Heavy-tailed longitudinal regression models for censored data: a robust parametric approach

Abstract

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.

Extending multivariate Student's‐t$$ t $$ semiparametric mixed models for longitudinal data with censored responses and heavy tails

“…However, our results showed that even when the percentage of censoring is high (20%), the obtained estimates do not present a strong bias or high variability. Finally, we note that the asymptotic confidence interval obtained using the standard error via the expected information matrix generates more conservative confidence intervals even when the sample size increases (see also, Matos et al, 41 for a similar situation related to the confidence intervals).…”

Flexible modeling of multiple nonlinear longitudinal trajectories with censored and non-ignorable missing outcomes

“…For example, Hughes 3 and Vaida et al 4 proposed the linear and nonlinear mixed-effects approaches for single-outcome longitudinal data with censored observations, referred to as the LMEC and NLMEC models, respectively. Further extensions of LMEC and NLMEC models to more complicated configurations can be found in Garay et al, 5 Lin and Wang, 6 Matos et al [7][8][9] and Wang et al 10 Methodological developments of novel methods for handling missing data in the literature are abundant, see the monograph by Little and Rubin 11 for a comprehensive overview of the state of the art. According to Rubin's 12 taxonomy, a mechanism is termed missing completely at random (MCAR) when the missingness is unrelated to both observed and missing data, and is referred to as missing at random (MAR) when the missingness depends only on the observed information.…”

Multivariate linear mixed models with censored and nonignorable missing outcomes, with application to AIDS studies

“…When censoring effects are ignored in the estimation, this may produce a loss of information that could lead to highly distorted inferences. We refer interested readers to Hughes (1999), Vaida et al (2007), Vaida and Liu (2009), Lachos et al (2011), Matos et al (2013), Bandyopadhyay et al (2015), Lin and Wang (2017), Wang et al (2018), Lachos et al (2019), Matos et al (2019), and Lin and Wang (2020) for some general introduction and numerical illustrations.…”

“…(2019), Matos et al. (2019), and Lin and Wang (2020) for some general introduction and numerical illustrations.…”