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.
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This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (305942/2012- 3).
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Martinez, E.Z., Achcar, J.A. A new straightforward defective distribution for survival analysis in the presence of a cure fraction. J Stat Theory Pract 12, 688–703 (2018). https://doi.org/10.1080/15598608.2018.1460885
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DOI: https://doi.org/10.1080/15598608.2018.1460885