Profile likelihood-based confidence interval of the intraclass correlation for binary outcome data sampled from...

Area of Science:

• Biostatistics
• Biomedical Data Analysis
• Statistical Modeling

Background:

• Intraclass correlation is crucial for binary outcome data in clustered biological and biomedical studies.
• Existing research extensively covers bias and efficiency of intraclass correlation estimators.
• Confidence interval construction for intraclass correlation in binary data has received limited attention.

Purpose of the Study:

• To generalize existing intraclass correlation estimators by constructing asymptotic confidence intervals.
• To address the under-coverage issue observed in standard asymptotic confidence intervals.
• To introduce and evaluate novel methods for constructing reliable confidence intervals for intraclass correlation in binary outcome data.

Main Methods:

• Construction of asymptotic confidence intervals for four point estimators.
• Development of Fisher's z-transformation approach.
• Application of profile likelihood based on the beta-binomial model.
• Implementation of a hybrid profile variance approach using quadratic estimating equations.

Main Results:

• Asymptotic confidence intervals showed significant under-coverage in simulations.
• Fisher's z-transformation, profile likelihood, and hybrid profile variance approaches improved coverage probabilities.
• The profile likelihood approach demonstrated excellent performance with coverage levels near nominal across various parameters.

Conclusions:

• The proposed confidence interval methods significantly enhance accuracy for intraclass correlation in binary clustered data.
• The profile likelihood approach is particularly effective, offering robust coverage.
• These improved methods are valuable for biological and biomedical data analysis where clustered binary outcomes are common.