Confidence intervals for intraclass correlation coefficients in variance components models

Confidence intervals for intraclass correlation coefficients in agreement studies with continuous outcomes are model-specific and no generic approach exists. This paper provides two generic approaches for intraclass correlation coefficients of the form Sigma q=1 2). The first approach uses Satterthwaite's approximation and an F-distribution. The second approach uses the first and second moments of the intraclass correlation coefficient estimate in combination with a Beta distribution. Both approaches are based on the restricted maximum likelihood estimates for the variance components involved. Simulation studies are conducted to examine the coverage probabilities of the confidence intervals for agreement studies with a mix of small sample sizes. Two different three-way variance components models and balanced and unbalanced one-way random effects models are investigated. The proposed approaches are compared with other approaches developed for these specific models. The approach based on the F-distribution provides acceptable coverage probabilities, but the approach based on the Beta distribution results in accurate coverages for most settings in both balanced and unbalanced designs. A real agreement study is provided to illustrate the approaches.