Likelihood-based inference for mixed-effects models with censored response using the multivariate-t distribution. Mixed-effects models are commonly used to fit longitudinal or repeated measures data. A complication arises when the response is censored, for example, due to limits of quantification of the assay used. Although normal distributions are commonly assumed for random effects and residual errors, such assumptions make inferences vulnerable to outliers. The sensitivity to outliers and the need for heavy tailed distributions for random effects and residual errors motivate us to develop a likelihood-based inference for linear and nonlinear mixed effects models with censored response (NLMEC/LMEC) based on the multivariate Student-t distribution. An ECM algorithm is developed for computing the maximum likelihood estimates for NLMEC/LMEC with the standard errors of the fixed effects and the exact likelihood value as a by-product. The algorithm uses closed-form expressions at the E-step, that rely on formulas for the mean and variance of a truncated multivariate-t distribution. The proposed algorithm is implemented in the R package tlmec. It is applied to analyze longitudinal HIV viral load data in two recent AIDS studies. In addition, a simulation study is conducted to examine the performance of the proposed method and to compare it with the approach of Vaida and Liu (2009).

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Lachos, Víctor H.; Cabral, Celso R. B.; Prates, Marcos O.; Dey, Dipak K.: Flexible regression modeling for censored data based on mixtures of Student-(t) distributions (2019)
  2. Matos, Larissa A.; Castro, Luis M.; Cabral, Celso R. B.; Lachos, Víctor H.: Multivariate measurement error models based on Student-(t) distribution under censored responses (2018)
  3. Lachos, Víctor H.; Moreno, Edgar J. López; Chen, Kun; Cabral, Celso Rômulo Barbosa: Finite mixture modeling of censored data using the multivariate Student-(t) distribution (2017)
  4. Matos, Larissa A.; Castro, Luis M.; Lachos, Víctor H.: Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads (2016)
  5. Tian, Yuzhu; Li, Er’qian; Tian, Maozai: Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates (2016)
  6. Yuan, Haijing; Yang, Fengkai: A non-iterative Bayesian sampling algorithm for censored Student-(t) linear regression models (2016)
  7. Castro, Luis Mauricio; Costa, Denise Reis; Prates, Marcos Oliveira; Lachos, Victor Hugo: Likelihood-based inference for Tobit confirmatory factor analysis using the multivariate Student-(t) distribution (2015)
  8. Rocha, Gustavo H. M. A.; Arellano-Valle, Reinaldo B.; Loschi, Rosangela H.: Maximum likelihood methods in a robust censored errors-in-variables model (2015)
  9. Costa, D. R.; Lachos, V. H.; Bazan, J. L.; Azevedo, C. L. N.: Estimation methods for multivariate tobit confirmatory factor analysis (2014)
  10. Prates, Marcos O.; Costa, Denise R.; Lachos, Victor H.: Generalized linear mixed models for correlated binary data with (t)-link (2014)
  11. Matos, Larissa A.; Prates, Marcos O.; Chen, Ming-Hui; Lachos, Victor H.: Likelihood-based inference for mixed-effects models with censored response using the multivariate-(t) distribution (2013)