Journal
BIOMETRICAL JOURNAL
Volume 54, Issue 3, Pages 405-425Publisher
WILEY-BLACKWELL
DOI: 10.1002/bimj.201000173
Keywords
Bayesian inference; Detection limit; HIV viral load; Linear mixed models; Skew-normal; independent distribution
Funding
- US National Institutes of Health (NIH) [P20RR017696, R03DE020114, R03DE021762]
- Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq-Brazil) [2008/201384-6]
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP-Brazil) [2011/17400-6]
- Chilean government [FONDECYT 11100076]
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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 KullbackLeibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.
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