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Cure Models based on Weibull Distribution with and without Covariates using Right Censored Data

Affiliations

  • Department of Mathematics and Statistics, Yobe State University, Nigeria
  • Department of Mathematics, Universiti Putra Malaysia Darul-Ehsan, Serdang Selangor, Selangor, Malaysia

Abstract


In this paper we use a methodology based on the Weibull distributions covariates in the presence of cure fraction models, censored data and covariates. Objective: The objective of the study is to check the performance of mixture and non-mixture cure models based on LPML. Methods/Analysis: Two models were explored here in which are the mixture and non-mixture cure fraction models. Inferences for the models are obtained under the Bayesian approach via Markov Chain Monte Carlo (MCMC) where the posterior estimates were obtained by using Metropolis-Hastings sampling methods in the presence of covariates and without covariates considering a real life time dataset and comparing the two cure models using the Log Pseudo Maximum Likelihood estimates (LPML) and some related special cases of the distribution. Findings/ Conclusion: We observed that the Weibull distribution has the least LPML value while its special cases where the two models are quite similar having the highest values on the other hand, the Mixture fits better than the non-mixture having the highest (LPML) based on the results obtain from all the models suggesting that the standard parametric cure (mixture) model fits the AML data which shows a great indication of similarity with the covariates and flexibility of the models.

Keywords

Bayesian Analysis, Cure Models, MCMC Algorithm, Right Censored Data, Survival Analysis, Weibull Distribution.

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References


  • Tsodikov AD, Ibrahim JG, Yakovlev AY. Estimating cure rates from survival data: An alternative to two-component mixture model. J Amer Statist Assoc. 2003; 98(464):1063–78.
  • Achcar JA, Coelho-Barros EA, Mazucheli J. Cure fraction models using mixture and non-mixture models. Tatra Mountains Mathematical Publications. 2012; 51:1–9.
  • Ibrahim NA, Taweab F, Arasan J. A parametric non-mixture cure survival model with censored data. Computational Problems in Engineering. Springer International Publishing. 2014; 307:231–8.
  • Aljawadi B, Bakar MRA, Ibrahim NA, Midi H. Parametric estimation of the cure fraction based on BCH Model using left-censored data with covariates. Modern Applied Science. 2011; 5(3):103–10.
  • Bakar MRA, et al. Bayesian approach for joint longitudinal and time-to-event data with survival fraction. Bulletin of the Malaysian Mathematical Sciences Society. 2009; 32(1):75–100.
  • Chen MH, Ibrahim JG, Sinha D. A new Bayesian model for survival data with a surviving fraction. Journal of the American Statistical Association. 1999; 94:909–19.
  • Berkson J, Gage R. Survival curve for cancer patients following treatment. Journal of American Statistical Association. 1952; 47:501–15.
  • Chib S, Greenberg E. Understanding the Metropolis-Hastings algorithm. The American Statistician. 1995; 49(4):327–35.
  • Cordeiro GM,Carrasco JMF, Ortega EM. A generalized modified Weibull distribution for lifetime modelling. Statistical Computation Anals. 2008; 53(2):450–62.
  • Cordeiro GM, Nadarajah S, Ortega EM. General results for the beta Weibull distribution. Journal of Statistical Computation and Simulation. 2013; 83(6):1082–114.
  • Copelan EA, Biggs JC, Thompson JM, Crilley P, Szer J, Klein JP, Atkinson K. Treatment for acute myelocytic leukemia with allogeneic bone marrow transplantation following preparation with BuCy2. NCBI. 1991; 78(3):838–43.
  • Famoye F, Lee C, Olumolade O. The beta Weibull distribution. J Stat Theory Appl. 2005; 4:121–36.
  • Gelfand AE, Dey DK, Chang H. Model determination using predictive distributions with implementation via sampling-based methods. 1992. No. TR-462.
  • Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. 2nd ed. CRC Press; 2003.
  • Geisser S, Eddy WF. A predictive approach to model selection. Journal of the American Statistical Association. 1979; 74(365):153–60.
  • Gupta AK, Nadarajah S. Editors. Handbook of beta distribution and its applications. CRC Press. 2004.
  • Irvine T. The Rayleigh distribution. 2012.
  • Kim S, Xi Y, Chen MH. A new latent cure rate marker model for survival data. The Annals of Applied Statistics. 2009; 3(3):1124–46.
  • Lee C, Famoye F, Olumolade O. BetaWeibull distribution: Some properties and applications to censored data. J Mod Appl Stat Methods. 2007; 6(1):173–86.
  • Martinez EZ, Achcar JA, Jcome AA, Santos JS. 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. 2013; 112(3):343–55.
  • Mudholkar GS, Srivastava DK, Kollia GD. A generalization of the Weibull distribution with application to the analysis of survival data. Journal of American Statistical Association. 1996; 91:1575–83.
  • Eugene N, Lee C, Famoye F. Beta-normal distribution and its applications. Communt Stat Theory Methods. 2002; 31(4):497–512.
  • Seppa K, Hakulinen T, Kim HJ, Laara E. Cure fraction model with random effects for regional variation in cancer survival. Statistics in Medicine. 2010; 29(27):2781–93.
  • R software. Available from: http://CRAN.R-project.org/package
  • Venables WN, Ripley BD. Modern Applied Statistics with S. 4th ed. Springer; 2002.
  • Weibull WA. A statistical distribution of wide applicability. Journal of Applied Mechanics. 1951; 18:293–7.
  • Wahed AS, Luong TM, Jeong JH. A new generalization of Weibull distribution with application to a breast cancer data set. Statistics in Medicine. 2009; 28(16):2077–94.
  • Xiang L, Ma X, Yau KK. Mixture cure model with random effects for clustered and interval censored survival data. NCBI. 2011; 30(9):995–1006.
  • Carrasco JMF, Ortega EMM, Cordeiro GM.A generalized modified Weibull distribution for lifetime modeling. Computational Statistics and Data Analysis. 2008; 53:450–62.
  • Pal M, Ali MM, Woo J. Exponentiated Weibull distribution Statistica. 2006; 66 (2):139–47.
  • Sarhan AM, Zaindin M. Modified Weibull distribution. Applied Sciences. 2009; 11:123–36.
  • Nadarajah S, Kotz S. The beta exponential distribution. Reliability Engineering and System Safety. 2006; 91(6):689–97.
  • Yusuf MU, Bakar MRBA. A Bayesian estimation on right
  • censored survival data with mixture and non-mixture
  • cured fraction model based on Beta-Weibull distribution.
  • In Innovations through Mathematical and Statistical
  • Research: Proceedings of the 2nd International Conference
  • on Mathematical Sciences and Statistics (ICMSS2016) (Vol.
  • , No. 1, p. 020079).,AIP Publishing. June 2016.

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