{"title":"A Mixture Model of Two Different Distributions Approach to the Analysis of Heterogeneous Survival Data","authors":"\u00dclk\u00fc Eri\u015fo\u011flu, Murat Eri\u015fo\u011flu, Hamza Erol","volume":54,"journal":"International Journal of Computer and Information Engineering","pagesStart":544,"pagesEnd":549,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/2675","abstract":"In this paper we propose a mixture of two different\r\ndistributions such as Exponential-Gamma, Exponential-Weibull and\r\nGamma-Weibull to model heterogeneous survival data. Various\r\nproperties of the proposed mixture of two different distributions are\r\ndiscussed. Maximum likelihood estimations of the parameters are\r\nobtained by using the EM algorithm. Illustrative example based on\r\nreal data are also given.","references":"[1] Angelis R. De, Capocaccia R., Hakulinen T., Soderman B. and\r\nVerdecchia A., Mixture Models for Cancer Survival Analysis:\r\nApplication to Population-Based Data With Covariates, Statistics in\r\nMedicine, 18, 441-454, 1999.\r\n[2] Berkson, J., Gage, R.P, Survival cure for cancer patients following\r\ntreatment. Journal of the American Statistical Association 47, 501-515,\r\n1952.\r\n[3] Chen W.C., Hill B.M., Greenhouse J.B. and Fayos J.V.,. Bayesian\r\nAnalysis of Survival Curves for Cancer Patients Following Treatment.\r\nBayesian Statistics 2, 299-328, 1985.\r\n[4] Colvert, R.E. and Boardman, T.J., Estimation in the piece-wise constant\r\nhazard rate model. Communication in Statistics-Theory. Methods.\r\n11:1013-1029, 1976.\r\n[5] Everitt B.S. and Hand D.J.,. Finite Mixture Distributions, Chapman and\r\nHall, London, 1981.\r\n[6] Jiang, R. and Murthy, D.N.P., Two sectional models involving three\r\nWeibull distributions. Quality and Reliability Engineering \u2500\u2591nternational\r\n13:83-96, 1997.\r\n[7] Kleinbanm D.G. and Klein M., Survival Analysis: A Self-Learning Text,\r\nSecond Edition, Springer, 2005.\r\n[8] Lawless J.F., Statistics Models and Methods for Lifetime Data, Second\r\nEdition, John Wiley & Sons, New Jersey, 2003\r\n[9] Lee E.T. and Wang J.W., Statistical Methods For Survival Data\r\nAnalysis, Third Edition, John Wiley &Sons, New York, 2003.\r\n[10] Machin D, Cheung Y.B. and Parmar M.K,. Survival Analysis: A\r\nPractical Approach, Second Edition, John Wiley & Sons, 2006.\r\n[11] Marin J.M., Rodriguez-Bernal M.T. and Wiper M.P., Using Weibull\r\nMixture Distributions to Model Heterogeneous Survival Data,\r\nCommunication in Statistics-Simulation and Computation, 34, 673-684,\r\n2005.\r\n[12] Mclachlan G.J. and G.J. Peel D., Finite Mixture Model, Wiley, New\r\nYork. 2001.\r\n[13] Quiang J., A Bayesian Weibull Survival Model. Unpublished Ph.D.\r\nThesis, Institute of Statistical and Decision Sciences, Duke University:\r\nNorth Corolina, 1994.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 54, 2011"}