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The concordance correlation coefficient (CCC) is a common tool to assess agreement among multiple observers for continuous and discrete responses. However, previous results in the statistical literature have shown that the CCC estimators may suffer from a bias problem under a misspecified model for normal data. In order to avoid fitting data with a misspecified model, thus yielding biased CCC estimates for longitudinal overdispersed Poisson data, this research proposes new model-averaged estimators of CCC by combining the estimators of the variance components (VC) approach with model selection via corrected conditional Akaike information criterion (CAICC) and corrected conditional Bayesian information criterion (CBICC) measures under extended overdispersed three-way Poisson mixed-effects models. In simulation studies, the performance of the proposed model-averaged estimators is compared with the VC estimators with and without model selection via CAICC and CBICC and other existing model-averaged estimators for longitudinal Poisson and overdispersed Poisson data sets. An application of corticospinal diffusion tensor tractography study is presented for illustration. It can be concluded that the proposed model-averaged approach is a reliable procedure yielding small mean square errors and nominal 95% coverage rates. Therefore, the new model-averaged estimator is more robust to model misspecification than other competitors. [ABSTRACT FROM AUTHOR]

For longitudinal overdispersed Poisson data sets, estimators of the intra-, inter-, and total concordance correlation coefficient through variance components have been proposed. However, biased estimators of quadratic forms are used in concordance correlation coefficient estimation. In addition, the generalized estimating equations approach has been used in estimating agreement for longitudinal normal data and not for longitudinal overdispersed Poisson data. Therefore, this paper proposes a modified variance component approach to develop the unbiased estimators of the concordance correlation coefficient for longitudinal overdispersed Poisson data. Further, the indices of intra-, inter-, and total agreement through generalized estimating equations are also developed considering the correlation structure of longitudinal count repeated measurements. Simulation studies are conducted to compare the performance of the modified variance component and generalized estimating equation approaches for longitudinal Poisson and overdispersed Poisson data sets. An application of corticospinal diffusion tensor tractography study is used for illustration. In conclusion, the modified variance component approach performs outstandingly well with small mean square errors and nominal 95% coverage rates. The generalized estimating equation approach provides in model assumption flexibility of correlation structures for repeated measurements to produce satisfactory concordance correlation coefficient estimation results. [ABSTRACT FROM AUTHOR]