Abstract
This paper presents estimates for the parameters included in long-term mixture and non-mixture lifetime models, applied to analyze survival data when some individuals may never experience the event of interest. We consider the case where the lifetime data have a three-parameter Burr XII distribution, which includes the popular Weibull mixture model as a special case.
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References
Burr IW (1942) Cumulative frequency functions. Ann Math Stat 13:215–232
Chen MH, Ibrahim JG, Sinha D (1999) A new Bayesian model for survival data with a surviving fraction. J Am Stat Assoc 94(447):909–919
Chib S, Greenberg E (1995) Undestanding the Metropolis-Hastings algorithm. Am Stat 49(4):327–335
Gelfand AE, Smith AFM (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85(410):398–409
Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481
Kersey JH, Weisdorf D, Nesbit ME, LeBien TW, Woods WG, McGlave PB, Kim T, Vallera DA, Goldman AI, Bostrom B (1987) Comparison of autologous and allogeneic bone marrow transplantation for treatment of high-risk refractory acute lymphoblastic leukemia. N Engl J Med 317(8):461–467
Lambert PC, Dickman PW, Weston CL, Thompson JR (2010) Estimating the cure fraction in population-based cancer studies by using finite mixture models. J R Stat Soc, Ser C, Appl Stat 59(1):35–55
Lambert PC, Thompson JR, Weston CL, Dickman PW (2007) Estimating and modeling the cure fraction in population-based cancer survival analysis. Biostatistics 8(3):576–594
Maller RA, Zhou X (1996) Survival analysis with long-term survivors. Wiley series in probability and statistics: applied probability and statistics. Wiley, Chichester
Rodrigues J, Cancho VG, de Castro M, Louzada-Neto F (2009) On the unification of long-term survival models. Stat Probab Lett 79(6):753–759
SAS (2010) The MCMC procedure, SAS/STAT® user’s guide, version 9.22. SAS Institute Inc., Cary, NC
Tsodikov AD, Ibrahim JG, Yakovlev AY (2003) Estimating cure rates from survival data: an alternative to two-component mixture models. J Am Stat Assoc 98(464):1063–1078
Yakovlev AY, Tsodikov AD, Asselain B (1996) Stochastic models of tumor latency and their biostatistical applications. World Scientific, Singapore
Yin G, Ibrahim JG (2005) Cure rate models: a unified approach. Can J Stat 33(4):559–570
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Coelho-Barros, E.A., Achcar, J.A., Mazucheli, J. (2015). Mixture and Non-mixture Cure Rate Model Considering the Burr XII Distribution. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_24
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DOI: https://doi.org/10.1007/978-3-319-13881-7_24
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