Bivariate lifetime modelling using copula functions in presence of mixture and non-mixture cure fraction models, censored data and covariates

Article type: Research Article

Authors: Achcar, Jorge Alberto^a | Martinez, Edson Zangiacomi^a | Tovar Cuevas, José Rafael^{b; *}

Affiliations: [a] Departamento de Medicina Social - FMRP, Universidade de Sao Paulo, Ribeiro Preto, SP, Brazil | [b] Escuela de Estadstica, Universidad del Valle, Santiago de Cali, Colombia

Correspondence: [*] Corresponding author: Jos Rafael Tovar Cuevas, Escuela de Estadstica, Universidad del Valle, Santiago de Cali, Colombia. Tel.: +57 2 3212138; E-mail:jose.r.tovar@correounivalle.edu.co

Abstract: In this paper, we introduce bivariate lifetime models derived from copula functions considering two copula functions, the Farlie Gumbel Morgenstern (FGM) commonly used to model very weak linear dependences and the Gumbel-Barnett copula which models very weak non necessarily linear dependences. Considering the presence of cure fractions for both lifetimes, censored data and covariates, we use standard MCMC (Markov Chain Monte Carlo) methods to get a Bayesian analysis for the proposed models. This new modelling approach gives a great flexibility of fit for bivariate data, since we could assume any existing parametric marginal lifetime distribution for the bivariate lifetimes as standard Weibull, log-normal, gamma, generalized gamma, generalized Weibull or generalized F distributions. An example, considering a medical data set is introduced to illustrate the proposed methodology.

Keywords: Bivariate lifetime data, copula functions, cure fraction, censored data, covariates, Bayesian methods

DOI: 10.3233/MAS-160372

Journal: Model Assisted Statistics and Applications, vol. 11, no. 4, pp. 261-276, 2016