A bivariate survival model for events with dependent failure times based on Archimedean copula functions. Application case: A sample of HIV patients

Abstract

This paper proposes a bivariate survival model for dependent failure times based on copula functions of the Archimedean family and the mean cumulative function for non-recurrent events of different types (MCFR ̅E) and uses it to estimate the probability of survival from the occurrence of events of different types on the same HIV/AIDS patient. The copula functions evaluate the dependence structure between the failure times of the events experienced by the same patient throughout their follow-up period, and the MCFR ̅E generates the marginal survival function for each event. The marginal function is a nonparametric estimator that gives the same estimated survival probability as the Kaplan-Meier estimator if the failure times of the different types of events are independent. If each patient experiences at least one event, a subset of them generates a compound event that affects the estimated probability of survival. The results show that the traditionally estimated survival probabilities are biased if dependent failure times are treated as independent.