Exact Methods for Testing the Equality of Proportions for Binary Clustered Data From Otolaryngologic Studies

For binary clustered data with cluster size of two, which often arises from otolaryngologic and ophthalmologic studies, the correlation between the outcomes is usually unknown. For this reason, an asymptotic approach based on normal approximation has been often used for comparing proportions between groups. This approach performs poorly with unacceptable Type I error control in small sample settings. Storer and Kim proposed an approximate unconditional method to control the Type I error associated with the asymptotic approach. However, both the asymptotic approach and the approximate unconditional approach do not guarantee the test size. Exact tests may be considered as alternatives to control the Type I error. Tang et al. studied the unconditional approach based on maximization for this type of data. It was shown to be overly conservative in most cases. We present two exact approaches to reduce the conservativeness of the exact test based on maximization: one is a conditional approach and the other is an unconditional approach based on estimation followed by maximization. We compare the performance of the competing approaches by studying the actual Type I error rate and power. The comparison is conducted by enumerating all possible contingency tables. A real example from a two-arm randomized clinical trial is provided to illustrate the various testing procedures. We recommend the two presented exact procedures for use in practice due to the guarantee of test size and power gain.