A new cure rate regression framework for bivariate data based on the Chen distribution.

The present study introduces a new multivariate mixture cure rate model based on the Chen probability distribution to model recurrent event data in the presence of cure fraction. In this context, we provide an alternative for the use of some usual modeling approaches as the semiparametric Cox proportional hazards model commonly used in lifetime data analysis, considering a new bivariate parametric model to be used in the data analysis of bivariate lifetime data assuming a mixture structure for the bivariate data in presence of covariates, censored data and cure fraction. Under a Bayesian setting, the proposed methodology was considered to analyze two real medical datasets from a retrospective cohort study related to leukemia and diabetic retinopathy diseases. The model validation process was addressed by using the Cox-Snell residuals, which allowed us to identify the suitability of the new proposed mixture cure rate model.

Bivariate lifetime models in presence of cure fraction: a comparative study with many different copula functions.

In time-to-event studies it is common the presence of a fraction of individuals not expecting to experience the event of interest; these individuals who are immune to the event or cured for the disease during the study are known as long-term survivors. In addition, in many studies it is observed two lifetimes associated to the same individual, and in some cases there exists a dependence structure between them. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. In this study, it is proposed a bivariate model based on a Weibull standard distribution with a dependence structure based on fifteen different copula functions. We assumed the Weibull distribution due to its wide use in survival data analysis and its greater flexibility and simplicity, but the presented methods can be adapted to other continuous survival distributions. Three examples, considering real data sets are introduced to illustrate the proposed methodology. A Bayesian approach is assumed to get the inferences for the parameters of the model where the posterior summaries of interest are obtained using Markov Chain Monte Carlo simulation methods and the Openbugs software. For the data analysis considering different real data sets it was assumed fifteen different copula models from which is was possible to find models with satisfactory fit for the bivariate lifetimes in presence of long-term survivors.