Exact confidence limits for proportion difference in clinical trials with bilateral outcome

Abstract

Bilateral data are frequently occur in medical research. Asymptotic approaches are traditionally used to construct confidence intervals for proportion difference. However, they are often have unsatisfactory performance with regards to coverage, with the actual coverage below the nominal level or being too conservative. For these reasons, we propose developing exact one-sided limits for proportion difference in a parallel study with bilateral data to guarantee the coverage probability when sample size is small to medium. A statistical quantity has to be used for sample space ordering in the exact limit calculation. Four asymptotic limits are utilized as statistical quantities: the Wald limits under the independence or dependence assumptions for variance estimates, the Wald limits with the difference estimate under the dependence assumption, and the bootstrap percentile limits. We compare the performance of these exact limits with regards to average length and the limits of all possible samples. A real example from a randomized clinical trial in otolaryngology is used to illustrate the application of the proposed exact limits.