The geometric power half-normal regression model with cure rate

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

Yolanda M. Gómez Heleno Bolfarine

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 $S_0(\cdot)$.

Keywords

Cure rate survival model, Half-normal distribution, Maximum likelihood, Power distribution

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.