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Statistica Sinica 23 (2013),




Larissa A. Matos$^{1}$, Marcos O. Prates$^{2}$, Ming-Hui Chen$^{3}$ and Victor H. Lachos$^{1}$

$^{1}$Universidade Estadual de Campinas, $^{2}$Universidade Federal de Minas Gerais
and $^{3}$University of Connecticut

Abstract: 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
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).

Key words and phrases: Censored data, ECM algorithm, HIV viral load, influential observations, mixed-effects models, outliers.

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