Lee Mei-Ling Ting, Whitmore G A
University of Maryland, College Park, MD, USA.
Lifetime Data Anal. 2010 Apr;16(2):196-214. doi: 10.1007/s10985-009-9138-0. Epub 2009 Dec 4.
Proportional hazards (PH) regression is a standard methodology for analyzing survival and time-to-event data. The proportional hazards assumption of PH regression, however, is not always appropriate. In addition, PH regression focuses mainly on hazard ratios and thus does not offer many insights into underlying determinants of survival. These limitations have led statistical researchers to explore alternative methodologies. Threshold regression (TR) is one of these alternative methodologies (see Lee and Whitmore, Stat Sci 21:501-513, 2006, for a review). The connection between PH regression and TR has been examined in previous published work but the investigations have been limited in scope. In this article, we study the connections between these two regression methodologies in greater depth and show that PH regression is, for most purposes, a special case of TR. We show two methods of construction by which TR models can yield PH functions for survival times, one based on altering the TR time scale and the other based on varying the TR boundary. We discuss how to estimate the TR time scale and boundary, with or without the PH assumption. A case demonstration is used to highlight the greater understanding of scientific foundations that TR can offer in comparison to PH regression. Finally, we discuss the potential benefits of positioning PH regression within the first-hitting-time context of TR regression.
比例风险（PH）回归是分析生存数据和事件发生时间数据的标准方法。然而，PH回归的比例风险假设并不总是合适的。此外，PH回归主要关注风险比，因此对生存的潜在决定因素没有提供太多见解。这些局限性促使统计研究人员探索替代方法。阈值回归（TR）就是这些替代方法之一（有关综述，请参阅Lee和Whitmore，《统计科学》21:501 - 513，2006年）。PH回归与TR之间的联系在以前发表的工作中已经进行了研究，但研究范围有限。在本文中，我们更深入地研究这两种回归方法之间的联系，并表明在大多数情况下，PH回归是TR的一个特例。我们展示了两种构建方法，通过这两种方法TR模型可以产生生存时间的PH函数，一种基于改变TR时间尺度，另一种基于改变TR边界。我们讨论了在有无PH假设的情况下如何估计TR时间尺度和边界。通过一个案例演示来突出与PH回归相比，TR能够提供对科学基础的更深入理解。最后，我们讨论了将PH回归置于TR回归的首次击中时间背景下的潜在益处。
