Bayesian and likelihood inference for cure rates based on defective inverse Gaussian regression models

Journal of Applied Statistics

Volumn 38, Issue 1, 2011, Pages 127-144

  Balka, Jeremy ^a   Desmond, Anthony F ^a   McNicholas, Paul D ^a  

^a UNIVERSITY OF GUELPH   (Canada)

Author keywords

Cure rates; Defective inverse Gaussian; Gibbs sampler; Survival analysis

Indexed keywords

EID: 78650038786     PISSN: 02664763     EISSN: 13600532     Source Type: Journal    
DOI: 10.1080/02664760903301127     Document Type: Article

References (37)

1. O.O. Aalen and H.K. Gjessing, Understanding the shape of the hazard rate: A process point of view, Stat. Sci. 16 (2001), pp. 1-22.
2. 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.
3. J. Berkson and R.P. Gage, Survival curve for cancer patients following treatment, J. Amer. Statist. Assoc. 47 (1952), pp. 501-515.
4. J.F. Bjornstad, Predictive likelihood: A review, Stat. Sci. 5 (1990), pp. 242-265.
5. J.W. Boag, Maximum likelihood estimates of the proportion of patients cured by cancer therapy, J. R. Stat. Soc. Ser. B 11 (1949), pp. 15-34.
6. V.G. Cancho and H. Bolfarine, Modelling the presence of immunes by using the exponentiated-Weibull model, J.Appl. Stat. 28 (2001), pp. 659-671.
7. 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.
8. M.H. Chen, J. Ibrahim, and S. Debajyoti, A new Bayesian model for survival data with a surviving fraction, J. Amer. Statist. Assoc. 94 (1999), pp. 909-919.
9. R. Chhikara and J.L. Folks, The inverse Gaussian distribution and its statistical application - A review, J. R. Stat. Soc. Ser. B 40 (1978), pp. 263-289.
10. R.S. Chhikara and J.L. Folks, The Inverse Gaussian Distribution: Theory, Methodology, and Applications, Marcel Dekker Inc., NewYork, NewYork, 1989.
11. D.R. Cox, Regression models and life-tables (with discussion), J. R. Stat. Soc. Ser. B 34 (1972), pp. 187-220.
12. V.T. Farewell, The use of mixture models for the analysis of survival data with long-term survivors, Biometrics 38 (1982), pp. 1041-1046.
13. V.T. Farewell, Mixture models in survival analysis: Are they worth the risk?, Canad. J. Statist. 14 (1986), pp. 257-262.
14. J. Geweke, Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, in Bayesian Statistics 4: Proceedings of the Fourth Valencia International Meeting, J.M. Bernardo J.O. Berger, A.P. Dawid, and A.F.M. Smith, eds., Clarendon Press, Oxford, 1992, pp. 169-193.
15. 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.
16. W.R. Gilks and P.Wild, Adaptive rejection sampling for Gibbs sampling, Appl. Stat. 41 (1992), pp. 337-348.
17. P. Heidelberger and P. Welch, Simulation run length control in the presence of an initial transient, Oper. Res. 31 (1983), pp. 1109-1144.
18. J.G. Ibrahim, M.H. Chen, and D. Sinha, Bayesian Survival Analysis, Springer-Verlag, NewYork, 2001.
19. J.N. Ichida, J.T. Wassell, M.D. Keller, and L.W. Ayers, Evaluation of protocol change in burn-care management using the Cox proportional hazards model with time-dependent covariates, Stat. Med. 12 (1993), pp. 301-310.
20. S.A. Ismail and H.A. Auda, Bayesian and fiducial inference for the inverse Gaussian distribution via Gibbs sampler, J. Appl. Stat. 33 (2006), pp. 787-805.
21. A.Kopp-Schneider, Mechanistic models in QRA: Cell kinetic approaches, Innformatik, Biometrie und Epidemiologie in Medizin und Biologic 25 (1994), pp. 242-249.
22. J.F. Lawless, Statistical Models and Methods for Lifetime Data, 2nd ed., John Wiley & Sons, New York, 2003.
23. M.L.T. Lee and G.A. Whitmore, Threshold regression for survival analysis: modeling event times by a stochastic process reaching a boundary, Stat. Sci. 21 (2006), pp. 501-513.
24. R Development Core Team, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, 2009; Software available at http://www.R-project.org.
25. A.E. Raftery and S.M. Lewis, Implementing MCMC, in Markov Chain Monte Carlo in Practice, S.Richardson. W. Gilks and D.J. Spiegelhalter, eds., Chapman and Hall/CRC, London, 1996, pp. 115-130.
26. N. Reid, A conversation with Sir David Cox, Stat. Sci. 9 (1994), pp. 439-455.
27. E. Schrödinger, Zur theorie der fall-und steigversuche an teilchen mit brownscher bewegung, Phys. Ze. 16 (1915), pp. 289-295.
28. V. Seshadri, The Inverse Gaussian Distribution: A Case Study in Exponential Families, Clarendon, Oxford, 1993.
29. A.F.M. Smith and G.O. Roberts, Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, J. R. Stat. Soc. Ser. B 55 (1993), pp. 2-21.
30. D.J. Spiegelhalter, L.S. Freedman, and M.K.B. Parmar, Bayesian approaches to randomized trials, J. R. Stat. Soc. Ser. A 157 (1994), pp. 357-416.
31. M.A. Tanner, Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 3rd ed., Springer Verlag, NewYork, 1996.
32. M.C.K. Tweedie, Inverse statistical variates, Nature 155 (1945), p. 453.
33. S.K. Upadhyay, R. Agrawal, and A.F.M. Smith, Bayesian analysis of inverse Gaussian non-linear regression by simulation, Sankhya Ser. B 58 (1996), pp. 363-378.
34. G.A. Whitmore, An inverse Gaussian model for labour turnover, J. R. Stat. Soc. Ser. A 142 (1979), pp. 468-478.
35. A.Y. Yakovlev, B. Asselain, V.-J. Bardou, A. Fourquet, T. Hoang, A. Rochefodiere, and A.D. Tsodikov A simple stochastic model of tumor recurrence and its applications to data on premenopausal breast cancer, in Biometrie et Analyse de Données Spatio-Temporelles, B. Asselain, M. Boniface, C. Duby, C. Lopez, J.P. Masson, and J. Tranchefort, eds., 1993, pp. 66-82.
36. A.Y.Yakovlev and A.D. Tsodikov, Stochastic Models of Tumor Latency and their Biostatistical Applications,World Scientific, New Jersey, 1996.
37. G.Yin and J.G. Ibrahim, Cure rate models: A unified approach, Canad. J. Statist. 33 (2005), pp. 559-570.