Nonlinear mixed-effects modeling: individualization and prediction.

The development of biomathematical models for the prediction of fatigue and performance relies on statistical techniques to analyze experimental data and model simulations. Statistical models of empirical data have adjustable parameters with a priori unknown values. Interindividual variability in estimates of those values requires a form of smoothing. This traditionally consists of averaging observations across subjects, or fitting a model to the data of individual subjects first and subsequently averaging the parameter estimates. However, the standard errors of the parameter estimates are assessed inaccurately by such averaging methods. The reason is that intra- and inter-individual variabilities are intertwined. They can be separated by mixed-effects modeling in which model predictions are not only determined by fixed effects (usually constant parameters or functions of time) but also by random effects, describing the sampling of subject-specific parameter values from probability distributions. By estimating the parameters of the distributions of the random effects, mixed-effects models can describe experimental observations involving multiple subjects properly (i.e., yielding correct estimates of the standard errors) and parsimoniously (i.e., estimating no more parameters than necessary). Using a Bayesian approach, mixed-effects models can be "individualized" as observations are acquired that capture the unique characteristics of the individual at hand. Mixed-effects models, therefore, have unique advantages in research on human neurobehavioral functions, which frequently show large inter-individual differences. To illustrate this we analyzed laboratory neurobehavioral performance data acquired during sleep deprivation, using a nonlinear mixed-effects model. The results serve to demonstrate the usefulness of mixed-effects modeling for data-driven development of individualized predictive models of fatigue and performance.