Cured Fraction Models on Survival Data and Covariates with a Bayesian Parametric Estimation Methods
DOI:
10.56566/sigmamu.v1i1.45Downloads
Abstract
A cure fraction models are usually meant for survival data that contains a proportion of non subject individuals for the event under study. In order to estimate the cure fraction, two models namely mixture model and non-mixture model were commonly deployed. In this work, mixture and non-mixture cure fraction models were presented with survival data structure based on the beta-Weibull distribution. The beta-Weibull distribution is a four parameter distribution developed in this work as an alternative extension to the Weibull distribution in the analysis of lifetime data. The proposed extension allows the inclusion of covariates analysis in the model, in which the estimation of parameters were done under Bayesian approach using Gibbs sampling methods
Keywords:
Bayesian analysis Beta-Weibull distribution Cure fraction models Survival analysis MCMC algorithmReferences
Achcar, J. A., Coelho-Barros, E. A., & Mazucheli, J. (2012). Cure fraction models using mixture and non-mixture models. Tatra Mountains Mathematical Publications, 51(1), 1–9. https://doi.org/doi:10.2478/v10127-012-0001-4
Aljawadi, B., Abu Bakar, M., Ibrahim, N., & Midi, H. (2011). Parametric Estimation of the Cure Fraction Based on BCH Model Using Left-Censored Data with Covariates. Modern Applied Science, 5. https://doi.org/10.5539/mas.v5n3p103
Carrasco, J. M. F., Ortega, E. M. M., & Cordeiro, G. M. (2008). A generalized modified Weibull distribution for lifetime modeling. Computational Statistics & Data Analysis, 53(2), 450–462. https://doi.org/https://doi.org/10.1016/j.csda.2008.08.023
Cordeiro, G. M., Gomes, A. E., Da-Silva, C. Q., & Ortega, E. M. M. (2013). The beta exponentiated weibull distribution. Journal of Statistical Computation and Simulation, 83(1), 114–138. https://doi.org/10.1080/00949655.2011.615838
Cordeiro, G. M., Nadarajah, S., & Ortega, E. M. M. (2013). General results for the beta Weibull distribution. Journal of Statistical Computation and Simulation, 83(6), 1082–1114. https://doi.org/10.1080/00949655.2011.649756
Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31(4), 497–512. https://doi.org/10.1081/STA-120003130
Gelfand, A., Dey, D., & Chang, H. (1992). Model determination using predictive distributions with implementation via sampling-based methods.
Gelman, A., Carlin, J., Stern, H., Dunson, D., & Vehtari, A. (2013). Bayesian data analysis.
Klein, J. P., & Moschberger KM, M. L. (2003). Survival analysis: techniques for censored and truncated data.
Martinez, E. Z., Achcar, J. A., Jácome, A. A. A., & Santos, J. S. (2013a). 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(3), 343–355. https://doi.org/https://doi.org/10.1016/j.cmpb.2013.07.021
Martinez, E. Z., Achcar, J. A., Jácome, A. A. A., & Santos, J. S. (2013b). 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(3), 343–355. https://doi.org/10.1016/j.cmpb.2013.07.021
mechanics, W. W.-J. of applied, & 1951, undefined. (n.d.). A statistical distribution function of wide applicability. Cecs.Pdx.Edu.
Pal, M., Statistics, M. T.-A. J. of, & 2014, undefined. (2014). The beta transmuted Weibull distribution. Ajs.or.At, 43(2), 133–149.
Sauerbrei, W., Royston, P., Bojar, H., Cancer, C. S.-… J. of, & 1999, undefined. (1999). Modelling the effects of standard prognostic factors in node-positive breast cancer. Nature.Com.
Schwertman, N. C., & de Silva, R. (2007). Identifying outliers with sequential fences. Computational Statistics & Data Analysis, 51(8), 3800–3810. https://doi.org/https://doi.org/10.1016/j.csda.2006.01.019
Stacy, E. W. (1962). A Generalization of the Gamma Distribution. The Annals of Mathematical Statistics, 33(3), 1187–1192. http://www.jstor.org/stable/2237889
Tsodikov, A. D., Ibrahim, J. G., & Yakovlev, A. Y. (2003). Estimating Cure Rates from Survival Data: An Alternative to Two-Component Mixture Models. Journal of the American Statistical Association, 98(464), 1063–1078. https://doi.org/10.1198/01622145030000001007
Wahed, A. S., Luong, T. M., & Jeong, J. H. (2009). A new generalization of Weibull distribution with application to a breast cancer data set. Statistics in Medicine, 28(16), 2077–2094. https://doi.org/10.1002/SIM.3598
Waloddi, W., & Stockholm, S. (1951). A Statistical Distribution Function of Wide Applicability. Journal of Applied Mechanics, 1951(September), 293–297.
License
Copyright (c) 2023 Umar Yusuf Madaki, Babangida Ibrahim Babura, Muhammad Sani, Ibrahim Abdullahi
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
