Statistical Methods for Measuring Agreement Involving Longitudinal Data

Recent research concerning measurements of agreement between different methods or different raters have received wide attention. The concordance correlation coefficient (CCC) has been used to assess agreement between two raters or two measuring methods while the measurements are taken on the same continuous scale. However, the circumstances of repeated measurements may arise, e.g. longitudinal studies in clinical trials or bioassay data with sub-samples. The random variables are not independent nor identically distributed in that kind of situation. To appropriately account for the covariance between measurements, we have fitted three-level linear mixed-effect models with random intercepts at two levels. The model parameters are estimated using an expectation-maximization [E-M] like approach by iterating between the Empirical Bayes [EB] estimates of the random effects and maximum marginal likelihood estimates of the fixed and covariance parameters. For comparing agreement between two raters, we utilize two-level and three-level models to estimate CCC and observe that three-level models fit better for the dataset we collected in GAIT study. In order to handle missing data, we did the analysis with missing values by using mixed-effects model, model imputation, multiple imputation and pattern mixed model. We have achieved at consistent results among all the methods handling missingness in the dataset. The proposed model also gives us the opportunities to evaluate agreement after adjusting for the other covariates. We also use an approach to get the generalized confidence interval of CCC for further statistical inference. Our approach represents a first attempt in evaluating CCC for data with multiple level variations.