Hirsch Katharina, Wienke Andreas, Kuss Oliver
Institute of Medical Epidemiology, Biostatistics, and Informatics, Faculty of Medicine, Martin-Luther-University Halle-Wittenberg, D-06097 Halle (Saale), Germany.
Institute of Medical Epidemiology, Biostatistics, and Informatics, Faculty of Medicine, Martin-Luther-University Halle-Wittenberg, D-06097 Halle (Saale), Germany.
Comput Methods Programs Biomed. 2016 Dec;137:167-175. doi: 10.1016/j.cmpb.2016.09.009. Epub 2016 Sep 14.
The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces.
In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models.
The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece.
The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters.
几十年来，人们已经知道具有分段常数基线风险函数的生存模型与泊松回归模型是等价的。正如最近的研究所表明的，这种等价性也适用于聚类生存数据：具有对数正态脆弱项的脆弱模型可以被解释和估计为具有二元响应、泊松似然和特定偏移的广义线性混合模型。通过这种方式，广义线性混合模型的统计理论和软件可以很容易地用于拟合脆弱模型。这种灵活性的提升代价很小，即（1）必须预先确定基线风险的分段数量，以及（2）必须将数据集按分段数量“展开”。
在本文中，我们通过使用更现实的基线风险（冈珀茨）并将所考虑的模型与竞争模型进行比较，扩展了先前研究的模拟。此外，还引入了SAS宏%PCFrailty，以便将泊松广义线性混合方法应用于脆弱模型。
模拟结果表明共享脆弱模型表现良好。我们新的%PCFrailty宏提供了恰当的估计，特别是在每段有4个事件的情况下。
基于%PCFrailty宏的对数正态脆弱模型的泊松广义线性混合方法在聚类生存数据分析中具有几个优点，包括对固定效应和随机效应进行更灵活的建模、精确（非近似意义上）的最大似然估计，以及为所有方差参数提供标准误差和不同类型的置信区间。
