Liu Mengling, Ying Zhiliang
Division of Biostatistics, School of Medicine, New York University, 650 First Avenue, New York, New York 10016, USA.
Biometrics. 2007 Jun;63(2):363-71. doi: 10.1111/j.1541-0420.2007.00708.x. Epub 2007 Apr 9.
Longitudinal data arise when subjects are followed over a period of time. A commonly encountered complication in the analysis of such data is the variable length of follow-up due to right censorship. This can be further exacerbated by the possible dependency between the censoring time and the longitudinal measurements. This article proposes a combination of a semiparametric transformation model for the censoring time and a linear mixed effects model for the longitudinal measurements. The dependency is handled via latent variables which are naturally incorporated. We show that the likelihood function has an explicit form and develops a two-stage estimation procedure to avoid direct maximization over a high-dimensional parameter space. The resulting estimators are shown to be consistent and asymptotically normal, with a closed form for the variance-covariance matrix that can be used to obtain a plug-in estimator. Finite sample performance of the proposed approach is assessed through extensive simulations. The method is applied to renal disease data.
当对受试者进行一段时间的随访时，就会产生纵向数据。在分析此类数据时，一个常见的复杂情况是由于右删失导致随访时间长度可变。审查时间与纵向测量之间可能存在的相关性会进一步加剧这种情况。本文提出了一种用于审查时间的半参数变换模型和一种用于纵向测量的线性混合效应模型的组合。通过自然纳入的潜在变量来处理相关性。我们表明似然函数具有显式形式，并开发了一种两阶段估计程序，以避免在高维参数空间上直接最大化。结果表明，所得估计量是一致的且渐近正态，其方差协方差矩阵具有封闭形式，可用于获得插件估计量。通过广泛的模拟评估了所提出方法的有限样本性能。该方法应用于肾脏疾病数据。
