Liu Hao, Qin Jing
Division of Biostatistics, Dan L. Duncan Cancer Center, Baylor College of Medicine, Houston, Texas 77030, U.S.A.
Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases National Institutes of Health, Bethesda, Maryland 20892, U.S.A.
Biometrics. 2018 Mar;74(1):68-76. doi: 10.1111/biom.12709. Epub 2017 Apr 24.
Multivariate current-status data are frequently encountered in biomedical and public health studies. Semiparametric regression models have been extensively studied for univariate current-status data, but most existing estimation procedures are computationally intensive, involving either penalization or smoothing techniques. It becomes more challenging for the analysis of multivariate current-status data. In this article, we study the maximum likelihood estimations for univariate and bivariate current-status data under the semiparametric probit regression models. We present a simple computational procedure combining the expectation-maximization algorithm with the pool-adjacent-violators algorithm for solving the monotone constraint on the baseline function. Asymptotic properties of the maximum likelihood estimators are investigated, including the calculation of the explicit information bound for univariate current-status data, as well as the asymptotic consistency and convergence rate for bivariate current-status data. Extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes. We demonstrate the estimation procedure with two real data examples in the areas of diabetic and HIV research.
多变量当前状态数据在生物医学和公共卫生研究中经常遇到。半参数回归模型已针对单变量当前状态数据进行了广泛研究，但大多数现有的估计程序计算量很大，涉及惩罚或平滑技术。对于多变量当前状态数据的分析，这变得更具挑战性。在本文中，我们研究了半参数概率单位回归模型下单变量和双变量当前状态数据的最大似然估计。我们提出了一种简单的计算程序，将期望最大化算法与相邻违规者合并算法相结合，以解决基线函数上的单调约束。研究了最大似然估计量的渐近性质，包括单变量当前状态数据的显式信息界的计算，以及双变量当前状态数据的渐近一致性和收敛速度。大量的模拟研究表明，所提出的计算程序在小样本或中等样本量下表现良好。我们用糖尿病和艾滋病研究领域的两个真实数据示例演示了估计程序。
