Bayesian and Maximum Likelihood Inference for the Defective Gompertz Cure Rate Model With Covariates: An Appliction to the Cervical Carcinoma Study
DOI:
https://doi.org/10.5902/2179460X24118Keywords:
Maximum likelihood estimation, Bayesian inference, Defective distributions, Survival analysis, Modified Gompertz distributionAbstract
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.Downloads
References
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Proceedings of the 2nd International Symposium on Information Theory, pp. 267–281.
Balka, J., Desmond, A. F., McNicholas, P. D. (2011). Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models. Journal of Applied Statistics, 38(1), 127–144.
Brenna, S. M., Silva, I. D., Zeferino, L. C., Pereira, J. S., Martinez, E. Z., Syrjänen, K. J. (2004). Prognostic value of P53 codon 72 polymorphism in invasive cervical cancer in Brazil. Gynecologic Oncology, 93(2), 374–380.
Cancho, V. G., Bolfarine, H. (2001). Modeling the presence of immunes by using the exponentiated-Weibull model. Journal of Applied Statistics, 28(6), 659–671.
Cantor, A. B., Shuster, J. J. (1992) Parametric versus nonparametric methods for estimating cure rates based on censored survival data. Statistics in Medicine, 11(7), 931–937.
Farewell, V. T. (1982). The use of mixture models for the analysis of survival data with long-term survivors. Biometrics, 38(4), 1041–1046.
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., Rubin, D. B. (2013). Bayesian Data Analysis, 3o edn. Chapman and Hall/CRC.
Gieser, P. W., Chang, M. N., Rao, P. V, Shuster, J. J., Pullen, J. (2014). Modelling cure rates using the Gompertz model with covariate information. Statistics in Medicine, 17(8), 831–839.
Henningsen, A., Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3), 443–458.
Klein, J. P., Moeschberger, M. L. (2005). Survival analysis: techniques for censored and truncated data, 2o edn. Springer Science & Business Media.
Lambert, P. C., Thompson, J. R., Weston, C. L., Dickman, P. W. (2007). Estimating and modeling the cure fraction in population-based cancer survival analysis. Biostatistics, 8(3), 576–594.
Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., Schabenberger, O. (2006). SAS for Mixed Models, 2o edn. SAS Institute.
Lunn, D. J., Thomas, A., Best, N., Spiegelhalter, D. (2000). WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10(4), 325–337.
Maller, R. A., Zhou, X. (1996). Survival Analysis with Long-Term Survivors, Wiley.
Millar, R. B. (2011). Maximum likelihood estimation and inference: with examples in R, SAS and ADMB, Vol. 111, Wiley.
R Development Core Team (2009). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, URL http: //www.R-project.org.
Rocha, R. F., Tomazella, V. L. D., Louzada, F. (2014). Bayesian and classic inference for the Defective Gompertz Cure Rate Model. Revista Brasileira de Biometria, 32(1), 104–114.
Rocha, R., Nadarajah, S., Tomazella, V., Louzada, F., Eudes, A. (2015). New defective models based on the Kumaraswamy family of distributions with application to cancer data sets. Statistical Methods in Medical Research, 1–23.
Rocha, R., Nadarajah, S., Tomazella, V., Louzada, F. (2017). A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling. Computational Statistics & Data Analysis, 107, 48–63.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., Linde, A. (2014). The deviance information criterion: 12 years on. Journal of the Royal Statistical Society: Series B Statistical Methodology, 76(3), 485–493.
Downloads
Published
How to Cite
Issue
Section
License
To access the DECLARATION AND TRANSFER OF COPYRIGHT AUTHOR’S DECLARATION AND COPYRIGHT LICENSE click here.
Ethical Guidelines for Journal Publication
The Ciência e Natura journal is committed to ensuring ethics in publication and quality of articles.
Conformance to standards of ethical behavior is therefore expected of all parties involved: Authors, Editors, Reviewers, and the Publisher.
In particular,
Authors: Authors should present an objective discussion of the significance of research work as well as sufficient detail and references to permit others to replicate the experiments. Fraudulent or knowingly inaccurate statements constitute unethical behavior and are unacceptable. Review Articles should also be objective, comprehensive, and accurate accounts of the state of the art. The Authors should ensure that their work is entirely original works, and if the work and/or words of others have been used, this has been appropriately acknowledged. Plagiarism in all its forms constitutes unethical publishing behavior and is unacceptable. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable. Authors should not submit articles describing essentially the same research to more than one journal. The corresponding Author should ensure that there is a full consensus of all Co-authors in approving the final version of the paper and its submission for publication.
Editors: Editors should evaluate manuscripts exclusively on the basis of their academic merit. An Editor must not use unpublished information in the editor's own research without the express written consent of the Author. Editors should take reasonable responsive measures when ethical complaints have been presented concerning a submitted manuscript or published paper.
Reviewers: Any manuscripts received for review must be treated as confidential documents. Privileged information or ideas obtained through peer review must be kept confidential and not used for personal advantage. Reviewers should be conducted objectively, and observations should be formulated clearly with supporting arguments, so that Authors can use them for improving the paper. Any selected Reviewer who feels unqualified to review the research reported in a manuscript or knows that its prompt review will be impossible should notify the Editor and excuse himself from the review process. Reviewers should not consider manuscripts in which they have conflicts of interest resulting from competitive, collaborative, or other relationships or connections with any of the authors, companies, or institutions connected to the papers.
