@article {wang_multiple_2011,
	title = {Multiple Imputation Methods for Multivariate One-Sided Tests with Missing Data},
	journal = {Biometrics},
	volume = {67},
	number = {4},
	year = {2011},
	month = {dec},
	pages = {1452{\textendash}1460},
	abstract = {Summary Multivariate one-sided hypotheses testing problems arise frequently in practice. Various tests have been developed. In practice, there are often missing values in multivariate data. In this case, standard testing procedures based on complete data may not be applicable or may perform poorly if the missing data are discarded. In this article, we propose several multiple imputation methods for multivariate one-sided testing problem with missing data. Some theoretical results are presented. The proposed methods are evaluated using simulations. A real data example is presented to illustrate the methods.},
	keywords = {Constrained inference, Multiple imputation, Order-restricted inference, Wald-type tests},
	issn = {1541-0420},
	doi = {10.1111/j.1541-0420.2011.01597.x},
	url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2011.01597.x/abstract},
	author = {Wang, Tao and WU, LANG}
}
@article {wu_identification_2002,
	title = {Identification of significant host factors for HIV dynamics modelled by non-linear mixed-effects models},
	journal = {Statistics in Medicine},
	volume = {21},
	number = {5},
	year = {2002},
	month = {mar},
	pages = {753{\textendash}771},
	abstract = {Non-linear mixed-effects models are powerful tools for modelling HIV viral dynamics. In AIDS clinical trials, the viral load measurements for each subject are often sparse. In such cases, linearization procedures are usually used for inferences. Under such linearization procedures, however, standard covariate selection methods based on the approximate likelihood, such as the likelihood ratio test, may not be reliable. In order to identify significant host factors for HIV dynamics, in this paper we consider two alternative approaches for covariate selection: one is based on individual non-linear least square estimates and the other is based on individual empirical Bayes estimates. Our simulation study shows that, if the within-individual data are sparse and the between-individual variation is large, the two alternative covariate selection methods are more reliable than the likelihood ratio test, and the more powerful method based on individual empirical Bayes estimates is especially preferable. We also consider the missing data in covariates. The commonly used missing data methods may lead to misleading results. We recommend a multiple imputation method to handle missing covariates. A real data set from an AIDS clinical trial is analysed based on various covariate selection methods and missing data methods. Copyright {\textcopyright} 2002 John Wiley \& Sons, Ltd.},
	keywords = {AIDS, HIV, HIV dynamics, missing data, mixed-effects models, Multiple imputation},
	issn = {1097-0258},
	doi = {10.1002/sim.1015},
	url = {http://onlinelibrary.wiley.com/doi/10.1002/sim.1015/abstract},
	author = {Wu, Hulin and 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}
}
