%0 Journal Article %1 bandyopadhyay_skew-normal/independent_2012 %A Bandyopadhyay, Dipankar %A Lachos, Victor H. %A Castro, Luis M. %A Dey, Dipak K. %D 2012 %J Biometrical Journal %K Bayesian Detection bias, effects, inference, limit, random skew %N 3 %P 405--425 %R 10.1002/bimj.201000173 %T Skew-Normal/Independent linear mixed models for censored responses with applications to HIV viral loads %U http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000173/abstract %V 54 %X Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral-load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew-normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-t, skew-slash, and skew-contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses that are either left- or right-censored. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte Carlo algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case-deletion influence diagnostics based on the Kullback–Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.

@article{bandyopadhyay_skew-normal/independent_2012, abstract = {Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral-load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew-normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-t, skew-slash, and skew-contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses that are either left- or right-censored. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte Carlo algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case-deletion influence diagnostics based on the Kullback–Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.}, added-at = {2017-01-09T13:57:26.000+0100}, author = {Bandyopadhyay, Dipankar and Lachos, Victor H. and Castro, Luis M. and Dey, Dipak K.}, biburl = {https://www.bibsonomy.org/bibtex/26731b10bc3d159df4745616cae5e33c7/yourwelcome}, copyright = {© 2012 Wiley-VCH Verlag GmbH \& Co. KGaA, Weinheim}, doi = {10.1002/bimj.201000173}, interhash = {0b6380b527c95bed4bc788a34acf2025}, intrahash = {6731b10bc3d159df4745616cae5e33c7}, issn = {1521-4036}, journal = {Biometrical Journal}, keywords = {Bayesian Detection bias, effects, inference, limit, random skew}, language = {en}, number = 3, pages = {405--425}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Skew-{Normal}/{Independent} linear mixed models for censored responses with applications to {HIV} viral loads}, url = {http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000173/abstract}, urldate = {2012-06-23}, volume = 54, year = 2012 }