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Estimation of a Change Point in a Hazard Function Based on Censored Data

机译：基于删失数据的危险函数变化点估计

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摘要

The hazard function plays an important role in reliability or survival studies since it describes the instantaneous risk of failure of items at a time point, given that they have not failed before. In some real life applications, abrupt changes in the hazard function are observed due to overhauls, major operations or specific maintenance activities. In such situations it is of interest to detect the location where such a change occurs and estimate the size of the change. In this paper we consider the problem of estimating a single change point in a piecewise constant hazard function when the observed variables are subject to random censoring. We suggest an estimation procedure that is based on certain structural properties and on least squares ideas. A simulation study is carried out to compare the performance of this estimator with two estimators available in the literature: an estimator based on a functional of the Nelson-Aalen estimator and a maximum likelihood estimator. The proposed least squares estimator turns out to be less biased than the other two estimators, but has a larger variance. We illustrate the estimation method on some real data sets.
机译：危害函数在可靠性或生存性研究中起着重要作用，因为它描述了某个项目在某个时间点失败的瞬时风险，因为这些项目以前从未发生过故障。在某些实际应用中，由于检修，主要操作或特定的维护活动，会观察到危险功能的突然变化。在这种情况下，检测发生这种变化的位置并估算变化的大小是很有意义的。在本文中，我们考虑当观测变量进行随机检查时，估计分段恒定风险函数中的单个变化点的问题。我们建议基于某些结构特性和最小二乘思想的估算程序。进行了仿真研究，以将该估计器的性能与文献中提供的两种估计器进行比较：基于Nelson-Aalen估计器功能的估计器和最大似然估计器。所提出的最小二乘估计量比其他两个估计量的偏差要小，但方差更大。我们说明了一些实际数据集的估计方法。

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