Matos Larissa A, Bandyopadhyay Dipankar, Castro Luis M, Lachos Victor H
Departamento de Estatística, IMECC-UNICAMP, Campinas, São Paulo, Brazil.
Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455.
J Multivar Anal. 2015 Oct 1;141:104-117. doi: 10.1016/j.jmva.2015.06.014.
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 analyse 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 et al. (2013b) recently proposed an exact EM-type algorithm for LMEC/NLMEC models using a multivariate Student's- 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- 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.
在关于HIV RNA动态变化的生物医学研究中，病毒载量产生了重复测量值，这些测量值常常受到检测上限和下限的影响，因此这些响应数据要么是左删失的，要么是右删失的。线性和非线性混合效应删失（LMEC/NLMEC）模型通常用于分析这些纵向数据，并对随机效应和残差误差做出正态性假设。然而，当这些潜在的正态性假设存在疑问时，尤其是存在异常值和厚尾分布时，由此得出的推断可能并不稳健。受此启发，马托斯等人（2013b）最近提出了一种用于LMEC/NLMEC模型的精确期望最大化（EM）型算法，该算法使用多元学生分布，在期望步骤有封闭形式的表达式。在本文中，我们基于完整数据对数似然的条件期望，利用多元学生密度为LMEC/NLMEC模型开发影响诊断方法。这部分消除了与库克（1977年，1986年）用于删失混合效应模型的方法相关的复杂性。通过对一个纵向HIV数据集的应用来说明这种新方法。此外，一项模拟研究探讨了所提出的测量方法在不同扰动和删失方案下检测重尾删失数据可能的影响观测值时的准确性。
