A Mixture Model of Two Different Distributions Approach to the Analysis of Heterogeneous Survival Data
In this paper we propose a mixture of two different
distributions such as Exponential-Gamma, Exponential-Weibull and
Gamma-Weibull to model heterogeneous survival data. Various
properties of the proposed mixture of two different distributions are
discussed. Maximum likelihood estimations of the parameters are
obtained by using the EM algorithm. Illustrative example based on
real data are also given.
[1] Angelis R. De, Capocaccia R., Hakulinen T., Soderman B. and
Verdecchia A., Mixture Models for Cancer Survival Analysis:
Application to Population-Based Data With Covariates, Statistics in
Medicine, 18, 441-454, 1999.
[2] Berkson, J., Gage, R.P, Survival cure for cancer patients following
treatment. Journal of the American Statistical Association 47, 501-515,
1952.
[3] Chen W.C., Hill B.M., Greenhouse J.B. and Fayos J.V.,. Bayesian
Analysis of Survival Curves for Cancer Patients Following Treatment.
Bayesian Statistics 2, 299-328, 1985.
[4] Colvert, R.E. and Boardman, T.J., Estimation in the piece-wise constant
hazard rate model. Communication in Statistics-Theory. Methods.
11:1013-1029, 1976.
[5] Everitt B.S. and Hand D.J.,. Finite Mixture Distributions, Chapman and
Hall, London, 1981.
[6] Jiang, R. and Murthy, D.N.P., Two sectional models involving three
Weibull distributions. Quality and Reliability Engineering ─░nternational
13:83-96, 1997.
[7] Kleinbanm D.G. and Klein M., Survival Analysis: A Self-Learning Text,
Second Edition, Springer, 2005.
[8] Lawless J.F., Statistics Models and Methods for Lifetime Data, Second
Edition, John Wiley & Sons, New Jersey, 2003
[9] Lee E.T. and Wang J.W., Statistical Methods For Survival Data
Analysis, Third Edition, John Wiley &Sons, New York, 2003.
[10] Machin D, Cheung Y.B. and Parmar M.K,. Survival Analysis: A
Practical Approach, Second Edition, John Wiley & Sons, 2006.
[11] Marin J.M., Rodriguez-Bernal M.T. and Wiper M.P., Using Weibull
Mixture Distributions to Model Heterogeneous Survival Data,
Communication in Statistics-Simulation and Computation, 34, 673-684,
2005.
[12] Mclachlan G.J. and G.J. Peel D., Finite Mixture Model, Wiley, New
York. 2001.
[13] Quiang J., A Bayesian Weibull Survival Model. Unpublished Ph.D.
Thesis, Institute of Statistical and Decision Sciences, Duke University:
North Corolina, 1994.
[1] Angelis R. De, Capocaccia R., Hakulinen T., Soderman B. and
Verdecchia A., Mixture Models for Cancer Survival Analysis:
Application to Population-Based Data With Covariates, Statistics in
Medicine, 18, 441-454, 1999.
[2] Berkson, J., Gage, R.P, Survival cure for cancer patients following
treatment. Journal of the American Statistical Association 47, 501-515,
1952.
[3] Chen W.C., Hill B.M., Greenhouse J.B. and Fayos J.V.,. Bayesian
Analysis of Survival Curves for Cancer Patients Following Treatment.
Bayesian Statistics 2, 299-328, 1985.
[4] Colvert, R.E. and Boardman, T.J., Estimation in the piece-wise constant
hazard rate model. Communication in Statistics-Theory. Methods.
11:1013-1029, 1976.
[5] Everitt B.S. and Hand D.J.,. Finite Mixture Distributions, Chapman and
Hall, London, 1981.
[6] Jiang, R. and Murthy, D.N.P., Two sectional models involving three
Weibull distributions. Quality and Reliability Engineering ─░nternational
13:83-96, 1997.
[7] Kleinbanm D.G. and Klein M., Survival Analysis: A Self-Learning Text,
Second Edition, Springer, 2005.
[8] Lawless J.F., Statistics Models and Methods for Lifetime Data, Second
Edition, John Wiley & Sons, New Jersey, 2003
[9] Lee E.T. and Wang J.W., Statistical Methods For Survival Data
Analysis, Third Edition, John Wiley &Sons, New York, 2003.
[10] Machin D, Cheung Y.B. and Parmar M.K,. Survival Analysis: A
Practical Approach, Second Edition, John Wiley & Sons, 2006.
[11] Marin J.M., Rodriguez-Bernal M.T. and Wiper M.P., Using Weibull
Mixture Distributions to Model Heterogeneous Survival Data,
Communication in Statistics-Simulation and Computation, 34, 673-684,
2005.
[12] Mclachlan G.J. and G.J. Peel D., Finite Mixture Model, Wiley, New
York. 2001.
[13] Quiang J., A Bayesian Weibull Survival Model. Unpublished Ph.D.
Thesis, Institute of Statistical and Decision Sciences, Duke University:
North Corolina, 1994.
@article{"International Journal of Information, Control and Computer Sciences:51805", author = "Ülkü Erişoğlu and Murat Erişoğlu and Hamza Erol", title = "A Mixture Model of Two Different Distributions Approach to the Analysis of Heterogeneous Survival Data", abstract = "In this paper we propose a mixture of two different
distributions such as Exponential-Gamma, Exponential-Weibull and
Gamma-Weibull to model heterogeneous survival data. Various
properties of the proposed mixture of two different distributions are
discussed. Maximum likelihood estimations of the parameters are
obtained by using the EM algorithm. Illustrative example based on
real data are also given.", keywords = "Exponential-Gamma, Exponential-Weibull, Gamma-Weibull, EM Algorithm, Survival Analysis.", volume = "5", number = "6", pages = "587-5", }