Defective models induced by gamma frailty term for survival data with cured fraction

References

• O.O. Aalen, Modelling heterogeneity in survival analysis by the compound Poisson distribution, Ann. Appl. Probab. 4 (1992), pp. 951–972. doi: 10.1214/aoap/1177005583
   Google Scholar
• O.O. Aalen and H.K. Gjessing, Understanding the shape of the hazard rate: A process point of view (with comments and a rejoinder by the authors), Stat. Sci. 16 (2001), pp. 1–22.
   Web of Science ®Google Scholar
• P. Andersen, O. Borgan, R. Gill and N. Keiding, Statistical models based on counting processes, Springer, NY, 1993.
   Google Scholar
• J. Balka, A.F. Desmond and P.D. McNicholas, Review and implementation of cure models based on first hitting times for wiener processes, Lifetime Data Anal. 15 (2009), pp. 147–176. doi: 10.1007/s10985-008-9108-y
   PubMed Web of Science ®Google Scholar
• J. Balka, A.F. Desmond and P.D. McNicholas, Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models, J. Appl. Stat. 38 (2011), pp. 127–144. doi: 10.1080/02664760903301127
   Web of Science ®Google Scholar
• J. Berkson and R.P. Gage, Survival curve for cancer patients following treatment, J. Am. Stat. Assoc. 47 (1952), pp. 501–515. doi: 10.1080/01621459.1952.10501187
   Web of Science ®Google Scholar
• J.W. Boag, Maximum likelihood estimates of the proportion of patients cured by cancer therapy, J. R. Stat. Soc. Ser. B Methodol. 11 (1949), pp. 15–53.
   Google Scholar
• P. Borges, Em algorithm-based likelihood estimation for a generalized Gompertz regression model in presence of survival data with long-term survivors: An application to uterine cervical cancer data, J. Stat. Comput. Simul. 87 (2017), pp. 1712–1722. doi: 10.1080/00949655.2017.1281927
   Web of Science ®Google Scholar
• V.F. Calsavara, A.S. Rodrigues, V.L.D. Tomazella and M. de Castro, Frailty models power variance function with cure fraction and latent risk factors negative binomial, Comm. Statist. Theory Methods 46 (2017), pp. 9763–9776. doi: 10.1080/03610926.2016.1218029
   Web of Science ®Google Scholar
• V.F. Calsavara, V.L.D. Tomazella and J.C. Fogo, Family generalized modified Weibull for analyzing long-term survival data, Adv. Appl. Stat. 23 (2011), pp. 59–76.
   Google Scholar
• V.F. Calsavara, V.L. Tomazella and J.C. Fogo, The effect of frailty term in the standard mixture model, Chil. J. Stat. 4 (2013), pp. 95–109.
   Google Scholar
• A.B. Cantor and J.J. Shuster, Parametric versus non-parametric methods for estimating cure rates based on censored survival data, Stat. Med. 11 (1992), pp. 931–937. doi: 10.1002/sim.4780110710
   PubMed Web of Science ®Google Scholar
• M.H. Chen, J.G. Ibrahim and D. Sinha, A new Bayesian model for survival data with a surviving fraction, J. Am. Stat. Assoc. 94 (1999), pp. 909–919. doi: 10.1080/01621459.1999.10474196
   Web of Science ®Google Scholar
• D.G. Clayton, A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika 65 (1978), pp. 141–151. doi: 10.1093/biomet/65.1.141
   Web of Science ®Google Scholar
• M.R. dos Santos, J.A. Achcar and E.Z. Martinez, Bayesian and maximum likelihood inference for the defective Gompertz cure rate model with covariates, Ciên. Nat. 39 (2017), p. 244.
   Google Scholar
• C. Elbers and G. Ridder, True and spurious duration dependence: The identifiability of the proportional hazard model, Rev. Econ. Stud. 49 (1982), pp. 403–409. doi: 10.2307/2297364
   Web of Science ®Google Scholar
• P.W. Gieser, M.N. Chang, P.V. Rao, J.J. Shuster and J. Pullen, Modelling cure rates using the Gompertz model with covariate information, Stat. Med. 17 (1998), pp. 831–839. doi: 10.1002/(SICI)1097-0258(19980430)17:8<831::AID-SIM790>3.0.CO;2-G
   PubMed Web of Science ®Google Scholar
• J.L. Haybittle, The estimation of the proportion of patients cured after treatment for cancer of the breast, Br. J. Radiol. 32 (1959), pp. 725–733. doi: 10.1259/0007-1285-32-383-725
   PubMed Web of Science ®Google Scholar
• P. Hougaard, A class of multivanate failure time distributions, Biometrika 73 (1986), pp. 671–678.
   Web of Science ®Google Scholar
• P. Hougaard, Survival models for heterogeneous populations derived from stable distributions, Biometrika 73 (1986), pp. 387–396. doi: 10.1093/biomet/73.2.387
   Web of Science ®Google Scholar
• P. Hougaard, Modelling heterogeneity in survival data, J. Appl. Probab. 28 (1991), pp. 695–701. doi: 10.2307/3214503
   Web of Science ®Google Scholar
• P. Hougaard, Frailty models for survival data, Lifetime. Data. Anal. 1 (1995), pp. 255–273. doi: 10.1007/BF00985760
   PubMedGoogle Scholar
• P. Hougaard, P. Myglegaard and K. Borch-Johnsen, Heterogeneity models of disease susceptibility, with application to diabetic nephropathy, Biometrics 50 (1994), pp. 1178–1188. doi: 10.2307/2533456
   PubMed Web of Science ®Google Scholar
• J.G. Ibrahim, M.H. Chen and D. Sinha, Bayesian semiparametric models for survival data with a cure fraction, Biometrics 57 (2001), pp. 383–388. doi: 10.1111/j.0006-341X.2001.00383.x
   PubMed Web of Science ®Google Scholar
• J.G. Ibrahim, M.H. Chen and D. Sinha, Bayesian Survival Analysis, Wiley Online Library, New York, 2005.
