Lin Tsung-I, Wang Wan-Lun
Institute of Statistics, National Chung Hsing University, Taichung, Taiwan.
Department of Public Health, China Medical University, Taichung, Taiwan.
Stat Methods Med Res. 2020 May;29(5):1288-1304. doi: 10.1177/0962280219857103. Epub 2019 Jun 26.
Multivariate longitudinal data arisen in medical studies often exhibit complex features such as censored responses, intermittent missing values, and atypical or outlying observations. The multivariate- linear mixed model (MtLMM) has been recognized as a powerful tool for robust modeling of multivariate longitudinal data in the presence of potential outliers or fat-tailed noises. This paper presents a generalization of MtLMM, called the MtLMM-CM, to properly adjust for censorship due to detection limits of the assay and missingness embodied within multiple outcome variables recorded at irregular occasions. An expectation conditional maximization either (ECME) algorithm is developed to compute parameter estimates using the maximum likelihood (ML) approach. The asymptotic standard errors of the ML estimators of fixed effects are obtained by inverting the empirical information matrix according to Louis' method. The techniques for the estimation of random effects and imputation of missing responses are also investigated. The proposed methodology is illustrated on two real-world examples from HIV-AIDS studies and a simulation study under a variety of scenarios.
医学研究中出现的多变量纵向数据通常呈现出复杂的特征，如删失响应、间歇性缺失值以及非典型或异常观测值。多元线性混合模型（MtLMM）已被公认为是在存在潜在异常值或厚尾噪声的情况下对多变量纵向数据进行稳健建模的有力工具。本文提出了MtLMM的一种推广形式，称为MtLMM-CM，以适当调整由于检测限导致的删失以及在不规则时间记录的多个结果变量中所包含的缺失情况。开发了一种期望条件最大化（ECME）算法，以使用最大似然（ML）方法计算参数估计值。固定效应的ML估计量的渐近标准误差是根据路易斯方法通过对经验信息矩阵求逆得到的。还研究了随机效应估计和缺失响应插补的技术。在来自艾滋病毒-艾滋病研究的两个实际例子以及各种场景下的模拟研究中展示了所提出的方法。
