The primary goal of this paper is to introduce a novel frailty model based on the weighted Lindley (WL) distribution for modeling clustered survival data. We study the statistical properties of the proposed model. In particular, the amount of unobserved heterogeneity is directly parameterized on the variance of the frailty distribution such as gamma and inverse Gaussian frailty models. Parametric and semiparametric versions of the WL frailty model are studied. A simple expectation-maximization (EM) algorithm is proposed for parameter estimation. Simulation studies are conducted to evaluate its finite sample performance. Finally, we apply the proposed model to a real data set to analyze times after surgery in patients diagnosed with colorectal cancer and compare our results with classical frailty models carried out in this application, which shows the superiority of the proposed model. We implement an R package that includes estimation for fitting the proposed model based on the EM-algorithm.
Joint modelling of recurrent and terminal events with discretely-distributed non-parametric frailty: application on re-hospitalizations and death in heart failure patients
Laplacian-P-splines for shared Gamma frailty models applied to clustered right-censored time-to-event data
Department of Neurodegeneration Diagnostics, University Hospital Bialystok, Poland（比亚韦斯托克医院神经退行性疾病诊断系）；Interuniversity Institute for Biostatistics and statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Belgium（哈瑟尔特大学生物统计与统计生物信息学跨大学研究所（I-BioStat））；Global Health Institute, Family Medicine and Population Health, University of Antwerp, Belgium（安特卫普大学全球健康学院）
Z-residual diagnostics for detecting misspecification of the functional form of covariates for shared frailty models
在生存分析中，风险函数往往依赖于一组协变量。鞅和偏差残差最广泛地用于检查协变量函数形式的有效性，通过检查其对连续协变量的散点图中是否存在可辨别的趋势。然而，目视检查鞅和偏差残差往往是主观的。此外，由于删失，这些残差缺乏参考分布。因此，它是具有挑战性的数值统计检验的基础上鞅或偏差残差。在本文中，我们扩展了随机生存概率的思想（Li et al. 2021），并开发了一种残差诊断工具，可以提供图形和数值检验，用于检查半参数共享脆弱模型中的协变量函数形式。我们开发了一个通用函数，它基于R中\texttt{survival}包中\texttt{coxph}函数的输出计算半参数共享脆弱模型的Z残差。我们广泛的模拟研究表明，基于Z-残差推导的数值检验方法对于检验协变量的函数形式有很大的作用。在急性髓性白血病患者生存时间建模的实际数据应用中，Z-残差诊断结果表明，具有对数变换的模型不适合建模生存时间，这不能通过其他诊断方法检测。
