Gallardo Diego I, Gómez Yolanda M, Santibañez John L, Venegas Osvaldo, Bourguignon Marcelo
Departamento de Estadísticas, Facultad de Ciencias, Univerisidad del Bío-Bío, Concepción, 4081112, Chile.
Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó, 1530000, Chile.
Sci Rep. 2025 Aug 17;15(1):30099. doi: 10.1038/s41598-025-15903-y.
A new multivariate shared frailty model based on the truncated normal distribution is proposed. For the basal distribution of failure times, we assume a parametric approach through the Weibull and piecewise exponential distributions and also a nonparametric approach. Similar to the traditional gamma frailty model, the Laplace transform, the hazard and survival functions of our proposal have a simple and closed form. In addition, the n-th derivative of the Laplace transform can be expressed recursively. Parameter estimation is performed by a classical approach through the EM algorithm. A simulation study is presented to demonstrate the consistency of the estimators in finite samples. Finally, two applications to medical data modelling the recurrence of infection in renal patients and patients with fibrosarcoma are presented to demonstrate the effectiveness of the model compared to other classical approaches in the literature. The computational implementation of the model is available in the extrafrail package of R.
提出了一种基于截断正态分布的新型多变量共享脆弱性模型。对于失效时间的基础分布，我们假设通过威布尔分布和分段指数分布的参数方法以及非参数方法。与传统的伽马脆弱性模型类似，我们提出的模型的拉普拉斯变换、危险函数和生存函数具有简单的封闭形式。此外，拉普拉斯变换的n阶导数可以递归表示。通过EM算法采用经典方法进行参数估计。进行了一项模拟研究以证明估计量在有限样本中的一致性。最后，给出了两个应用于医学数据的例子，对肾病患者和纤维肉瘤患者感染复发进行建模，以证明该模型与文献中其他经典方法相比的有效性。该模型的计算实现可在R语言的extrafrail包中获取。
