The Bivariate Defective Gompertz Distribution Based on Clayton Copula with Applications to Medical Data

TL;DR

This paper introduces a new bivariate defective Gompertz distribution model utilizing Clayton copula to better analyze medical data with cure rates, capturing dependence between lifetimes and improving modeling accuracy.

Contribution

It proposes a novel bivariate defective Gompertz model with Clayton copula for medical data with cure rates, including estimation and application methods.

Findings

Simulation study shows low bias and MSE of estimators.

Model effectively captures dependence in medical lifetime data.

Applications demonstrate practical usefulness of the proposed model.

Abstract

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.