期刊
AUSTRIAN JOURNAL OF STATISTICS
卷 51, 期 2, 页码 144-168出版社
AUSTRIAN STATISTICAL SOC
DOI: 10.17713/ajs.v51i2.1285
关键词
Clayton copula; cure rate; defective Gompertz distribution; survival analysis
The study proposed a bivariate model based on a defective Gompertz distribution and Clayton copula function to capture the dependence structure between lifetimes. Extensive simulation study evaluated biases and mean squared errors of maximum likelihood estimators, showing the usefulness of the model in medical data applications. Maximum likelihood and Bayesian methods were used to estimate model parameters.
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. Maximum likelihood and Bayesian methods were used to estimate the parameters of the model.
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