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Censored linear regression models for irregularly observed longitudinal data using the multivariate-t distribution

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Author(s):
Garay, Aldo M. ; Castro, Luis M. ; Leskow, Jacek ; Lachos, Victor H.
Total Authors: 4
Document type: Journal article
Source: STATISTICAL METHODS IN MEDICAL RESEARCH; v. 26, n. 2, p. 25-pg., 2017-04-01.
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. (AU)

FAPESP's process: 13/21468-0 - Measurement error-in-variables models for censored data using scale mixtures of skew-normal distributions
Grantee:Aldo William Medina Garay
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 14/02938-9 - Estimation and diagnostics for censored mixed effects models using scale mixtures of skew-normal distributions
Grantee:Víctor Hugo Lachos Dávila
Support Opportunities: Regular Research Grants
FAPESP's process: 14/11831-3 - Modern computational methods in stochastic modeling
Grantee:Víctor Hugo Lachos Dávila
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 12/19445-0 - Flexible modeling of complex longitudinal data using skew-elliptical distributions
Grantee:Víctor Hugo Lachos Dávila
Support Opportunities: Research Grants - Visiting Researcher Grant - International