We present a new method for estimating a change point in the hazard function of a survival distribution assuming a constant hazard rate after the change point and a decreasing hazard rate before the change point. Our method is based on fitting a stump regression to p values for testing hazard rates in small time intervals. We present three real data examples describing survival patterns of severely ill patients, whose excess mortality rates are known to persist far beyond hospital discharge. For designing survival studies in these patients and for the definition of hospital performance metrics (e.g. mortality), it is essential to define adequate and objective end points. The reliable estimation of a change point will help researchers to identify such end points. By precisely knowing this change point, clinicians can distinguish between the acute phase with high hazard (time elapsed after admission and before the change point was reached), and the chronic phase (time elapsed after the change point) in which hazard is fairly constant. We show in an extensive simulation study that maximum likelihood estimation is not robust in this setting, and we evaluate our new estimation strategy including bootstrap confidence intervals and finite sample bias correction.

中文翻译：

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具有部分恒定风险率的生存分布的非参数变化点估计。

我们提出了一种新的方法来估计生存分布的危险函数中的变化点，其中假设变化点之后的危害率恒定，而变化点之前的危害率降低。我们的方法基于将树桩回归拟合为p在较小的时间间隔内测试危险率的值。我们提供了三个真实的数据示例，这些示例描述了重症患者的生存模式，这些患者的超额死亡率一直持续到出院为止。为了设计这些患者的生存研究并定义医院绩效指标（例如死亡率），定义适当和客观的终点至关重要。对变化点的可靠估计将有助于研究人员识别这些终点。通过准确地知道该变化点，临床医生可以区分出危险程度高的急性期（入院后和到达变化点之前的时间）和危险度相当恒定的慢性期（进入变化点后的时间）。