90 / 2019-10-05 16:15:33

Evaluation of Method to Construct Confidence Interval for Proportion Difference

Interval Estimation,Proportion Difference,Coverage Probability

For interval estimation of proportion difference, arising from independent binomial distributions, the nominal coverage probability cannot be achieved exactly because of discreteness. Methods with too large coverage probability are too conservative and generally produce a wider interval, and methods with too small coverage probability lead to an inflation in type I error rate. In this paper, we compared six methods in terms of actual coverage probability and expected width. The Newcomb method and Miettinen-Nurminen (score) method both perform better than the rest methods in our study with the actual coverage probability close to the nominal level while still producing a shorter confidence interval. However, the MN score method show drastic fluctuation when the proportions are close to zero or one. We further investigated the performance of lower bound and higher bound of the intervals respectively, from which we concluded that the drastic fluctuation of MN Score method comes from higher bound of the interval and the lower bound performs well. In addition, the lower bound of MN Score method have an actual coverage probability higher than Newcomb method while the length of interval from both methods are similar. In conclusion, we recommend MN score method for superiority and non-inferiority trials, and Newcomb method for equivalence trials and for exploratory studies.