Discrete and continuous bivariate lifetime models in presence of cure rate: a comparative study under Bayesian approach

References

• J.A. Achcar and R.A. Leandro, Use of Markov Chain Monte Carlo methods in a Bayesian analysis of the Block and Basu bivariate exponential distribution, Ann. Inst. Statist. Math. 50 (1998), pp. 403–416. doi: 10.1023/A:1003582409664
   Web of Science ®Google Scholar
• J.A. Achcar, E.A. Coelho-Barros, and J. Mazucheli, Cure fraction models using mixture and non-mixture models, Tatra. Mt. Math. Publ. 51 (2012), pp. 1–9.
   Google Scholar
• J.A. Achcar, E.A. Coelho-Barros, and J. Mazucheli, Block and Basu bivariate lifetime distribution in the presence of cure fraction, J. Appl. Stat. 40 (2013), pp. 1864–1874. doi: 10.1080/02664763.2013.798630
   Web of Science ®Google Scholar
• J.A Achcar, N. Davarzani, and R. Souza, Basu–Dhar bivariate geometric distribution in the presence of covariates and censored data: A Bayesian approach, J. Appl. Stat. 43 (2016), pp. 1636–1648. doi: 10.1080/02664763.2015.1117589
   Web of Science ®Google Scholar
• B.C. Arnold, A characterization of the exponential distribution by multivariate geometric compounding, Sankhyā 37 (1975), pp. 164–173.
   Google Scholar
• A.P. Basu and S. Dhar, Bivariate geometric distribution, J. Appl. Statist. Sci. 2 (1995), pp. 33–44.
   Google Scholar
• H.W. Block and A. Basu, A continuous bivariate exponential extension, J. Amer. Statist. Assoc. 69 (1974), pp. 1031–1037.
   Web of Science ®Google Scholar
• G.E. Box and G.C. Tiao, Bayesian Inference in Statistical Analysis, Vol. 40, John Wiley & Sons, 2011.
   Google Scholar
• V.G. Cancho and H. Bolfarine, Modeling the presence of immunes by using the exponentiated-Weibull model, J. Appl. Stat. 28 (2001), pp. 659–671. doi: 10.1080/02664760120059200
   Web of Science ®Google Scholar
• S. Chib and E. Greenberg, Understanding the Metropolis–Hastings algorithm, Am. Stat. 49 (1995), pp. 327–335.
   Web of Science ®Google Scholar
• D.R. Cox, Regression models and life tables (with discussion), J. R. Stat. Soc. Ser. B 34 (1972), pp. 187–220.
   Web of Science ®Google Scholar
• N. Davarzani, J.A. Acgcar, E.N. Smirno, and R. Peeters, Bivariate lifetime geometric distribution in presence of cure fractions, J. Data Sci. 13 (2015), pp. 755–770.
   Google Scholar
• R. De Angelis, R. Capocaccia, T. Hakulinen, B. Soderman, and A. Verdecchia, Mixture models for cancer survival analysis: Application to population-based data with covariates, Stat. Med. 18 (1999), pp. 441–454. doi: 10.1002/(SICI)1097-0258(19990228)18:4<441::AID-SIM23>3.0.CO;2-M
   PubMed Web of Science ®Google Scholar
• A.E. Gelfand and A.F.M. Smith, Sampling-based approaches to calculating marginal densities, J. Amer. Statist. Assoc. 85 (1990), pp. 398–409. doi: 10.1080/01621459.1990.10476213
   Web of Science ®Google Scholar
• E.J. Gumbel, Bivariate exponential distributions, J. Amer. Statist. Assoc. 55 (1960), pp. 698–707. doi: 10.1080/01621459.1960.10483368
   Web of Science ®Google Scholar
• W.J. Huster, R. Brookmeyer, and S.G. Self, Modelling paired survival data with covariates, Biometrics45 (1989), pp. 145–156. doi: 10.2307/2532041
   PubMed Web of Science ®Google Scholar
• J.G. Ibrahim, M.H. Chen, and D. Sinha, Bayesian Survival Analysis, Wiley Online Library, 2005.
   Google Scholar
• G. John, C. Louis, A. Berner, and D. Genné, Data from: Tobacco stained fingers and its association with death and hospital admission: A retrospective cohort study (2015). Available at https://doi.org/10.5061/dryad.4478v.
