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Intraclass correlation coefficient for data in a clustered study is traditionally estimated from a one-way random-effects model. This model assumes normality for the random cluster effect and the residual effect. When the normality assumption is questionable, we find that the estimated correlation could be much below the nominal level when data are highly skewed or data have low kurtosis. We develop a bias-corrected estimator based on the approach by Thomas and Hultquist for a study with unbalanced cluster sizes. For multivariate normal data or non-normal data with moderate skewness, we compare the performance of the new bias-corrected estimator with two existing estimators with regards to accuracy and precision. When correlation is small, the existing ANOVA estimator works well. When correlation is medium to large, the proposed new estimator has the correlation close to the nominal level, and its mean squared error is smaller than others.

Estimation of bias-corrected intraclass correlation coefficient for unbalanced clustered studies with continuous outcomes