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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.

New model-averaged estimators of concordance correlation coefficients: simulation and application to longitudinal overdispersed Poisson data