A new straightforward defective distribution for survival analysis in the presence of a cure fraction

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.

KEYWORDS:

• Dagum distribution
• survival analysis
• defective distributions
• Bayesian methods
• censored data

AMS SUBJECT CLASSIFICATION:

• 62N01

Additional information

Funding

This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (305942/2012- 3).