Abstract
Bivariate survival cure rate models extend the understanding of time-to-event data by allowing for a cured fraction of the population and dependence between paired units and make more accurate and informative conclusions. In this paper, we propose a Bayesian bivariate cure rate mode where a correlation coefficient is used for the association between bivariate cure rate fractions and a new generalized Farlie Gumbel Morgenstern (FGM) copula function is applied to model the dependence structure of bivariate survival times. For each marginal survival time, we apply a Weibull distribution, a log normal distribution, and a flexible three-parameter generalized extreme value (GEV) distribution to compare their performance. For the survival model fitting, DIC and LPML are used for model comparison. We perform a goodness-of-fit test for the new copula. Finally, we illustrate the performance of the proposed methods in simulated data and real data via Bayesian paradigm.
Highlights
In survival analysis, it is of primary interest to measure the association between two time-to-event random variables associated with one individual
We propose a Bayesian bivariate cure rate mode where a correlation coefficient is used for the association between bivariate cure rate fractions and a new generalized Farlie Gumbel Morgenstern (FGM) copula function is applied to model the dependence structure of bivariate survival times
An analytical structure of the statistical methodology was developed to model the dependence between cure rate fractions, and an extremely flexible generalized extreme value distribution was employed to model the logarithm of the survival time
Summary
It is of primary interest to measure the association between two time-to-event random variables associated with one individual. Suzuki, and Cancho (2013) proposed an FGM long-term bivariate survival copula model. They assumed a mixture cure rate model for the marginal distribution of each lifetime and assumed fixed cure fraction for the entire population. The literature has introduced many other modelling approaches for bivariate long term data using copula functions, as for example the paper introduced by Louzada et al (2013). The authors only present more simple cure fraction survival model situation assuming dependence with a FGM copula function structure. The test is extended to the case of mixture cure rate model for individual survival function. We discuss how to identify the susceptible subjects in the mixture cure rate model in order to produce a PIOS test statistic
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