Stratified Wilson and Newcombe Confidence Intervals for Multiple Binomial Proportions

This article proposes the stratified Wilson confidence interval for multiple binomial proportions and the stratified Newcombe confidence intervals for multiple binomial proportion differences. Both confidence intervals are presented in closed forms to facilitate easy calculations. The confidence levels of the proposed intervals are theoretically justified and demonstrated through extensive simulations. The coverage rates are found to be rather satisfactory. When the Wilson and Newcombe methods are used in unstratified analysis, the proposed methods may serve as the counterparts for stratified analysis. The proposed methods are applied to a vaccine trial to compute the stratified sero-conversion rate and rate difference over multiple clinical centers.