Proportional hazard (PH) models can be formulated with or without assuming a probability distribution for survival times. The former assumption leads to parametric models, whereas the latter leads to the semi-parametric Cox model which is by far the most popular in survival analysis. However, a parametric model may lead to more efficient estimates than the Cox model under certain conditions. Only a few parametric models are closed under the PH assumption, the most common of which is the Weibull that accommodates only monotone hazard functions. We propose a generalization of the log-logistic distribution that belongs to the PH family. It has properties similar to those of log-logistic, and approaches the Weibull in the limit. These features enable it to handle both monotone and nonmonotone hazard functions. Application to four data sets and a simulation study revealed that the model could potentially be very useful in adequately describing different types of time-to-event data.

中文翻译：

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广义对数逻辑比例风险模型及其在生存分析中的应用

可以假设存在或不假设生存时间的概率分布来制定比例危害（PH）模型。前者的假设导致参数化模型，而后者的假设导致了半参数Cox模型，该模型是迄今为止在生存分析中最流行的模型。但是，在某些条件下，参数模型可能会比Cox模型产生更有效的估计。在PH假设下，只有少数参数模型是封闭的，其中最常见的是仅容纳单调危害函数的Weibull。我们提出属于PH系列的对数逻辑分布的一般化。它具有类似于对数逻辑的性质，并在极限范围内接近Weibull。这些功能使它能够处理单调和非单调危险功能。