A comparison of confidence interval methods for the intraclass correlation coefficient based on the one-way random effects model

Abstract

Abstract Intraclass correlation coefficients are widely used not only in medicine but also in various other fields. This study focuses on the intraclass correlation coefficient based on the one-way random effects model. We review the methods for constructing confidence intervals and compare their performance through simulations. Donner and Wells (Biometrics 42:401–412, 1986) and Ukoumunne (Stat Med 21(24):3757–3774, 2002) conducted simulation studies to compare some methods. However, in this study, we also include methods developed after their studies. These include a method based on the nonparametric bootstrap by Ukoumunne et al. (Stat Med 22(24):3805–3821, 2003), a method based on the restricted maximum likelihood (REML) by Burch (Comput Stat Data Anal 55(2):1018–1028, 2011), and a method based on the beta distribution by Demetrashvili et al. (Stat Methods Med Res 25(5):2359–2376, 2016). Our simulations reveal that under the normality of random effects and errors, the REML-based method performs best overall in terms of coverage probability of confidence intervals, upper and lower error rates, and mean interval width.

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