title: Censored linear regression models for irregularly observed longitudinal data using the multivariate- t distribution.
abstract: In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.
authors.affiliation: 1 Departamento de Estatística, Universidade Estadual de Campinas, Campinas, Brazil.
authors.forename: Aldo M
authors.initials: AM
authors.lastname: Garay
authors.affiliation: 2 Departamento de Estadística, Universidad de Concepción, Concepción, Chile.
authors.forename: Luis M
authors.initials: LM
authors.lastname: Castro
authors.affiliation: 3 Institute of Mathematics, Cracow Technical University, Cracow, Poland.
authors.forename: Jacek
authors.initials: J
authors.lastname: Leskow
authors.affiliation: 1 Departamento de Estatística, Universidade Estadual de Campinas, Campinas, Brazil.
authors.forename: Victor H
authors.initials: VH
authors.lastname: Lachos
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000821:virology; D000465:Algorithms; D056808:Biostatistics / Q000379:methods; D003198:Computer Simulation; D015497:HIV-1; D006801:Humans; D016013:Likelihood Functions; D057230:Limit of Detection; D016014:Linear Models; D008137:Longitudinal Studies; D015999:Multivariate Analysis; D012367:RNA, Viral / Q000097:blood; D019562:Viral Load / Q000706:statistics & numerical data
chemical_list: D012367:RNA, Viral
keywords: HIV viral load; censored data; expectation conditional maximization algorithm; longitudinal data; outliers