Semiparametric modeling and analysis of longitudinal method comparison data.

Studies comparing two or more methods of measuring a continuous variable are routinely conducted in biomedical disciplines with the primary goal of measuring agreement between the methods. Often, the data are collected by following a cohort of subjects over a period of time. This gives rise to longitudinal method comparison data where there is one observation trajectory for each method on every subject. It is not required that observations from all methods be available at each observation time. The multiple trajectories on the same subjects are dependent. We propose modeling the trajectories nonparametrically through penalized regression splines within the framework of mixed-effects models. The model also uses random effects of subjects and their interactions to capture dependence in observations from the same subjects. It additionally allows the within-subject errors of each method to be correlated. It is fit using the method of maximum likelihood. Agreement between the methods is evaluated by performing inference on measures of agreement, such as concordance correlation coefficient and total deviation index, which are functions of parameters of the assumed model. Simulations indicate that the proposed methodology performs reasonably well for 30 or more subjects. Its application is illustrated by analyzing a dataset of percentage body fat measurements.