Influence assessment in censored mixed-effects models using the multivariate Student's-t distribution

Larissa A. Matos, Dipankar Bandyopadhyay, Luis M. Castro, Victor H. Lachos

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6 Scopus citations


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, Matos etal. (2013) 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 Cook (1977, 1986) 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.

Original languageEnglish (US)
Pages (from-to)104-117
Number of pages14
JournalJournal of Multivariate Analysis
StatePublished - Oct 1 2015

Bibliographical note

Funding Information:
We thank the Editor, the Associate Editor and two referees whose constructive comments led to an improved presentation. Bandyopadhyay acknowledges support from grants R03DE021762 and R03DE023372 from the US National Institutes of Health . V.H. Lachos acknowledges support from CNPq-Brazil (Grant 305054/2011-2 ) and from FAPESP-Brazil (Grant 2014/02938-9 ). L.M. Castro acknowledges funding support by Grant FONDECYT 1130233 from the Chilean government and Grant 2012/19445-0 from FAPESP-Brazil . L.A. Matos acknowledges support from FAPESP-Brazil (Grant 2011/22063-9 ).

Publisher Copyright:
© 2015 Elsevier Inc.


  • Case-deletion diagnostics
  • Censored data
  • ECM algorithm
  • Linear mixed-effects model
  • Multivariate Student's-t distribution
  • Non-linear mixed-effects model


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