Khan Shahedul A
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK, S7N 5E6, Canada.
Lifetime Data Anal. 2018 Apr;24(2):328-354. doi: 10.1007/s10985-017-9394-3. Epub 2017 Mar 27.
The Weibull, log-logistic and log-normal distributions are extensively used to model time-to-event data. The Weibull family accommodates only monotone hazard rates, whereas the log-logistic and log-normal are widely used to model unimodal hazard functions. The increasing availability of lifetime data with a wide range of characteristics motivate us to develop more flexible models that accommodate both monotone and nonmonotone hazard functions. One such model is the exponentiated Weibull distribution which not only accommodates monotone hazard functions but also allows for unimodal and bathtub shape hazard rates. This distribution has demonstrated considerable potential in univariate analysis of time-to-event data. However, the primary focus of many studies is rather on understanding the relationship between the time to the occurrence of an event and one or more covariates. This leads to a consideration of regression models that can be formulated in different ways in survival analysis. One such strategy involves formulating models for the accelerated failure time family of distributions. The most commonly used distributions serving this purpose are the Weibull, log-logistic and log-normal distributions. In this study, we show that the exponentiated Weibull distribution is closed under the accelerated failure time family. We then formulate a regression model based on the exponentiated Weibull distribution, and develop large sample theory for statistical inference. We also describe a Bayesian approach for inference. Two comparative studies based on real and simulated data sets reveal that the exponentiated Weibull regression can be valuable in adequately describing different types of time-to-event data.
威布尔分布、对数逻辑斯蒂分布和对数正态分布被广泛用于对事件发生时间数据进行建模。威布尔分布族仅适用于单调风险率，而对数逻辑斯蒂分布和对数正态分布则广泛用于对单峰风险函数进行建模。具有广泛特征的寿命数据的可得性不断增加，促使我们开发更灵活的模型，以适应单调和非单调风险函数。这样的一种模型就是指数化威布尔分布，它不仅能适应单调风险函数，还允许出现单峰和浴盆形状的风险率。这种分布在事件发生时间数据的单变量分析中已显示出相当大的潜力。然而，许多研究的主要重点更多地在于理解事件发生时间与一个或多个协变量之间的关系。这就导致了对生存分析中可以用不同方式构建的回归模型的考虑。一种这样的策略涉及为加速失效时间分布族构建模型。用于此目的最常用的分布是威布尔分布、对数逻辑斯蒂分布和对数正态分布。在本研究中，我们表明指数化威布尔分布在加速失效时间族下是封闭的。然后我们基于指数化威布尔分布构建一个回归模型，并为统计推断发展大样本理论。我们还描述了一种用于推断的贝叶斯方法。基于真实数据集和模拟数据集的两项比较研究表明，指数化威布尔回归在充分描述不同类型的事件发生时间数据方面可能很有价值。
