sample especially. The performance of each test method is examined by simulation under various parameter configurations, which suggest 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.