@article {wu_simultaneous_2004,
	title = {Simultaneous inference for longitudinal data with detection limits and covariates measured with errors, with application to AIDS studies},
	journal = {Statistics in Medicine},
	volume = {23},
	number = {11},
	year = {2004},
	month = {jun},
	pages = {1715{\textendash}1731},
	abstract = {In AIDS studies such as HIV viral dynamics, statistical inference is often complicated because the viral load measurements may be subject to left censoring due to a detection limit and time-varying covariates such as CD4 counts may be measured with substantial errors. Mixed-effects models are often used to model the response and the covariate processes in these studies. We propose a unified approach which addresses the censoring and measurement errors simultaneously. We estimate the model parameters by a Monte-Carlo EM algorithm via the Gibbs sampler. A simulation study is conducted to compare the proposed method with the usual two-step method and a naive method. We find that the proposed method produces approximately unbiased estimates with more reliable standard errors. A real data set from an AIDS study is analysed using the proposed method. Copyright {\textcopyright} 2004 John Wiley \& Sons, Ltd.},
	keywords = {EM algorithm, Gibbs sampler, HIV, mixed-effects model},
	issn = {1097-0258},
	doi = {10.1002/sim.1748},
	url = {http://onlinelibrary.wiley.com/doi/10.1002/sim.1748/abstract},
	author = {WU, LANG}
}
@article {wu_missing_2002,
	title = {Missing time-dependent covariates in human immunodeficiency virus dynamic models},
	journal = {Journal of the Royal Statistical Society: Series C (Applied Statistics)},
	volume = {51},
	number = {3},
	year = {2002},
	month = {jul},
	pages = {297{\textendash}318},
	abstract = {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.},
	keywords = {Acquired immune deficiency syndrome, Gibbs sampler, Hierarchical model, Human immunodeficiency virus dynamics, Markov chain Monte Carlo methods, missing data, Multiple imputation, Non-linear mixed effects model},
	issn = {1467-9876},
	doi = {10.1111/1467-9876.00270},
	url = {http://onlinelibrary.wiley.com/doi/10.1111/1467-9876.00270/abstract},
	author = {WU, LANG and Wu, Hulin}
}
