Exact and approximate inferences for nonlinear mixed-effects models with missing covariates

Nonlinear mixed-effects (NLME) models are popular in many longitudinal studies, including human immunodeficiency virus (HIV) viral dynamics, pharmacokinetic analyses, and studies of growth and decay. In practice, covariates in these studies often contain missing data, and so standard complete-data methods are not directly applicable. In this article we propose Monte Carlo parameter-expanded (PX)-EM algorithms for exact and approximate likelihood inferences for NLME models with missing covariates when the missing-data mechanism is ignorable. We allow arbitrary missing-data patterns and allow the covariates to be categorical, continuous, and mixed. The PX-EM algorithm maintains the simplicity and stability of the standard EM algorithm and may converge much faster than EM. The approximate method is computationally more efficient and may be preferable to the exact method when the exact method exhibits convergence problems, such as slow convergence or nonconvergence. It becomes an exact method for linear mixed-effects models and certain NLME models with missing covariates. We also discuss several sampling methods and convergence of the Monte Carlo (PX) EM algorithms. We illustrate the methods using a real data example from the study of HIV viral dynamics and compare the methods via a simulation study.