Bivariate distributions based on copulas functions: developments and applications in medical studies

• Autor(a) principal: Peres, Marcos Vinicius de Oliveira
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/17/17139/tde-11062021-090710/
• topic: Abordagem Bayesiana; Análise de sobrevida; Bayesian approach; Bioestatística; Biostatistics; Bivariate models; Cancer studies; Copula functions; Cure rate; Estudos de câncer; Estudos médicos; Fração de cura; Função cópula; Medical studies; Modelos bivariados; Survival analysis

Multivariate survival data are found in several studies, in particular, studies where there are two observed lifetimes associated to the same individual, and in some cases there exists a dependence structure between the two lifetimes. In addition, with the recent advances of medicine and improvement of treatments, there is an increasing of fraction of individuals not expecting to experience the event of interest. These individuals are immune to the event or cured for the disease during the study and known as long-term survivors or cured individuals. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. For the modeling of bivariate data the use of copula survival functions is an alternative explored in this study, also assuming individuals in the presence of cure fractions modeled with standard mixture models, non-mixture models and also defective distributions. Motived by this, in this study it was introduced some continuous lifetime bivariate distributions considering copula functions in presence of censored data and lifetime data with long-term survivors. The proposed models are useful in medical situations to study the dependence structure of pair of lifetimes and in presence of cure rates. This work also proposed to compare the bivariate Kaplan-Meier estimator with the surface estimated from copulas by means of simple calculations of the distance between matrices. This methodology presented efficient results to compare bivariate models estimated by copulas with empirical survival estimates obtained using the bivariate Kaplan-Meier non-parametric estimator. Another interesting result obtained in this study is that the use bivariate distributions in presence of censoring and cure rate have better computational performance to get the inferences of interest under a Bayesian approach. According to the results obtained in our study, another interesting point is that the selected models lead to accurate estimation of the cure rate using Markov Chain Monte Carlo (MCMC) simulation algorithms with good stability in the generation of Gibbs samples of interest in the applications. Finally, it is possible to emphasize that the programing routine to get Bayesian inference of interest can be easily executed by free and open source softwares as OpenBUGS, JAGS or R with low computational costs.