Confidence interval construction for proportion difference in small‐sample paired studies

Abstract

Paired dichotomous data may arise in clinical trials such as pre-/post-test comparison studies and equivalence trials. Reporting parameter estimates (e.g. odds ratio, rate difference and rate ratio) along with their associated confidence interval estimates becomes a necessity in many medical journals. Various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions. Nevertheless, the performance of these asymptotic methods may have poor coverage properties in small samples. In this article, we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small-sample paired data. Specifically, we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test. The exact unconditional confidence interval guarantees the coverage probability, and it is recommended if strict control of coverage probability is required. However, the exact method tends to be overly conservative and computationally demanding. Our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small-sample designs, and yet they are relatively easy to implement computationally. We illustrate the methods using real examples from a pain management study and a cancer study.