Jacqmin-Gadda H, Thiébaut R, Chêne G, Commenges D
Institut National de la Santé et de la Recherche Médicale U330, 146 rue Léo Saignat, 33076 Bordeaux cedex, France.
Biostatistics. 2000 Dec;1(4):355-68. doi: 10.1093/biostatistics/1.4.355.
The classical model for the analysis of progression of markers in HIV-infected patients is the mixed effects linear model. However, longitudinal studies of viral load are complicated by left censoring of the measures due to a lower quantification limit. We propose a full likelihood approach to estimate parameters from the linear mixed effects model for left-censored Gaussian data. For each subject, the contribution to the likelihood is the product of the density for the vector of the completely observed outcome and of the conditional distribution function of the vector of the censored outcome, given the observed outcomes. Values of the distribution function were computed by numerical integration. The maximization is performed by a combination of the Simplex algorithm and the Marquardt algorithm. Subject-specific deviations and random effects are estimated by modified empirical Bayes replacing censored measures by their conditional expectations given the data. A simulation study showed that the proposed estimators are less biased than those obtained by imputing the quantification limit to censored data. Moreover, for models with complex covariance structures, they are less biased than Monte Carlo expectation maximization (MCEM) estimators developed by Hughes (1999) Mixed effects models with censored data with application to HIV RNA Levels. Biometrics 55, 625-629. The method was then applied to the data of the ALBI-ANRS 070 clinical trial for which HIV-1 RNA levels were measured with an ultrasensitive assay (quantification limit 50 copies/ml). Using the proposed method, estimates obtained with data artificially censored at 500 copies/ml were close to those obtained with the real data set.
用于分析HIV感染患者标志物进展情况的经典模型是混合效应线性模型。然而，由于存在较低的定量限，病毒载量的纵向研究因测量值的左删失而变得复杂。我们提出一种全似然方法，用于从左删失高斯数据的线性混合效应模型中估计参数。对于每个受试者，似然贡献是完全观测结果向量的密度与删失结果向量的条件分布函数（给定观测结果）的乘积。分布函数的值通过数值积分计算。最大化通过单纯形算法和马夸特算法相结合来执行。通过修正的经验贝叶斯方法估计个体特异性偏差和随机效应，用给定数据下的条件期望替换删失测量值。一项模拟研究表明，所提出的估计量比通过将定量限代入删失数据获得的估计量偏差更小。此外，对于具有复杂协方差结构的模型，它们比休斯（1999年）开发的蒙特卡罗期望最大化（MCEM）估计量偏差更小。《带有删失数据的混合效应模型及其在HIV RNA水平中的应用》（《生物统计学》55卷，625 - 629页）。该方法随后应用于ALBI - ANRS 070临床试验的数据，该试验使用超灵敏检测法（定量限50拷贝/毫升）测量HIV - 1 RNA水平。使用所提出的方法，在人为删失数据设定为500拷贝/毫升时获得的估计值与使用真实数据集获得的估计值相近。
