Skew-normal/independent linear mixed models for censored responses with applications to HIV viral loads.
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.
Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, 55455, USA. dbandyop@umn.edu
Dipankar
D
Bandyopadhyay
Victor H
VH
Lachos
Luis M
LM
Castro
Dipak K
DK
Dey
D000163:Acquired Immunodeficiency Syndrome / Q000188:drug therapy / Q000821:virology; D001499:Bayes Theorem; D002986:Clinical Trials as Topic; D015497:HIV-1 / Q000187:drug effects / Q000472:pathogenicity / Q000502:physiology*; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008390:Markov Chains; D009010:Monte Carlo Method; D015999:Multivariate Analysis; D016011:Normal Distribution; D019562:Viral Load / Q000187:drug effects