A novel quantification of information for longitudinal data analyzed by mixed-effects modeling

Nonlinear mixed-effects (NLME) modeling is one of the most powerful tools for analyzing longitudinal data especially under the sparse sampling design. The determinant of the Fisher information matrix is a commonly used global metric of the information that can be provided by the data under a given model. However, in clinical studies, it is also important to measure how much information the data provide for a certain parameter of interest under the assumed model, for example, the clearance in population pharmacokinetic models. This paper proposes a new, easy-to-interpret information metric, the "relative information" (RI), which is designed for specific parameters of a model and takes a value between 0% and 100%. We establish the relationship between interindividual variability for a specific parameter and the variance of the associated parameter estimator, demonstrating that, under a "perfect" experiment (eg, infinite samples or/and minimum experimental error), the RI and the variance of the model parameter estimator converge, respectively, to 100% and the ratio of the interindividual variability for that parameter and the number of subjects. Extensive simulation experiments and analyses of three real datasets show that our proposed RI metric can accurately characterize the information for parameters of interest for NLME models. The new information metric can be readily used to facilitate study designs and model diagnosis.