论文标题
基于Clayton Copula的双变量有缺陷的Gompertz分布，并应用于医疗数据
The Bivariate Defective Gompertz Distribution Based on Clayton Copula with Applications to Medical Data
论文作者
论文摘要
在医学研究中，很常见的是没有感兴趣的患者的一部分。这些患者是没有发生事件风险或在研究期间治愈的患者。免疫或治愈患者的比例在文献中被称为治愈率。通常，传统的现有寿命统计模型不适用于以治愈速率（包括双变量寿命）建模数据集。在本文中，提出了基于有缺陷的gompertz分布的双变量模型，并使用Clayton Copula函数来捕获寿命之间的可能依赖性结构。进行了广泛的仿真研究，以评估与拟议分布相关的参数的最大似然估计器的偏差和平方误差。提出了一些使用医疗数据的应用程序，以显示提出的模型的有用性。
In medical studies, it is common the presence of a fraction of patients who do not experience the event of interest. These patients are people who are not at risk of the event or are patients who were cured during the research. The proportion of immune or cured patients is known in the literature as cure rate. In general, the traditional existing lifetime statistical models are not appropriate to model data sets with cure rate, including bivariate lifetimes. In this paper, it is proposed a bivariate model based on a defective Gompertz distribution and also using a Clayton copula function to capture the possible dependence structure between the lifetimes. An extensive simulation study was carried out in order to evaluate the biases and the mean squared errors for the maximum likelihood estimators of the parameters associated to the proposed distribution. Some applications using medical data are presented to show the usefulness of the proposed model.
