Confidence interval construction for the difference between two correlated proportions with missing observations

Abstract

Under the assumption of missing at random, eight confidence intervals (CIs) for the difference between two correlated proportions in the presence of incomplete paired binary data are constructed on the basis of the likelihood ratio statistic, the score statistic, the Wald-type statistic, the hybrid method incorporated with the Wilson score and Agresti–Coull (AC) intervals, and the Bootstrap-resampling method. Extensive simulation studies are conducted to evaluate the performance of the presented CIs in terms of coverage probability and expected interval width. Our empirical results evidence that the Wilson-score-based hybrid CI and the Wald-type CI together with the constrained maximum likelihood estimates perform well for small-to-moderate sample sizes in the sense that (i) their empirical coverage probabilities are quite close to the prespecified confidence level, (ii) their expected interval widths are shorter, and (iii) their ratios of the mesial non-coverage to non-coverage probabilities lie in interval [0.4, 0.6]. An example from a neurological study is used to illustrate the proposed methodologies.

KeyWords:

• Bootstrap confidence interval
• correlated proportion difference
• missing data
• paired binary data
• squaring-and-adding confidence interval

Acknowledgments

The authors are grateful to the editor, associate editor, and two referees for providing some constructive comments and suggestions.

Additional information

Funding

This research was supported by grants from the National Science Fund for Distinguished Young Scholars of China (11225103), and Research Fund for the Doctoral Program of Higher Education of China (20115301110004).