Open Access Open Badges Research article

Bias-corrected estimator for intraclass correlation coefficient in the balanced one-way random effects model

Eshetu G Atenafu1, Jemila S Hamid24, Teresa To345, Andrew R Willan34, Brian M Feldman345 and Joseph Beyene2345*

Author Affiliations

1 Princess Margaret Hospital, Toronto, Canada

2 Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Canada

3 Child Health Evaluative Sciences Hospital for Sick Children, Toronto, Canada

4 Division of Biostatistics, Dalla Lana School of Public Health, University of Toronto, Toronto, Canada

5 Departments of Pediatrics, Health Policy and Management, University of Toronto, Toronto, Canada

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BMC Medical Research Methodology 2012, 12:126  doi:10.1186/1471-2288-12-126

Published: 20 August 2012



Intraclass correlation coefficients (ICCs) are used in a wide range of applications. However, most commonly used estimators for the ICC are known to be subject to bias.


Using second order Taylor series expansion, we propose a new bias-corrected estimator for one type of intraclass correlation coefficient, for the ICC that arises in the context of the balanced one-way random effects model. A simulation study is performed to assess the performance of the proposed estimator. Data have been generated under normal as well as non-normal scenarios.


Our simulation results show that the new estimator has reduced bias compared to the least square estimator which is often referred to as the conventional or analytical estimator. The results also show marked bias reduction both in normal and non-normal data scenarios. In particular, our estimator outperforms the analytical estimator in a non-normal setting producing estimates that are very close to the true ICC values.


The proposed bias-corrected estimator for the ICC from a one-way random effects analysis of variance model appears to perform well in the scenarios we considered in this paper and can be used as a motivation to construct bias-corrected estimators for other types of ICCs that arise in more complex scenarios. It would also be interesting to investigate the bias-variance trade-off.