Institute of Mathematical and Computer Sciences, University of São Paulo, São Paulo, São Carlos, 13566-590, Brazil.
Department of Statistics, Federal University of São Carlos, São Paulo, São Carlos, 13565-905, Brazil.
Lifetime Data Anal. 2021 Oct;27(4):561-587. doi: 10.1007/s10985-021-09529-1. Epub 2021 Jul 30.
In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of São Paulo, Brazil.
在本文中，我们提出了一种新的脆弱性模型，用于对生存数据中存在的未观测到的异质性进行建模。我们的模型是通过使用加权林德利分布作为脆弱性分布来推导的。各自的脆弱性分布具有简单的拉普拉斯变换函数，这对于获得边缘生存和危险函数很有用。我们假设威布尔和戈默特茨分布的危险函数作为基准危险函数。提出了一种基于最大似然法的经典推断程序。进一步进行了广泛的模拟研究，以验证在不同右删失比例下最大似然估计量的行为，并评估似然比检验在不同样本量下检测未观测到的异质性的性能。最后，为了演示所提出模型的适用性，我们将其应用于分析来自巴西圣保罗州肺癌发病的基于人群的病例研究的医学数据集。
