The proportional hazards (PH) model is arguably one of the most popular models used to analyze time to event data arising from clinical trials and longitudinal studies. In many such studies, the event time is not directly observed but is known relative to periodic examination times; i.e., practitioners observe either current status or interval-censored data. The analysis of data of this structure is often fraught with many difficulties since the event time of interest is unobserved. Further exacerbating this issue, in some such studies the observed data also consists of instantaneous failures; i.e., the event times for several study units coincide exactly with the time at which the study begins. In light of these difficulties, this work focuses on developing a mixture model, under the PH assumptions, which can be used to analyze interval-censored data subject to instantaneous failures. To allow for modeling flexibility, two methods of estimating the unknown cumulative baseline hazard function are proposed; a fully parametric and a monotone spline representation are considered. Through a novel data augmentation procedure involving latent Poisson random variables, an expectation–maximization (EM) algorithm is developed to complete model fitting. The resulting EM algorithm is easy to implement and is computationally efficient. Moreover, through extensive simulation studies the proposed approach is shown to provide both reliable estimation and inference. The motivation for this work arises from a randomized clinical trial aimed at assessing the effectiveness of a new peanut allergen treatment in attaining sustained unresponsiveness in children.

中文翻译：

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对于存在瞬时故障的间隔检查数据，扩展了比例风险模型。

比例风险（PH）模型可以说是最受欢迎的模型之一，用于分析临床试验和纵向研究产生的事件数据。在许多此类研究中，事件时间不是直接观察到的，而是相对于定期检查时间已知的。即，从业者观察当前状态或间隔检查的数据。由于没有观察到感兴趣的事件时间，因此对这种结构的数据进行分析常常会遇到很多困难。进一步加剧了这个问题，在某些此类研究中，观察到的数据还包括瞬时故障。即，几个研究单元的事件时间与研究开始的时间完全一致。鉴于这些困难，这项工作着重于在PH假设下开发混合模型，可以用来分析遭受瞬时故障的间隔检查数据。为了允许建模的灵活性，提出了两种估计未知的累积基准危害函数的方法：考虑完全参数化和单调样条表示。通过涉及潜在泊松随机变量的新颖数据扩充程序，开发了期望最大化（EM）算法以完成模型拟合。所得的EM算法易于实现，并且计算效率高。此外，通过广泛的仿真研究，所提出的方法被证明可以提供可靠的估计和推断。这项工作的动机来自一项旨在评估新的花生过敏原治疗对儿童持续无反应的疗效的随机临床试验。