Exact methods of testing the homogeneity of prevalences for correlated binary data

Correlated binary data arise in many ophthalmological and otolaryngological clinical trials. To test the homogeneity of prevalences among different groups is an important issue when conducting these trials. The equal correlation coefficients model proposed by Donner in 1989 is a popular model handling correlated binary data. The asymptotic chi-square test works well when the sample size is large. However, it would fail to maintain the type I error rate when the sample size is relatively small. In this paper, we propose several exact methods to deal with small sample scenarios. Their performances are compared with respect to type I error rate and power. The ‘M approach’ and the ‘E + M approach’ seem to outperform the others. A real work example is given to further explain how these approaches work. Finally, the computational efficiency of the exact methods is discussed as a pressing issue of future work.