### The defective generalized Gompertz distribution and its use in the analysis of lifetime data in presence of cure fraction, censored data and covariates

#### Abstract

#### References

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Proceedings of the 2nd International Symposium on Information Theory, pages 267-281.

Balka, J., Desmond, A. F. and 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.

Boag, J. W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society. Series B (Methodological), 11(1):15-53.

Cancho, V. G. and 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.

El-Gohary, A., Alshamrani, A. and Al-Otaibi, A. N. (2013). The generalized Gompertz distribution. Applied Mathematical Modelling, 37(1):13-24.

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. and Rubin, D. B. (2013). Bayesian Data Analysis, 3 edn. Chapman and Hall/CRC.

Ghitany, M. E., Maller, R. A. and Zhou, S. (1994). Exponential mixture models with long-term survivors and covariates. Journal of Multivariate Analysis, 49(2):218-241.

Gieser, P. W., Chang, M. N., Rao, P. V, Shuster, J. J. and Pullen, J. (2014). Modelling cure rates using the Gompertz model with covariate information. Statistics in Medicine, 17(8):831-839.

Henningsen, A. and Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3):443-458.

Kalbeisch, J. D., Prentice, R. L. (1980) The statistical analysis of failure time data, John Wiley & Sons

Lambert, P. C., Thompson, J. R., Weston, C. L. and Dickman, P. W. (2007). Estimating and modeling the cure fraction in population-based cancer survival analysis. Biostatistics, 8(3):576-594.

Lunn, D. J., Thomas, A., Best, N. and Spiegelhalter, D. (2000). WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10(4):325-337.

Morbiducci, M., Nardi, A. and Rossi, C. (2003). Classification of "cured" individuals in survival analysis: the mixture approach to the diagnostic prognostic problem. Computational Statistics & Data Analysis, 41(3):515-529.

Oehlert, G. W. (1992). A note on the delta method. The American Statistician, 46(1):27-29.

Rocha, R., Nadarajah, S., Tomazella, V., Louzada, F. and 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. and 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.

Rocha, R. F., Tomazella, V. L. D. and Louzada, F. (2014). Bayesian and classic inference for the Defective Gompertz Cure Rate Model. Revista Brasileira de Biometria, 32(1):104-114.

Santos, M. R., Achcar, J. A. and Martinez, E. Z. (2017). Bayesian and maximum likelihood inference for the defective Gompertz cure rate model with covariates: an application to the cervical carcinoma study. Ciencia e Natura, in press.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2014). The deviance information criterion: 12 years on (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(3):485-493.

Full Text: pdf