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Influence assessment in censored mixed-effects models using the multivariate Student’s-\(t\) distribution. (English) Zbl 1331.62429

Summary: In biomedical studies on HIV RNA dynamics, viral loads generate repeated measures that are often subjected to upper and lower detection limits, and hence these responses are either left- or right-censored. Linear and non-linear mixed-effects censored (LMEC/NLMEC) models are routinely used to analyze these longitudinal data, with normality assumptions for the random effects and residual errors. However, the derived inference may not be robust when these underlying normality assumptions are questionable, especially the presence of outliers and thick-tails. Motivated by this, L. A. Matos et al. [Stat. Sin. 23, No. 3, 1323–1345 (2013; Zbl 06202709)] recently proposed an exact EM-type algorithm for LMEC/NLMEC models using a multivariate Student’s-\(t\) distribution, with closed-form expressions at the E-step. In this paper, we develop influence diagnostics for LMEC/NLMEC models using the multivariate Student’s-\(t\) density, based on the conditional expectation of the complete data log-likelihood. This partially eliminates the complexity associated with the approach of R. D. Cook [Technometrics 19, 15–18 (1977; Zbl 0371.62096); J. R. Stat. Soc., Ser. B 48, 133–169 (1986; Zbl 0608.62041)] for censored mixed-effects models. The new methodology is illustrated via an application to a longitudinal HIV dataset. In addition, a simulation study explores the accuracy of the proposed measures in detecting possible influential observations for heavy-tailed censored data under different perturbation and censoring schemes.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J20 Diagnostics, and linear inference and regression
62J05 Linear regression; mixed models
62F15 Bayesian inference
62N01 Censored data models

Software:

lmec
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References:

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