Por Jorge Achcar (Medical School, Universidade de São Paulo).

Abstract: Univariate or multivariate lifetime data analysis in presence of censoring and covariates usually assumes continuous data under parametrical or non-parametrical approaches. For univariate lifetime data it is observed in the literature, especially in recent years, a large number of new parametrical models usually generalizing standard popular lifetime models as the Weibull, log-normal or gamma distributions but not too many new parametrical models for the bivariate or multivariate lifetime data. An alternative in the lifetime data analysis is to consider discrete lifetime data since in many cases in medical or engineering applications the data in fact are discrete or could be assumed discrete. In this talk, we explore especially for the bivariate case, some existing parametrical bivariate models proposed in the literature (see for example, Arnold, 1988 or Basu and Dhar, 1995) in presence of censored data and covariates. Inferences are obtained using standard maximum likelihood methods and Bayesian approaches where the posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) simulation methods. Some comparisons are studied considering standard approaches to analyze bivariate lifetime assuming some popular parametrical continuous bivariate lifetime models introduced in the literature or assuming bivariate lifetime models derived from copula functions, showing some computational and statistical advantages for the use of bivariate discrete parametrical models (see for example, Davarzani et.al., 2015, 2017; Achcar et al, 2010, 2011, 2015; 2016a, 2016b) for the analysis of bivariate lifetime data. Some generalizations are also presented for the trivariate case (recurrent events) and some applications with real medical data and simulated data.