Missing and mismeasured covariates in nonlinear mixed effects models

The nonlinear mixed effects model is a standard framework for repeated measurement data in pharmacokinetics, disease dynamics, and other areas. A common objective is to elucidate associations among individual-specific model parameters and individual-level covariates; however, covariates may be measured with error, or may be missing for some individuals. We consider methods for handling mismeasured and missing covariates for the nonlinear mixed effects model.;For covariates with additive measurement error, we show substitution of mismeasured covariates for true covariates in popular inferential methods may lead to biased estimators both for fixed effects and random effects covariance parameters, while regression calibration methods may eliminate bias in fixed effects but fail to correct that in covariance parameters. We develop methods for taking account of measurement error that correct this bias and may be implemented with standard software and demonstrate their utility via simulation and application to data from a study of HIV dynamics.;For missing covariates in nonlinear mixed effects models, we develop likelihood and semiparametric weighted estimating equations methods for improving efficiency from complete case analysis, under missing completely at random and missing at random assumptions and compare the efficiency of those methods. Small sample simulation results fail to support that the likelihood method implemented with standard software and the semiparametric weighted estimating equation approach may provide estimators for fixed effects that are more efficient estimators than complete case analysis for nonlinear mixed effects models. However, we show theoretically that increases in efficiency are possible, and demonstrate that the semiparametric weighted estimating equation approach may lead to estimators that are more efficient over complete case analysis for simple linear models.