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

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 (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, the skew-t, skew-slash and the skew-contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses which are either left- or right-censored. For our analysis, we adopt a Bayesian framework and develop a MCMC 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 a HIV case study involving analysis of longitudinal viral loads.

Robust Joint Non-linear Mixed-Effects Models and Diagnostics for Censored HIV Viral Loads with CD4 Measurement Error

“…. , n with specifications for the random terms as in (5), we have, marginally (Bandyopadhyay et al 2012),…”

“…, b qi ) is the vector of random effects (q ≤ s). Following Bandyopadhyay et al (2012), we assume that for i = 1, . .…”

“…Furthermore, the censoring was ignored via ad-hoc imputation. Recently, Bandyopadhyay et al (2012) proposed a skew-normal independent (SNI) LME model for censored responses (SNI-LMEC), accommodating both skewness and thick tails with proper considerations for censoring. We set forward to explore the potential of the SNI class of densities, and propose a Bayesian parametric framework for the NLMEC model (henceforth, SNI-NLMEC model) that insulates parameter estimation from the aforementioned complexities.…”

Maximum-likelihood estimation and influence analysis in multivariate skew-normal reproductive dispersion mixed models for longitudinal data

“…[4] All the above mentioned models assume that responses follow the normal distribution or exponential family distribution. But in some applications such as the AIDS clinical study, [5] responses may not follow an exponential family distribution but a non-exponential family distribution such as Gumbel distribution or simplex distribution [6] or Birnbaum-Saunders distribution. [7] To this end, we here consider a new mixed model with responses from a reproductive dispersion model, [6] which includes normal, binomial, exponential, Poisson, Gamma, von Mises, simplex and Gumbel distributions as its special cases.…”

Asymptotic expansions for moments of skew-normal extremes

“…Its applications are too many to list. Some applications of the skew normal distribution that have appeared in the past year alone include: the distribution of threshold voltage degradation in nanoscale transistors by using reaction-diffusion and percolation theory (Islam and Alam, 2011); population structure of Schima superba in Qingliangfeng National Nature Reserve (Liu et al, 2011); rain height models to predict fading due to wet snow on terrestrial links (Paulson and Al-Mreri, 2011); modeling of seasonal rainfall in Africa (Siebert and Ward, 2011); modeling of HIV viral loads (Bandyopadhyay et al, 2012); multisite flooding hazard assessment in the Upper Mississippi River (Ghizzoni et al, 2012); modeling of diabetic macular Edema data (Mansourian et al, 2012); risks of macroeconomic forecasts (Pinheiro and Esteves, 2012); modeling of current account balance data (Saez et al, 2012); automated neonatal EEG classification (Temko et al, 2012).…”