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

Abstract

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.

KEYWORDS:

• Confidence interval
• continuity correction
• paired data
• relative difference
• Wilson score interval

Acknowledgments

The authors are very grateful to the Editor, Associate Editor, and three reviewers for their insightful comments that help improve the manuscript. We would like to thank Dr. Pete Laud from the University of Sheffield gave us permission to use, modify, and redistribute the functions in his developed R package ratesci.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Shan's research is partially supported by the National Institutes of Health [award numbers R01AG070849 and R03CA248006].