The intraclass correlation coefficient (ICC), often denoted by ρ, was first introduced by Fisher
 to study the familial resemblance between siblings. Since then it has obtained a wide range of applications in many areas such as psychology, epidemiology, genetics and genomics. See Donner
 for an extensive review of inference procedures. In psychology, it plays a fundamental role in studying inter-rater reliability
[3, 4]. It is used as a measure of heritability in classical genetic linkage studies to quantify the proportion of variance in traits of interest explained by genetic factors
. Intraclass correlation obtained from genome-wide association data has recently been used to provide a better estimate of heritability
 . Sensitivity analysis is another application where ρ may be used as a means of investigating the effectiveness of an experimental treatment
. The intraclass correlation has also found some interesting application in genomics where it has been used to assess methodological and biological variations in DNA microarray analysis
The intraclass correlation coefficient also plays a key role in study design such as design of cluster randomized trials where it is traditionally used to quantify the degree of similarity between individuals within clusters
Over the last decade, ICCs have received more attention in the literature and there has been an increasing awareness and appreciation of methodological issues related to these indices
The most fundamental interpretation of ICCs is as a measure of the proportion of variance of a given outcome variable explained by a factor of interest in an analysis of variance model where it measures the relative homogeneity within groups
[14, 15]. The first and essential step, therefore, is to specify an appropriate analysis of variance (ANOVA) model that best describes the study. The choice of the model is dictated by the specific situation defined by the experimental design and conceptual intent of the study
. Moreover, various forms of ICCs arise depending on the chosen model and the nature of the study
For reasons mentioned above, inference procedures for ρ are closely related to the more general statistical problem of variance components
[14, 18]. It is well known that estimation and hypothesis testing procedures for ICCs are, in general, sensitive to the assumption of normality and are subject to unstable variance
[1, 19]. One, therefore, needs to consider normalizing and variance-stabilizing transformations on the basis of the rate of convergence to normality when constructing confidence intervals for the ICC. One of the well known and most commonly used normalization technique is Fisher’s Z transformation
. Other types of transformations have also been considered for the intraclass correlation coefficient
Another important issue concerning ICCs is bias
[21, 22]. The two most commonly used estimators, maximum likelihood and least square estimators, are known to be negatively biased. Although a Minimum Variance Unbiased (MVU) estimator for the intraclass correlation coefficient under two normal distributions is derived by
, use of this estimator has been hindered because of absence of a closed form. Consequently, the MVU estimator is less widely recognized while the least square and maximum likelihood estimators are well-known. A computationally intensive FORTRAN subroutine is provided by Donoghue and Collins (1990).
The purpose of this paper is, therefore, to provide a bias-corrected estimator for the intraclass correlation coefficient which is much simpler to compute and hence useful in practice. We consider a particular type of ICC in which we consider the estimation problem for ICC resulting from a one-way random effects analysis of variance model. We approximate the bias using a second-order Taylor series expansion and adjust the estimator to reduce the bias.
The paper is organized as follows. We provide a brief background about the one-way random effects model and define the particular ICC of interest in Section “Methods”. In Section “Bias-corrected estimator for the intraclass correlation coefficient”, we propose a technique for approximating the bias resulting from the conventional estimator of ρ and we derive a new bias-corrected estimator for the parameter. We present simulation results in Section “Simulation Study” and provide a brief discussion in Section “Discussion”. Finally an Appendix consisting of some technical results is given at the end of the paper.