Semiparametric Probit Regression Model with General Interval-Censored Failure Time Data

Interval-censored data frequently arise in various biomedical areas involving periodical follow-ups where the failure or event time of interest cannot be observed exactly but is only known to fall into a time interval. This article considers a semiparametric probit regression model, a valuable alternative to other commonly used semiparametric models in survival analysis, to investigate potential risk factors for the interval-censored failure time of interest. We develop an expectation-maximization (EM) algorithm to conduct the pseudo maximum likelihood estimation (MLE) using the working independence strategy for general or mixed-case interval-censored data. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal with the empirical process techniques. In addition, we propose a novel penalized EM algorithm for simultaneously achieving variable selection and parameter estimation in the case of high-dimensional covariates. The proposed variable selection method can be readily implemented with some existing software and considerably reduces the estimation error of the proposed pseudo-MLE approach. Simulation studies demonstrate the satisfactory performance of the proposed methods. An application to a set of interval-censored data on prostate cancer further confirms the utility of the methodology. Supplementary materials for this article are available online.区间截尾数据（interval-censored data）常出现于各类涉及定期随访的生物医学研究领域，此类场景中，所关注的失效或事件发生时间无法被精准观测，仅能知晓其落在某一时间区间内。本文针对半参数probit回归模型展开研究，该模型是生存分析中其他常用半参数模型的极具价值的替代方案，用于探究所关注的区间截尾失效时间的潜在风险因素。我们开发了期望最大化算法（expectation-maximization, EM），借助工作独立策略，针对一般情形或混合情形的区间截尾数据实现伪极大似然估计（pseudo maximum likelihood estimation, MLE）。借助经验过程理论，可证明所得回归参数估计量具有一致性且服从渐近正态分布。此外，针对高维协变量情形，我们提出了一种新颖的惩罚EM算法，可同时实现变量选择与参数估计。所提出的变量选择方法可借助现有软件便捷实现，且能显著降低所提伪极大似然估计方法的估计误差。模拟研究验证了所提方法的优异性能。针对一组前列腺癌相关区间截尾数据的实际应用进一步证实了该方法论的实用性。本文补充材料可在线获取。