Cross-Validation for Nonlinear Mixed Effects Models

Cross-validation is frequently used for model selection in a variety of applications. However, it is difficult to apply cross-validation to mixed effects models (including nonlinear mixed effects models or NLME models) due to the fact that cross-validation requires "out-of-sample" predictions of the outcome variable, which cannot be easily calculated when random effects are present. We describe two novel variants of cross-validation that can be applied to nonlinear mixed effects models. One variant, where out-of-sample predictions are based on post hoc estimates of the random effects, can be used to select the overall structural model. Another variant, where cross-validation seeks to minimize the estimated random effects rather than the estimated residuals, can be used to select covariates to include in the model. We show that these methods produce accurate results in a variety of simulated data sets and apply them to two publicly available population pharmacokinetic data sets.