A bivariate regression model with cure fraction

Abstract

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we introduce a location-scale model for bivariate survival times based on the copula to model the dependence of bivariate survival data with cure fraction. We create the correlation structure between the failure times using the Clayton family of copulas, which is assumed to have any distribution. It turns out that the model becomes very flexible with respect to the choice of the marginal distributions. For the proposed model, we consider inferential procedures based on constrained parameters under maximum likelihood. We derive the appropriate matrices for assessing local influence under different perturbation schemes and present some ways to perform global influence analysis. The relevance of the approach is illustrated using a real data set and a diagnostic analysis is performed to select an appropriate model.

The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis

“…Recently, some authors have investigated the assessment of local influence in different regression models, with the presence and absence of censored data, for instance, Lemonte and Patriota [3] considered the problem of assessing local influence in Birnbaum-Saunders nonlinear regression models; Rondon et al [4] adapted local influence methods to Birnbaum-Saunders nonlinear regression models; Matos et al [5] investigated local influence in linear and nonlinear mixedeffects models with censored data; Paula [6] derived curvature calculations under various perturbation schemes in double generalized linear models and Fachini et al [7] investigated local influence in location-scale models for bivariate survival times based on the copula to model the dependence of bivariate survival data with cure fraction. We develop a similar methodology to detect influential subjects in LOLLW regression models for censored data.…”

A new extended Birnbaum-Saunders model with cure fraction: classical and Bayesian approach

“…Further, Peng and Dear (2000) investigated a nonparametric MM for cure estimation, Sy and Taylor (2000) considered estimation in a proportional hazards cure model and Yu and Peng (2008) extended MMs to bivariate survival data by modeling marginal distributions. Fachini et al (2014) recently proposed a scale model for bivariate survival times based on the copula that model the dependence of bivariate survival data with cure fraction, Hashimoto et al (2015) introduced the new long-term survival model with interval-censored data, Ortega et al (2015) proposed the power series beta Weibull regression model to predict breast carcinoma, Lanjoni et al (2016) conducted extended Burr XII regression models and Ortega et al (2017) proposed regression models generated by gamma random variables with long-term survivors.…”

The odd log-logistic logarithmic generated family of distributions with applications in different areas

“…Some proposals have been made recently in the literature by more long term survival to model lifetimes with covariates. For example, Ortega et al (2012) considered the problem of assessing local influence in the negative binomial beta Weibull regression model to predict the cure of prostate cancer, Hashimoto et al (2013) derived curvature quantities under various perturbation schemes in Neyman type A beta-Weibull model for long-term survivors, Fachini et al (2014) adapted local influence methods to a bivariate regression model with cure fraction and, recently, Ortega et al (2015) used local influence methods to the power series beta-Weibull regression model for predicting breast carcinoma. The MMs allow simultaneously estimating whether the event of interest will occur, which is called incidence, and when it will occur, given that it can occur, which is called latency.…”