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http://dx.doi.org/10.5351/CSAM.2017.24.1.043

Regression models generated by gamma random variables with long-term survivors  

Ortega, Edwin M.M. (Departamento de Ciencias Exatas, USP)
Cordeiro, Gauss M. (Departamento de Estatistica, UFPE)
Hashimoto, Elizabeth M. (Departamento Academico de Matematicas, UTFPR)
Suzuki, Adriano K. (Departamento de Matematica Aplicada e Estatistica, USP)
Publication Information
Communications for Statistical Applications and Methods / v.24, no.1, 2017 , pp. 43-65 More about this Journal
Abstract
We propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution and the time for the event follows the gamma-G family of distributions. The extended family of gamma-G failure-time models with long-term survivors is flexible enough to include many commonly used failure-time distributions as special cases. We consider a frequentist analysis for parameter estimation and derive appropriate matrices to assess local influence on the parameters. Further, various simulations are performed for different parameter settings, sample sizes and censoring percentages. We illustrate the performance of the proposed regression model by means of a data set from the medical area (gastric cancer).
Keywords
gamma-G family; lifetime data; long-term survivors; Poisson distribution; regression model; sensitivity analysis;
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1 Balakrishnan N and Pal S (2012). EM algorithm-based likelihood estimation for some cure rate models, Journal of Statistical Theory and Practice, 6, 698-724.   DOI
2 Balakrishnan N and Pal S (2013). Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family, Computational Statistics and Data Analysis, 67, 41-67.   DOI
3 Balakrishnan N and Pal S (2015a). Likelihood inference for flexible cure rate models with gamma lifetimes, Communications in Statistics-Theory and Methods, 44, 4007-4048.   DOI
4 Balakrishnan N and Pal S (2015b). An EM algorithm for the estimation of flexible cure rate model parameters with generalized gamma lifetime and model discrimination using likelihood- and information-based methods, Computational Statistics, 30, 151-189.   DOI
5 Balakrishnan N and Pal S (2016). Expectation maximization-based likelihood inference for flexible cure rate models with Weibull lifetimes, Statistical Methods in Medical Research, 25, 1535-1563.   DOI
6 Balakrishnan N, Koutras MV, Milienos F, and Pal S (2016). Piecewise linear approximations for cure rate models and associated inferential issues, Methodology and Computing in Applied Probability, 18, 937-966.   DOI
7 Chen MH, Ibrahim JG, and Sinha D (1999). A new Bayesian model for survival data with a surviving fraction, Journal of the American Statistical Association, 94, 909-919.   DOI
8 Cook RD (1986). Assessment of local influence, Journal of the Royal Statistical Society Series B (Methodological), 48, 133-169.   DOI
9 Cooner F, Banerjee S, Carlin BP, and Sinha D (2007). Flexible cure rate modeling under latent activation schemes, Journal of the American Statistical Association, 102, 560-572.   DOI
10 Cooray K and Ananda MMA (2008). A generalized of the half-normal distribution with applications to lifetime data, Communications in Statistics - Theory and Methods, 37, 1323-1337.
11 Fachini JB, Ortega EMM, and Cordeiro GM (2014). A bivariate regression model with cure fraction, Journal of Statistical Computation and Simulation, 84, 1580-1595.   DOI
12 Flajolet P and Odlyzko A (1990). Singularity analysis of generating functions, SIAM Journal on Discrete Mathematics, 3, 216-240.   DOI
13 Gradshteyn IS and Ryzhik IM (2000). Table of Integrals, Series and Products(6th ed), Academic Press, San Diego, CA.
14 Hashimoto EM, Cordeiro GM, Ortega EMM (2013). The new Neyman type A beta Weibull model with long-term survivors, Computational Statistics, 28, 933-954.   DOI
15 Ibrahim JG, Chen MH, and Sinha D (2001). Bayesian Survival Analysis, Springer, New York.
16 Maller RA and Zhou X (1996). Survival Analysis with Long-Term Survivors, John Wiley & Sons, New York.
17 Martinez EZ, Achcar JA, Jacome AAA, and Santos JS (2013). Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data, Computer Methods and Programs in Biomedicine, 112, 343-355.   DOI
18 Nadarajah S, Cordeiro GM, and Ortega EMM (2015). The Zografos-Balakrishnan-G family of distributions: mathematical properties and applications, Communications in Statistics - Theory and Methods, 44, 186-215.   DOI
19 Nadarajah S and Kotz S (2006). The beta exponential distribution, Reliability Engineering and System Safety, 91, 689-697.   DOI
20 Ortega EMM, Cordeiro GM, Campelo AK, Kattan MW, and Cancho VG (2015). A power series beta Weibull regression model for predicting breast carcinoma, Statistics in Medicine, 34, 1366-1388.   DOI
21 Ortega EMM, Cordeiro GM, and Kattan MW (2012). The negative binomial-beta Weibull regression model to predict the cure of prostate cancer, Journal of Applied Statistics, 39, 1191-1210.   DOI
22 Ristic MM and Balakrishnan N (2012). The gamma-exponentiated distribution, Journal of Statistical Computation and Simulation, 82, 1191-1206.   DOI
23 Rodrigues J, Cancho VG, de Castro M, and Louzada-Neto F (2009). On the unification of the longterm survival models, Statistics and Probability Letters, 79, 753-759.   DOI
24 Tsodikov AD, Ibrahim JG, and Yakovlev AY (2003). Estimating cure rates from survival data: an alternative to two-component mixture models, Journal of the American Statistical Association, 98, 1063-1078.   DOI
25 Yakovlev AY and Tsodikov AD (1996). Stochastic Models of Tumor Latency and Their Biostatistical Applications, World Scientific Publishing, Singapore.
26 Zhu H, Ibrahim JG, Lee S, and Zhang H (2007). Perturbation selection and influence measures in local influence analysis, The Annals of Statistics, 35, 2565-2588.   DOI
27 Zografos K and Balakrishnan N (2009). On families of beta-and generalized gamma-generated distributions and associated inference, Statistical Methodology, 6, 344-362.   DOI