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Flexible longitudinal linear mixed models for multiple censored responses data
Author(s) -
Lachos Victor H.,
A. Matos Larissa,
Castro Luis M.,
Chen MingHui
Publication year - 2018
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8017
Subject(s) - autocorrelation , mathematics , statistics , context (archaeology) , generalization , unobservable , series (stratigraphy) , data set , exponential function , generalized linear mixed model , mixed model , random effects model , computer science , econometrics , medicine , mathematical analysis , paleontology , meta analysis , biology
In biomedical studies and clinical trials, repeated measures are often subject to some upper and/or lower limits of detection. Hence, the responses are either left or right censored. A complication arises when more than one series of responses is repeatedly collected on each subject at irregular intervals over a period of time and the data exhibit tails heavier than the normal distribution. The multivariate censored linear mixed effect (MLMEC) model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this context, we develop a robust generalization of the MLMEC based on the scale mixtures of normal distributions. To take into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. For this complex longitudinal structure, we propose an exact estimation procedure to obtain the maximum‐likelihood estimates of the fixed effects and variance components using a stochastic approximation of the EM algorithm. This approach allows us to estimate the parameters of interest easily and quickly as well as to obtain the standard errors of the fixed effects, the predictions of unobservable values of the responses, and the log‐likelihood function as a byproduct. The proposed method is applied to analyze a set of AIDS data and is examined via a simulation study.