A new straightforward defective distribution for survival analysis in the presence of a cure fraction. (2nd October 2018)

• Record Type: Journal Article
• Authors: Martinez, Edson Z.; Achcar, Jorge A.
• Is Part Of: Journal of statistical theory and practice. Volume 12:Number 4(2018)
• Page Start: 688
• Page End: 703
• Publication Date: 2018-10-02
• Subjects: Dagum distribution -- survival analysis -- defective distributions -- Bayesian methods -- censored data; 62N01; 519.505
• DOI: 10.1080/15598608.2018.1460885
• Languages: English
• ISSNs: 1559-8608

Abstract

ABSTRACT: In this article we introduce a new distribution, namely, the defective Dagum distribution (DDD). This improper distribution can be seen as an extension of the Type I Dagum distribution and it is useful to accommodate survival data in the presence of a cure fraction. In the applications of survival methods to medical data, the cure fraction is defined as the proportion of patients who are cured of disease and become long-term survivors. The great advantage of the DDD is that the cure fraction can be written as a function of only one parameter. We also considered the presence of censored data and covariates. Maximum likelihood and Bayesian methods for estimation of the model parameters are presented. A simulation study is provided to evaluate the performance of the maximum likelihood method in estimating parameters. In the Bayesian analysis, posterior distributions of the parameters are estimated using the Markov-chain Monte Carlo (MCMC) method. An example involving a real data set is presented. The model based on the new distribution is easy to use and it is a good alternative for the analysis of real time-to-event data in the presence of censored information and a cure fraction.