Skew-normal/independent linear mixed models for censored responses with applications to HIV viral loads

Dipankar Bandyopadhyay, Victor H. Lachos, Luis M. Castro, Dipak K. Dey

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)405-425
Number of pages21
JournalBiometrical Journal
Issue number3
StatePublished - May 2012


  • Bayesian inference
  • Detection limit
  • HIV viral load
  • Linear mixed models
  • Skew-normal/independent distribution


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