Conservative confidence intervals for the intraclass correlation coefficient for clustered binary data

Abstract

Asymptotic approaches are traditionally used to calculate confidence intervals for intraclass correlation coefficient in a clustered binary study. When sample size is small to medium, or correlation or response rate is near the boundary, asymptotic intervals often do not have satisfactory performance with regard to coverage. We propose using the importance sampling method to construct the profile confidence limits for the intraclass correlation coefficient. Importance sampling is a simulation based approach to reduce the variance of the estimated parameter. Four existing asymptotic limits are used as statistical quantities for sample space ordering in the importance sampling method. Simulation studies are performed to evaluate the performance of the proposed accurate intervals with regard to coverage and interval width. Simulation results indicate that the accurate intervals based on the asymptotic limits by Fleiss and Cuzick generally have shorter width than others in many cases, while the accurate intervals based on Zou and Donner asymptotic limits outperform others when correlation and response rate are close to their boundaries.

Keywords:

• Clustered binary data
• confidence interval
• importance sampling
• intraclass correlation coefficient
• profile confidence limit

Acknowledgements

The authors are very grateful to the Editor, Associate Editor, and two reviewers for their insightful comments that help improve the manuscript. Research reported in this publication was supported by the National Institutes of Health under Award Number R01AG070849, and R03CA248006.

Disclosure statement

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

Additional information

Funding

Research reported in this publication was supported by the National Institutes of Health under Award Number R01AG070849, and R03CA248006.