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A Mixture Model of Two Different Distributions Approach to the Analysis of Heterogeneous Survival Data

Authors: Ülkü Erişoğlu, Murat Erişoğlu, Hamza Erol

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057689

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[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.