The Gamma-Akash probability Model for Survival Analysis of Cancer Patients
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Abstract
The search for a suitable probability models for the survival analysis of cancer patients are really challenging because survival times of cancer patients are stochastic in nature and are highly positively skewed. The classical well-known one parameter and two-parameter probability models rarely provide better fit to survival times of cancer patients. In this paper a compound probability model called gamma-Akash distribution, which is a compounding of gamma and Akash distribution, has been proposed for the modeling of survival times of cancer patients. Many important properties of the suggested distribution including its shape, moments (negative moments), hazard function, reversed hazard function, quantile function have been discussed. Method of maximum likelihood has been used to estimate its parameters. A simulation study has been conducted to know the consistency of maximum likelihood estimators. Two real datasets, one relating to acute bone cancer and the other relating to head and neck cancer, has been considered to examine the applicability, suitability and flexibility of the proposed distribution. The goodness of fit of the proposed distribution shows quite satisfactory fit over other considered distributions.
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References
Abdi, M., Asgharzadeh, A., Bakouch, H.S. & Alipour, Z. A new compound Gamma and Lindley distribution with Application to failure data, Austrian Journal of Statistics, 48 ,54-75, (2019). http://dx.doi.org/10.17713/ajs.v48i3.843
Ahmed, M.A., Mahmoud M.R. & Elsherbini E.A. The New Kumraswami Family of Generalized Distributions with Application , Pakistan Journal of Statistics and Operation Research, 11(2),159-180, (2015) https://www.mdpi.com/2227-7390/8/11/1989#
Cordeiro,G.M.,Ortega, E.M.M & Da-Cunha, D.C.C. The exponentiated Generalized Class of Distributions, Journal of Data Science ,11(1),1-27, (2013). https://doi.org/10.6339/JDS.2013.11%281%29.1086
Cordeiro,G.M.,Ortega,E.M.M & Nadarajah,S. The Kumaraswamy Weibull Distribution with Application to failure data , Journal of Franklin Institute ,347(8),1399-1429, (2010). https://doi.org/10.1016/j.jfranklin.2010.06.010
Efron B.Logistic regression, survival analysis, and the Kaplan-Meier curve, Journal of the American statistical Association , 83(402),414–425, (1988). https://doi.org/10.2307/2288857
Eissa, F.H.The Exponentiated Kumaraswamy-Weibull Distribution with Application to Real Data, International Journal of Statistics and Probability , 6(6) ,167-182, (2017). http://dx.doi.org/10.5539/ijsp.v6n6p167
Famoye,F., Lee,C. and Olumolade,O. The Beta-Weibull Distribution, Journal of Statistical Theory and Applications, 4(2),121-136, (2005). doi: 10.22237/jmasm/1177992960
Glaser,R.E.Bathtub and Related Failure Rate Characterizations, Journal of the American Statistical Association, 75,667-672,(1980). https://doi.org/10.2307/2287666
Klakattawi, H.S. Survival Analysis of Cancer Patients using a New Extended Weibull Distribution, PLOS ONE ,17(2), 1-20, (2022). https://doi.org/10.1371/journal.pone.0264229
Lindley, D.V. Fiducial Distribution and Bayes’ Theorem, Journal of The Royal Statistical Society, 20(1), 102-107, (1958). https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
Mansour M., Yousof H.M., Shehata W.A. & Ibrahim M. A new two parameter Burr XII distribution: properties, copula, different estimation methods and modeling acute bone cancer data, Journal of Nonlinear Science and Applications, 13(5),223–238,(2020). http://dx.doi.org/10.22436/jnsa.013.05.01
Nassar,M. Alzaatreh,A., Mead M. & Abo-Kasem,O. Alpha Power Weibull Distribution: Properties and Applications, Communications in Statistics-theory and Methods , 46(20), 10236-10252, (2017). http://dx.doi.org/10.1080/03610926.2016.1231816
Ray, M. & Shanker, R. A Compound of Gamma and Shanker Distribution, Reliability Theory & Applications, 18(2), 87-99, (2023a).
Ray, M. & Shanker, R. A Compound of Exponential and Shanker Distribution with an Application, Journal of Scientific Research of The Banaras Hindu University, 67(4), 39-46, (2023b). http://dx.doi.org/10.37398/JSR.2023.670407
Shaked, M. & Shanthikumar, J.G. Stochastic Orders and Their Applications. Academic Press New Work, (1994)
Shanker, R., Baishya, J.,Ray, M., & Prodhani, H.,R. Power Uma distribution with properties and Applications in Survival Analysis ,Journal of Xidian University, 17(12),849-860. http://dx.doi.org/10.37896/jxu17.12/077
Shanker, R., Shukla, K.K., Shanker, R. & Tekie, A.L. On modelling of Lifetime data using two-parameter gamma and Weibull distributions, Biometrics & Biostatistics International journal, 4(5), 201 – 206, (2016) http://dx.doi.org/10.15406/bbij.2016.04.00107
Shanker, R. Shanker Distribution and its Applications, International Journal of Statistics and Applications,5(6),338-348,(2015a) doi:10.5923/j.statistics.20150506.08
Shanker ,R. Akash distribution and its Applications, Biometrics and Biostatistics International Journal, 4(3), 65-75, (2015b).doi:10.5923/j.ijps.20150403.01
Weibull W. A statistical distribution function of wide applicability, Journal of applied mechanics, 18(3):293–297, (1951). https://doi.org/10.1115/1.4010337