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，我们提出了一种新颖的脆弱模型，用于对生存数据中存在的未观察到的异质性进行建模。我们的模型是通过使用加权 Lindley 分布作为脆弱分布得出的。各自的脆弱分布具有简单的拉普拉斯变换函数，可用于获得边际生存和危险函数。我们假设 Weibull 和 Gompertz 分布的风险函数作为基线风险函数。提出了一种基于最大似然法的经典推理过程。进一步进行了广泛的模拟研究，以验证最大似然估计量在不同右删失比例下的行为，并评估似然比检验在不同样本量中检测未观察到的异质性的性能。最后，