Abstract: In this paper we propose a new bivariate long-term distribution based on the Farlie-Gumbel-Morgenstern copula model. The proposed model allows for the presence of censored data and covariates in the cure parameter. For inferential purpose a Bayesian approach via Markov Chain Monte Carlo (MCMC) is considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we develop a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated on artificial and real HIV data.
Abstract: In this paper the log-exponentiated-Weibull regression model is modified to allow the possibility that long term survivors are present in the data. The modification leads to a log-exponentiated-Weibull regression model with cure rate, encompassing as special cases the log-exponencial regression and log-Weibull regression models with cure rate typically used to model such data. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction; that is, the proportion of the population for which the event never occurs. Assuming censored data, we consider a classic analysis and Bayesian analysis for the parameters of the proposed model. The normal curvatures of local influence are derived under various perturbation schemes and two deviance-type residuals are proposed to assess departures from the log-exponentiated-Weibull error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.
Abstract: In this paper we propose a new three-parameters lifetime distribu tion with decreasing hazard function, the long-term exponential geometric distribution. The new distribution arises on latent competing risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the minimum lifetime value among all risks, and there is presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its survival and hazard functions, order statistics, Bonferroni function and the Lorenz curve. The parameter estimation is based on the usual maximum likelihood approach. We compare the new distribution with its particular case, the long-term exponential distribution, as well as with the long-term Weibull distribution on two real datasets, observing its poten tial and competitiveness in comparison with an usual lifetime distribu