   Google Scholar
• G. John, C. Louis, A. Berner, and D. Genné, Tobacco stained fingers and its association with death and hospital admission: A retrospective cohort study, PLoS ONE 10 (2015), p. e0138211. doi: 10.1371/journal.pone.0138211
   PubMed Web of Science ®Google Scholar
• G. John, S. Pasche, N. Rothen, A. Charmoy, C. Delhumeau-Cartier, and D. Genné, Tobacco-stained fingers: A clue for smoking-related disease or harmful alcohol use? A case-control study, BMJ Open 3 (2013), p. e003304. doi: 10.1136/bmjopen-2013-003304
   PubMed Web of Science ®Google Scholar
• E.L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), pp. 457–481. doi: 10.1080/01621459.1958.10501452
   Web of Science ®Google Scholar
• P.C. Lambert, J.R. Thompson, C.L. Weston, and P.W. Dickman, Estimating and modeling the cure fraction in population-based cancer survival analysis, Biostatistics 8 (2007), pp. 576–594. doi: 10.1093/biostatistics/kxl030
   PubMed Web of Science ®Google Scholar
• W. Lu, Efficient estimation for an accelerated failure time model with a cure fraction, Statist. Sinica 20 (2010), p. 661.
   PubMed Web of Science ®Google Scholar
• R.A. Maller and X. Zhou, Survival Analysis with Long-term Survivors, Wiley, New York, 1996.
   Google Scholar
• M. Othus, B. Barlogie, M.L. LeBlanc, and J.J. Crowley, Cure models as a useful statistical tool for analyzing survival, Clin. Cancer Res. 18 (2012), pp. 3731–3736. doi: 10.1158/1078-0432.CCR-11-2859
   PubMed Web of Science ®Google Scholar
• D.L. Price and A.K. Manatunga, Modelling survival data with a cured fraction using frailty models, Stat. Med. 20 (2001), pp. 1515–1527. doi: 10.1002/sim.687
   PubMed Web of Science ®Google Scholar
• R CoreTeam, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2016). Available at https://www.R-project.org/.
   Google Scholar
• M. Schemper, A. Kaider, S. Wakounig, and G. Heinze, Estimating the correlation of bivariate failure times under censoring, Stat. Med. 32 (2013), pp. 4781–4790. doi: 10.1002/sim.5874
   PubMed Web of Science ®Google Scholar
• D. Spiegelhalter, A. Thomas, N. Best, and D. Lunn, OpenBUGS User Manual, Version 3.0. 2, MRC Biostatistics Unit, Cambridge, 2007.
   Google Scholar
• K. Sun and A.P. Basu, A characterization of a bivariate geometric distribution, Statist. Probab. Lett. 23 (1995), pp. 307–311. doi: 10.1016/0167-7152(94)00129-V
   Web of Science ®Google Scholar
• A. Tsodikov, J. Ibrahim, and A. Yakovlev, Estimating cure rates from survival data: An alternative to two-component mixture models, J. Amer. Statist. Assoc. 98 (2003), pp. 1063–1078. doi: 10.1198/01622145030000001007
   PubMed Web of Science ®Google Scholar
• M. Vahidpour, Cure rate models, Ph.D. diss., École Polytechnique de Montréal, 2016.
   Google Scholar
• A. Wienke, P. Lichtenstein, and A.I. Yashin, A bivariate frailty model with a cure fraction for modeling familial correlations in diseases, Biometrics 59 (2003), pp. 1178–1183. doi: 10.1111/j.0006-341X.2003.00135.x
   PubMed Web of Science ®Google Scholar
• A. Wienke, I. Locatelli, and A.I. Yashin, The modelling of a cure fraction in bivariate time-to-event data, Austrian J. Statist. 35 (2006), pp. 67–76. doi: 10.17713/ajs.v35i1.349
   Google Scholar
• G. Yin and J.G. Ibrahim, Cure rate models: A unified approach, Canad. J. Statist. 33 (2005), pp. 559–570. doi: 10.1002/cjs.5550330407
   Web of Science ®Google Scholar
• B. Yu, R.C. Tiwari, K.A. Cronin, and E.J. Feuer, Cure fraction estimation from the mixture cure models for grouped survival data, Stat. Med. 23 (2004), pp. 1733–1747. doi: 10.1002/sim.1774
   PubMed Web of Science ®Google Scholar