Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

On Estimation of Bivariate Survival Function from Random Censored Data

At present there are several approaches to estimate survival functions of vectors of lifetimes. However, some of these estimators are either inconsistent or not fully defined in the range of joint survival functions. Therefore they are not applicable in practice. In this paper three types of estimates of exponential-hazard, product-limit and relative-risk power structures for the bivariate survival function are considered when the number of summands in empirical estimates is replaced with a sequence of Poisson random variables. It is shown that proposed estimates are asymptotically equivalent. Keywords: bivariate survival function, Poisson random variables, empirical estimates

Modeling Data With Semicompeting Risks: An Application to Chronic Kidney Disease in Colombia

In this paper, the structure of semicompeting risks data, dened by Fine, Jiang & Chappell (2001), is studied. Two events are of interest: a nonterminal and a terminal event, the last one, can censor the non-terminal event, but not vice versa. Due to the possible dependence between the times until the occurrence of such events, two approaches are evaluated: modelling the bivariate survival function through Archimedean copulas and a shared frailty model. A simulation is conducted to examine its performance and both approaches are applied to a real data set of patients with chronic kidney disease (CKD).