In an attempt to provide a statistical tool for disease screening and prediction, we propose a semiparametric approach to analysis of the Cox proportional hazards cure model in situations where the observations on the event time are subject to right censoring and some covariates are missing not at random. To facilitate the methodological development, we begin with semiparametric maximum likelihood estimation (SPMLE) assuming that the (conditional) distribution of the missing covariates is known. A variant of the EM algorithm is used to compute the estimator. We then adapt the SPMLE to a more practical situation where the distribution is unknown and there is a consistent estimator based on available information. We establish the consistency and weak convergence of the resulting pseudo‐SPMLE, and identify a suitable variance estimator. The application of our inference procedure to disease screening and prediction is illustrated via empirical studies. The proposed approach is used to analyze the tuberculosis screening study data that motivated this research. Its finite‐sample performance is examined by simulation.

中文翻译：

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Cox治愈模型中的估计值（并非随机丢失协变量），适用于疾病筛查/预测

为了提供一种用于疾病筛查和预测的统计工具，我们提出了一种半参数方法，用于分析事件时间的观察值受到正确审查且某些协变量缺失并非随机的情况下的Cox比例风险治愈模型分析。为了促进方法学的发展，我们从半参数最大似然估计（SPMLE）开始，假设丢失的协变量的（条件）分布是已知的。EM算法的一种变体用于计算估计量。然后，我们将SPMLE调整到一个更实际的情况，即分布未知，并且根据可用信息有一个一致的估计量。我们建立了所得伪SPMLE的一致性和弱收敛性，并确定了合适的方差估计量。通过经验研究说明了我们的推理程序在疾病筛查和预测中的应用。所提出的方法用于分析激发这项研究的结核病筛查研究数据。通过仿真检查了其有限样本性能。