Prentice R L, Kalbfleisch J D
Biometrics. 1979 Mar;35(1):25-39.
Many problems, particularly in medical research, concern the relationship between certain covariates and the time to occurrence of an event. The hazard or failure rate function provides a conceptually simple representation of time to occurrence data that readily adapts to include such generalizations as competing risks and covariates that vary with time. Two partially parametric models for the hazard function are considered. These are the proportional hazards model of Cox (1972) and the class of log-linear or accelerated failure time models. A synthesis of the literature on estimation from these models under prospective sampling indicates that, although important advances have occurred during the past decade, further effort is warranted on such topics as distribution theory, tests of fit, robustness, and the full utilization of a methodology that permits non-standard features. It is further argued that a good deal of fruitful research could be done on applying the same models under a variety of other sampling schemes. A discussion of estimation from case-control studies illustrates this point.
许多问题，尤其是在医学研究中，涉及某些协变量与事件发生时间之间的关系。风险率或失效率函数为事件发生时间数据提供了一个概念上简单的表示，它很容易适应包括竞争风险和随时间变化的协变量等一般情况。本文考虑了两种风险函数的部分参数模型。它们是Cox（1972）的比例风险模型以及对数线性或加速失效时间模型类别。对前瞻性抽样下这些模型估计的文献综述表明，尽管在过去十年中取得了重要进展，但在分布理论、拟合检验、稳健性以及充分利用允许非标准特征的方法等主题上仍需进一步努力。进一步认为，在各种其他抽样方案下应用相同模型可以开展大量富有成效的研究。对病例对照研究估计的讨论说明了这一点。
