Molina Katy C, Calsavara Vinicius F, Tomazella Vera D, Milani Eder A
Institute of Mathematics and Computer Sciences, University of São Paulo, São Carlos, SP, Brazil.
Department of Statistics, Federal University of São Carlos, São Carlos, SP, Brazil.
Stat Methods Med Res. 2021 Aug;30(8):1874-1889. doi: 10.1177/09622802211011187. Epub 2021 May 6.
Survival models with a frailty term are presented as an extension of Cox's proportional hazard model, in which a random effect is introduced in the hazard function in a multiplicative form with the aim of modeling the unobserved heterogeneity in the population. Candidates for the frailty distribution are assumed to be continuous and non-negative. However, this assumption may not be true in some situations. In this paper, we consider a discretely distributed frailty model that allows units with zero frailty, that is, it can be interpreted as having long-term survivors. We propose a new discrete frailty-induced survival model with a zero-modified power series family, which can be zero-inflated or zero-deflated depending on the parameter value. Parameter estimation was obtained using the maximum likelihood method, and the performance of the proposed models was performed by Monte Carlo simulation studies. Finally, the applicability of the proposed models was illustrated with a real melanoma cancer data set.
具有脆弱项的生存模型作为Cox比例风险模型的扩展被提出，其中在风险函数中以乘法形式引入随机效应，目的是对总体中未观察到的异质性进行建模。脆弱分布的候选者被假定为连续且非负的。然而，在某些情况下这个假设可能不成立。在本文中，我们考虑一个离散分布的脆弱模型，该模型允许存在零脆弱性的个体，也就是说，它可以被解释为具有长期存活者。我们提出了一个新的具有零修正幂级数族的离散脆弱诱导生存模型，根据参数值，它可以是零膨胀或零收缩的。使用最大似然法进行参数估计，并通过蒙特卡罗模拟研究来评估所提出模型的性能。最后，用一个真实的黑色素瘤癌症数据集说明了所提出模型的适用性。
