Confidence intervals of proportion differences for stratified combined unilateral and bilateral data

In otolaryngologic studies, subjects may contribute either unilateral observations from only one ear or bilateral observations from a pair of ears. For bilateral subjects, each person contributes information from two ears, the values of which are generally highly correlated. To avoid the confounding effect in stratified otolaryngologic studies, stratified data analysis is an important research topic. Based on the dependence model in stratified designs, this article presents five simultaneous confidence intervals (CIs) and two bootstrap simultaneous CIs for proportion differences with combined unilateral and bilateral data. Six approximate CIs and two bootstrap CIs for the common proportion difference are also developed. The proposed CIs are evaluated by empirical coverage probability, empirical coverage width and the ratio of mesial non-coverage probability to the non-coverage probability. Simulation results show that the simultaneous CIs based on Wilson method, the inverse hyperbolic tangent transformation, score statistic and the bootstrap percentile simultaneous CIs perform well and hence be recommended for applications, score CI and the CI based on Cochran statistic for the common proportion difference behave well even under small sample sizes, other CIs produce good performance when sample size is not small. A real otolaryngology study data is used to illustrate the proposed methodologies.