   Google Scholar
• J. Kettunen, et al., Transition intensities from unemployment, Tech. Rep. 1991.
   Google Scholar
• J.A. Laurie, C.G. Moertel, T.R. Fleming, H.S. Wieand, J.E. Leigh, J. Rubin, G.W. McCormack, J.B. Gerstner, J.E. Krook and J. Malliard, Surgical adjuvant therapy of large-bowel carcinoma: An evaluation of levamisole and the combination of levamisole and fluorouracil. the north central cancer treatment group and the Mayo Clinic. J. Clin. Oncol. 7 (1989), pp. 1447–1456. doi: 10.1200/JCO.1989.7.10.1447
   PubMed Web of Science ®Google Scholar
• I.M. Longini Jr and M.E. Halloran, A frailty mixture model for estimating vaccine efficacy, Appl. Stat. 45 (1996), pp. 165–173. doi: 10.2307/2986152
   Web of Science ®Google Scholar
• T.I. Missov, Analytic expressions for life expectancy in gamma-Gompertz mortality settings, Tech. Rep. Max Planck Institute for Demographic Research, Rostock, Germany, 2010.
   Google Scholar
• T.I. Missov, Gamma-Gompertz life expectancy at birth, Demogr. Res. 28 (2013), pp. 259–270. doi: 10.4054/DemRes.2013.28.9
   Web of Science ®Google Scholar
• D. Oakes, A model for association in bivariate survival data, J. R. Stat. Soc. Ser. B Methodol. 44 (1982), pp. 414–422.
   Google Scholar
• Y. Peng, J.M. Taylor and B. Yu, A marginal regression model for multivariate failure time data with a surviving fraction, Lifetime Data Anal. 13 (2007), pp. 351–369. doi: 10.1007/s10985-007-9042-4
   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 Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. Available at http://www.R-project.org/, 2016.
   Google Scholar
• R. Rocha, S. Nadarajah, V. Tomazella and F. Louzada, Two new defective distributions based on the Marshall–Olkin extension, Lifetime Data Anal. 22 (2015), pp. 1–25.
   Web of Science ®Google Scholar
• R. Rocha, S. Nadarajah, V. Tomazella and F. Louzada, A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling, Comput. Stat. Data Anal. 107 (2017), pp. 48–63. doi: 10.1016/j.csda.2016.10.001
   Web of Science ®Google Scholar
• R. Rocha, S. Nadarajah, V. Tomazella, F. Louzada and A. Eudes, New defective models based on the Kumaraswamy family of distributions with application to cancer data sets, Stat. Meth. Med. Res. 26 (2015), pp. 1–15. doi: 10.1016/j.stamet.2015.03.001
   Web of Science ®Google Scholar
• R. Rocha, V. Tomazella and F. Louzada, Inferência clássica e Bayesiana para o modelo de frção de cura Gompertz defeituoso, Revis Brasil Biomet 32 (2014), pp. 104–114.
   Google Scholar
• J. Rodrigues, V.G. Cancho, M. de Castro and F. Louzada-Neto, On the unification of long-term survival models, Statist. Probab. Lett. 79 (2009), pp. 753–759. doi: 10.1016/j.spl.2008.10.029
   Web of Science ®Google Scholar
• D. Sinha and D.K. Dey, Semiparametric Bayesian analysis of survival data, J. Am. Stat. Assoc. 92 (1997), pp. 1195–1212. doi: 10.1080/01621459.1997.10474077
   Web of Science ®Google Scholar
• V.L.D. Tomazella, Modelagem de dados de eventos recorrentes via processo de Poisson com termo de fragilidade, Ph.D. diss. Instituto de Ciências Matemáticas e de Computação, 2003.
   Google Scholar
• J.W. Vaupel, K.G. Manton and E. Stallard, The impact of heterogeneity in individual frailty on the dynamics of mortality, Demography 16 (1979), pp. 439–454. doi: 10.2307/2061224
   PubMed Web of Science ®Google Scholar
• G.A. Whitmore, An inverse Gaussian model for labour turnover, J. Roy. Statist. Soc. Ser. A 142 (1979), pp. 468–478. doi: 10.2307/2982553
   Google Scholar
• A. Wienke, Frailty models, Statistics Reference Online, Wiley StatsRef, 2003.
   Google Scholar
• A.Y. Yakovlev and A.D. Tsodikov, Stochastic models of tumor latency and their biostatistical applications, Vol.1, World Scientific, River Edge, NJ, 1996.
   Google Scholar
• K.K. Yau and A.S. Ng, Long-term survivor mixture model with random effects: Application to a multi-centre clinical trial of carcinoma, Stat. Med. 20 (2001), pp. 1591–1607. doi: 10.1002/sim.932
   PubMed Web of Science ®Google Scholar
• B. Yu and Y. Peng, Mixture cure models for multivariate survival data, Comput. Stat. Data. Anal. 52 (2008), pp. 1524–1532. doi: 10.1016/j.csda.2007.04.018
   Web of Science ®Google Scholar