Bivariate random effect model using skew‐normal distribution with application to HIV‐RNA

Correlated data arise in a longitudinal studies from epidemiological and clinical research. Random effects models are commonly used to model correlated data. Mostly in the longitudinal data setting we assume that the random effects and within subject errors are normally distributed. However, the normality assumption may not always give robust results, particularly if the data exhibit skewness. In this paper, we develop a Bayesian approach to bivariate mixed model and relax the normality assumption by using a multivariate skew‐normal distribution. Specifically, we compare various potential models and illustrate the procedure using a real data set from HIV study. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  Gregory C. Reinsel,et al.  Estimation and Prediction in a Multivariate Random Effects Generalized Linear Model , 1984 .

[2]  G. Verbeke,et al.  A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population , 1996 .

[3]  A. Azzalini,et al.  The multivariate skew-normal distribution , 1996 .

[4]  R. Royce,et al.  Sexual transmission of HIV. , 1997, The New England journal of medicine.

[5]  L. Kingsley,et al.  High viral load in semen of human immunodeficiency virus type 1-infected men at all stages of disease and its reduction by therapy with protease and nonnucleoside reverse transcriptase inhibitors , 1997, Journal of virology.

[6]  J. Eron,et al.  Effects of reverse transcriptase inhibitor therapy on the HIV-1 viral burden in semen. , 1997, Journal of acquired immune deficiency syndromes and human retrovirology : official publication of the International Retrovirology Association.

[7]  David A. Schoenfeld,et al.  A Random-Effects Model for Multiple Characteristics with Possibly Missing Data , 1997 .

[8]  Y. Matsuyama,et al.  Mixed models for bivariate response repeated measures data using Gibbs sampling. , 1997, Statistics in medicine.

[9]  P. Vernazza,et al.  Quantification of HIV in semen: correlation with antiviral treatment and immune status , 1997, AIDS.

[10]  P. Vernazza,et al.  High levels of human immunodeficiency virus type 1 in blood and semen of seropositive men in sub-Saharan Africa. , 1998, The Journal of infectious diseases.

[11]  P. Vernazza,et al.  Association of CD4 cell depletion and elevated blood and seminal plasma human immunodeficiency virus type 1 (HIV-1) RNA concentrations with genital ulcer disease in HIV-1-infected men in Malawi. , 1998, The Journal of infectious diseases.

[12]  A. Collier,et al.  Association between culturable human immunodeficiency virus type 1 (HIV-1) in semen and HIV-1 RNA levels in semen and blood: evidence for compartmentalization of HIV-1 between semen and blood. , 1998, The Journal of infectious diseases.

[13]  P. Vernazza,et al.  Sexual transmission of HIV: infectiousness and prevention. , 1999, AIDS.

[14]  A. Azzalini,et al.  Statistical applications of the multivariate skew normal distribution , 2009, 0911.2093.

[15]  Myron S. Cohen,et al.  Antiretroviral-Drug Concentrations in Semen: Implications for Sexual Transmission of Human Immunodeficiency Virus Type 1 , 2000, Antimicrobial Agents and Chemotherapy.

[16]  A. Pewsey.  Problems of inference for Azzalini's skewnormal distribution , 2000 .

[17]  D. Dey,et al.  A General Class of Multivariate Skew-Elliptical Distributions , 2001 .

[18]  P. Sen,et al.  Viral burden in genital secretions determines male-to-female sexual transmission of HIV-1: a probabilistic empiric model , 2001, AIDS.

[19]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[20]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[21]  A. Azzalini,et al.  Graphical models for skew-normal variates , 2003 .

[22]  Pranab K Sen,et al.  Estimating correlation by using a general linear mixed model: evaluation of the relationship between the concentration of HIV‐1 RNA in blood and semen , 2003, Statistics in medicine.

[23]  S. Sahu,et al.  A new class of multivariate skew distributions with applications to bayesian regression models , 2003 .

[24]  Bradley P Carlin,et al.  Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages , 2004 .

[25]  A. Brix.  Bayesian Data Analysis, 2nd edn , 2005 .

[26]  M. Genton,et al.  On fundamental skew distributions , 2005 .