Heavy-tailed longitudinal regression models for censored data: a robust parametric approach
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Longitudinal HIV-1 RNA viral load measures are often subject to censoring due to upper and lower detection limits depending on the quantification assays. A complication arises when these continuous measures present a heavy-tailed behavior because inference can be seriously affected by the misspecification of their parametric distribution. For such data structures, we propose a robust nonlinear censored regression model based on the scale mixtures of normal distributions. By taking into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. A stochastic approximation of the EM algorithm is developed to obtain the maximum likelihood estimates of the model parameters. The main advantage of this new procedure os to allow estimating the parameters of interest and evaluating the log-likelihood function easily and quickly. Furthermore, the standard errors of the fixed effects and predictions of unobservable values of the response can be obtained as a byproduct. The practical utility of the proposed method is exemplified using both simulated and real data.
KeywordsHIV viral load Longitudinal data Nonlinear models SAEM algorithm Outliers
Mathematics Subject Classification62F10 62J05
We are grateful to two anonymous referees and the associate editor for very useful comments and suggestions, which greatly improved this paper. We also acknowledge the support from FAPESP-Brazil (Grants 2011/22063-9, 2015/05385-3, 2014/ 02938-9 and 2018/05013-7), CNPq-Brazil (Grant 305054/2011-2), Grant FONDECYT 1170258 from the Chilean government and the Ministry of Science and Technology of Taiwan (Grant MOST105-2118-M-005-003-MY2).