Bayesian and Maximum Likelihood Inference for the Defective Gompertz Cure Rate Model With Covariates: An Appliction to the Cervical Carcinoma Study


  • Milene Regina dos Santos Universidade de São Paulo, USP
  • Jorge Alberto Achcar Universidade de São Paulo, USP
  • Edson Zangiacomi Martinez Universidade de São Paulo, USP



Maximum likelihood estimation, Bayesian inference, Defective distributions, Survival analysis, Modified Gompertz distribution


Survival analysis is a class of statistical methods to study the time until the occurrence of a specified event. The usual methods assume that all individuals under study are subjects to the event the interest. However, there are situations where this case is unrealistic. For example, in a clinical research, a proportion of patients could respond favourably to the treatment under investigation and consequently they would not die from the disease. Models based on defective distributions are a suitable way to analyse data with these characteristics. In this paper, we present Bayesian and maximum likelihood inference for the defective Gompertz cure rate model in presence of covariates. An example with application to disease-free survival of women treated for cervical carcinoma is used to illustrate the proposed methodology. In the Bayesian analysis, posterior distributions of parameters are estimated using the Markov chain Monte Carlo (MCMC) method. R, SAS and OpenBUGS codes are provided in the appendix at the end of the paper so that reader can carry out their own analysis.


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Author Biographies

Milene Regina dos Santos, Universidade de São Paulo, USP

Jorge Alberto Achcar, Universidade de São Paulo, USP

Edson Zangiacomi Martinez, Universidade de São Paulo, USP


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How to Cite

Santos, M. R. dos, Achcar, J. A., & Martinez, E. Z. (2017). Bayesian and Maximum Likelihood Inference for the Defective Gompertz Cure Rate Model With Covariates: An Appliction to the Cervical Carcinoma Study. Ciência E Natura, 39(2), 244–258.