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Year 2018, Volume: 47 Issue: 2, 437 - 446, 01.04.2018

Abstract

References

  • Akaike, H. (1974). A new look at the statistical model identication. IEEE Transactions of Automatic Control, 19(6), 716-723.
  • Berkson, J., Gage, R. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association, 47, 501-515.
  • Boag, J.W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society B, 11,15-53.
  • Cancho, V.G., Louzada, F., Barriga, G.D.C. (2011) The Geometric Birnbaum-Saunders regression model with cure rate. Journal of Statistical Planning an Inference, 142, 993-1000.
  • Cooray, K. and Ananda, M.M.A. (2008). A Generalization of the Half-Normal Distribution with Applications to Lifetime Data. Communications in Statistics - Theory and Methods, 37, 1323-1337.
  • Durrans, S.R. (1992). Distributions of fractional order statistics in hydrology. Water Resources Research, 28, 16491655.
  • Gómez, Y.M., Bolfarine, H. (2015). Likelihood-based inference for power half-normal distri- bution. Journal of Statistical Theory and Applications, 14, 383398.
  • Gupta, D. and Gupta, R.C. (2008). Analyzing skewed data by power normal model. Test, 17, 197210.
  • Lehmann, E.L. (1953). The power of rank tests. Annals of Mathematical Statistics, 24, 2343.
  • Maller, R.A., Zhou, X., (1996). Survival Analysis with Long-Term Survivors. Wiley, New York.
  • Marshall A.W. and Olkin I. (2007). Life distributions: Structure of nonparametric, semi- parametric, and parametric families. Springer Science+Business Media, LLC, New York.
  • Perdona, G.S.C., Louzada-Neto, F. (2011). A general hazard model for lifetime data in the presence of cure rate. Journal of Applied Statistics 38, 1395-1405.
  • Pescim, R.R., Demétrio, C.G.B., Cordeiro, G.M., Ortega, E.M.M and Urbano, M.R. (2010). The beta generalized half-normal distribution. Computational Statistics and Data Analysis, 54, 945-957.
  • Pewsey, A., Gómez, H.W. and Bolfarine, H. (2012). Likelihood-based inference for power distributions. Test, 21(4), 775-789.
  • R Development Core Team R. (2016). A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Rodrigues, J., Cancho, V.G., De Castro, M., Louzada-Neto, F. (2009). On the unication of the long-term survival models. Statistics and probability Letters, 79, 753-759.
  • Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6, 461-464.

The geometric power half-normal regression model with cure rate

Year 2018, Volume: 47 Issue: 2, 437 - 446, 01.04.2018

Abstract

In this paper we consider the geometric cure rate model defined in [16], using for $S_0(\cdot)$, the survival function of carcinogenic cells, an extension of the half-normal distribution based on the distribution of the maximum of a random sample. The implementation of maximum likelihood estimation for the model parameters is discussed and, nally, the model is fitted to a real database (Melanoma data set), and comparisons are performed with alternatives to the new $S_0(\cdot)$.

References

  • Akaike, H. (1974). A new look at the statistical model identication. IEEE Transactions of Automatic Control, 19(6), 716-723.
  • Berkson, J., Gage, R. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association, 47, 501-515.
  • Boag, J.W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society B, 11,15-53.
  • Cancho, V.G., Louzada, F., Barriga, G.D.C. (2011) The Geometric Birnbaum-Saunders regression model with cure rate. Journal of Statistical Planning an Inference, 142, 993-1000.
  • Cooray, K. and Ananda, M.M.A. (2008). A Generalization of the Half-Normal Distribution with Applications to Lifetime Data. Communications in Statistics - Theory and Methods, 37, 1323-1337.
  • Durrans, S.R. (1992). Distributions of fractional order statistics in hydrology. Water Resources Research, 28, 16491655.
  • Gómez, Y.M., Bolfarine, H. (2015). Likelihood-based inference for power half-normal distri- bution. Journal of Statistical Theory and Applications, 14, 383398.
  • Gupta, D. and Gupta, R.C. (2008). Analyzing skewed data by power normal model. Test, 17, 197210.
  • Lehmann, E.L. (1953). The power of rank tests. Annals of Mathematical Statistics, 24, 2343.
  • Maller, R.A., Zhou, X., (1996). Survival Analysis with Long-Term Survivors. Wiley, New York.
  • Marshall A.W. and Olkin I. (2007). Life distributions: Structure of nonparametric, semi- parametric, and parametric families. Springer Science+Business Media, LLC, New York.
  • Perdona, G.S.C., Louzada-Neto, F. (2011). A general hazard model for lifetime data in the presence of cure rate. Journal of Applied Statistics 38, 1395-1405.
  • Pescim, R.R., Demétrio, C.G.B., Cordeiro, G.M., Ortega, E.M.M and Urbano, M.R. (2010). The beta generalized half-normal distribution. Computational Statistics and Data Analysis, 54, 945-957.
  • Pewsey, A., Gómez, H.W. and Bolfarine, H. (2012). Likelihood-based inference for power distributions. Test, 21(4), 775-789.
  • R Development Core Team R. (2016). A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Rodrigues, J., Cancho, V.G., De Castro, M., Louzada-Neto, F. (2009). On the unication of the long-term survival models. Statistics and probability Letters, 79, 753-759.
  • Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6, 461-464.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

Yolanda M. Gómez This is me

Heleno Bolfarine This is me

Publication Date April 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 2

Cite

APA Gómez, Y. M., & Bolfarine, H. (2018). The geometric power half-normal regression model with cure rate. Hacettepe Journal of Mathematics and Statistics, 47(2), 437-446.
AMA Gómez YM, Bolfarine H. The geometric power half-normal regression model with cure rate. Hacettepe Journal of Mathematics and Statistics. April 2018;47(2):437-446.
Chicago Gómez, Yolanda M., and Heleno Bolfarine. “The Geometric Power Half-Normal Regression Model With Cure Rate”. Hacettepe Journal of Mathematics and Statistics 47, no. 2 (April 2018): 437-46.
EndNote Gómez YM, Bolfarine H (April 1, 2018) The geometric power half-normal regression model with cure rate. Hacettepe Journal of Mathematics and Statistics 47 2 437–446.
IEEE Y. M. Gómez and H. Bolfarine, “The geometric power half-normal regression model with cure rate”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, pp. 437–446, 2018.
ISNAD Gómez, Yolanda M. - Bolfarine, Heleno. “The Geometric Power Half-Normal Regression Model With Cure Rate”. Hacettepe Journal of Mathematics and Statistics 47/2 (April 2018), 437-446.
JAMA Gómez YM, Bolfarine H. The geometric power half-normal regression model with cure rate. Hacettepe Journal of Mathematics and Statistics. 2018;47:437–446.
MLA Gómez, Yolanda M. and Heleno Bolfarine. “The Geometric Power Half-Normal Regression Model With Cure Rate”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, 2018, pp. 437-46.
Vancouver Gómez YM, Bolfarine H. The geometric power half-normal regression model with cure rate. Hacettepe Journal of Mathematics and Statistics. 2018;47(2):437-46.