Continuity Corrected Wilson Interval for the Difference of Two Independent Proportions

Confidence interval for the difference of two proportions has been studied for decades. Many methods were developed to improve the approximation of the limiting distribution of test statistics, such as the profile likelihood method, the score method, and the Wilson method. For the Wilson interval developed by Beal (Biometrics 43:941, 1987), the approximation of the Z test statistic to the standard normal distribution may be further improved by utilizing the continuity correction, in the observation of anti-conservative intervals from the Wilson interval. We theoretically prove that the Wilson interval is nested in the continuity corrected Wilson interval under mild conditions. We compare the continuity corrected Wilson interval with the commonly used methods with regards to coverage probability, interval width, and mean squared error of coverage probability. The proposed interval has good performance in many configurations. An example from a Phase II cancer trial is used to illustrate the application of these methods.