Continuity corrected score confidence interval for the difference in proportions in paired data

For paired binary data, the hybrid method and the score method are often recommended for use to calculate the confidence interval for risk difference. These asymptotic intervals do not control the coverage probability. We propose to develop a new score interval with continuity correction to further improve the performance of the existing intervals. The traditional correction value may be too large which leads to a wide interval. For that reason, we propose three different correction values to identify the optimal correction interval with balanced coverage probability and interval width. From simulation studies, we find that a small correction value for the score interval has good performance. In addition, we derive the non-iterative solutions for the developed continuity correction score intervals.