A tolerance interval approach for assessment of agreement in method comparison studies with repeated measurements

This paper generalizes the tolerance interval approach for assessing agreement between two methods of continuous measurement for repeated measurement data—a common scenario in applications. The repeated measurements may be longitudinal or they may be replicates of the same underlying measurement. Our approach is to first model the data using a mixed model and then construct a relevant asymptotic tolerance interval (or band) for the distribution of appropriately defined differences. We present the methodology in the general context of a mixed model that can incorporate covariates, heteroscedasticity and serial correlation in the errors. Simulation for the no-covariate case shows good small-sample performance of the proposed methodology. For the longitudinal data, we also describe an extension for the case when the observed time profiles are modelled nonparametrically through penalized splines. Two real data applications are presented.