We propose a convenient correction method to calculate the Cochran-Mantel-Haenszel (CMH) confidence interval on stratified rate difference when observed rates are 100% among partial or all clinical centers. It is an important practical problem arising from vaccine trials. The proposed correction method is based on the Law of Laplace Succession that takes sample size into account in the estimation of variance when the observed rate is 100%. The method improves the usual variance estimation when the observed rate is 100%. The CMH confidence intervals with theLaplace correction are compared with thewell-accepted Newcombe-Wilson confidence intervals in terms of various sample sizes and observed rates. It is found that the CMH confidence interval with the Laplace correction can be used as a method for the stratified analysis of the rate comparison, in which the Newcombe-Wilson method is used for the unstratified analysis and the stratified analysis is required by the regulatory guidelines and observed rates are 100%.

Cochran-Mantel-Haenszel interval, Laplace Law of Succession, stratification, Wilson-Newcombe confidence interval.