Missing time-dependent covariates in human immunodeficiency virus dynamic models

Summary. The study of human immunodeficiency virus dynamics is one of the most important areas in research into acquired immune deficiency syndrome in recent years. Non-linear mixed effects models have been proposed for modelling viral dynamic processes. A challenging problem in the modelling is to identify repeatedly measured (time-dependent), but possibly missing, immunologic or virologic markers (covariates) for viral dynamic parameters. For missing time-dependent covariates in non-linear mixed effects models, the commonly used complete-case, mean imputation and last value carried forward methods may give misleading results. We propose a three-step hierarchical multiple-imputation method, implemented by Gibbs sampling, which imputes the missing data at the individual level but can pool information across individuals. We compare various methods by Monte Carlo simulations and find that the multiple-imputation method proposed performs the best in terms of bias and mean-squared errors in the estimates of covariate coefficients. By applying the favoured multiple-imputation method to clinical data, we conclude that there is a negative correlation between the viral decay rate (a virological response parameter) and CD4 or CD8 cell counts during the treatment; this is counter-intuitive, but biologically interpretable on the basis of findings from other clinical studies. These results may have an important influence on decisions about treatment for acquired immune deficiency syndrome patients.