Shared frailty models with baseline generalized Pareto distribution

References

• Armitage, P. 1959. The comparison of survival curves. Journal of the Royal Statistical Society, A 122 (3):279–300. doi:10.2307/2342794.
   Web of Science ®Google Scholar
• Chhikara, R. S., and J. L. Folks. 1986. The inverse Gaussian distribution. New York: Marcel Dekker.
   Google Scholar
• Clayton, D. G. 1978. A model for association in bivariate life tables and its applications to epidemiological studies of familial tendency in chronic disease incidence. Biometrica 65 (1):141–51. doi:10.1093/biomet/65.1.141.
   Web of Science ®Google Scholar
• Clayton, D. G., and J. Cuzick. 1985. Multivariate generalizations of the proportional hazards model (with discussion). Journal of Royal Statistical Society, A 148 (2):82–117. doi:10.2307/2981943.
   Google Scholar
• Cox, D. R. 1972. Regression models and life tables. Journal of the Royal Statistical Society, B 34: 187–220.
   Web of Science ®Google Scholar
• Crowder, M. 1985. A distributional model for repeated failure time measurements. Journal of Royal Statistical Society, B 47: 447–52.
   Google Scholar
• Duchateau, L., and P. Janssen. 2008. The frailty model. New York: Springer.
   Google Scholar
• Fan, J. J., L. Hsu, and R. L. Prentice. 2000. Dependence estimation over a finite bivariate failure time region. Lifetime Data Analysis 6 (4):343–55.
   PubMed Web of Science ®Google Scholar
• Fine, J. P., D. V. Glidden, and K. E. Lee. 2003. A simple estimator for a shared frailty regression model. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65 (1):317–29. 10.1111/1467-9868.00388.
   Google Scholar
• Gelfand, A. E., and S. K. Ghosh. 1998. Model choice: a minimum posterior predictive loss approach. Biometrika 85 (1):1–11. doi:10.1093/biomet/85.1.1.
   Web of Science ®Google Scholar
• Gelman, A., and D. B. Rubin. 1992. A single series from the Gibbs sampler provides a false sense of security. In Bayesian statistics 4, ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, 625–632. Oxford: Oxford University Press.
   Google Scholar
• Genest, C., and J. Mackay. 1986. Joy of copulas: Bivariate distributions with uniform marginals. The American Statistician 40 (4):280–3. doi:10.2307/2684602.
   Web of Science ®Google Scholar
• Geweke, J. 1992. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bayesian statistics 4, ed. J. M. Bernardo, J. Berger, A. P. Dawid and A. F. M. Smith, 169–193. Oxford: Oxford University Press.
   Google Scholar
• Glidden, D. V. 1999. Checking the adequacy of the gamma frailty model for multivariate failure times. Biometrika 86 (2):381–94. doi:10.1093/biomet/86.2.381.
   Web of Science ®Google Scholar
• Hanagal, D. D. 2005. A positive stable frailty regression model in bivariate survival data. Journal of Indian Society for Probability and Statistics 9:35–44.
   Google Scholar
• Hanagal, D. D. 2006. A gamma frailty regression model in bivariate survival data. IAPQR Transactions 31:73–83.
   Google Scholar
• Hanagal, D. D. 2007. Gamma frailty regression models in mixture distributions. Economic Quality Control 22 (2):295–302.
   Google Scholar
• Hanagal, D. D. 2011. Modeling Survival Data Using Frailty Models. Chapman & Hall/CRC.
   Google Scholar
• Hanagal, D. D., and A. Pandey. 2015. Gamma frailty models for bivariate survival data. Journal of Statistical Computation and Simulation 85 (15):3172–89. doi:10.1080/00949655.2014.958086.
   Web of Science ®Google Scholar
• Hanagal, D. D., and A. Pandey. 2014. Gamma shared frailty model based on reversed hazard rate for bivariate survival data. Statistics and Probability Letters 88:190–6. doi:10.1016/j.spl.2014.02.008.
   Web of Science ®Google Scholar
• Hougaard, P. 1984. Life table methods for heterogeneous populations. Biometrika 71 (1):75–83. doi:10.1093/biomet/71.1.75.
   Web of Science ®Google Scholar
• Hougaard, P. 1986. A class of multivariate failure time distributions. Biometrika 73 (3):671–8. doi:10.2307/2336531.
   Web of Science ®Google Scholar
• Hougaard, P. 1987. Modelling multivariate survival. Scandinavian Journal of Statistics 14 (4):291–304.
   Google Scholar
• Hougaard, P. 2000. Analysis of multivariate survival data. New York: Springer-Verlag.
   Google Scholar
• Ibrahim, J. G., M. H. Chen, and D. Sinha. 2001. Bayesian survival analysis. New York: Springer-Verlag.
   Google Scholar
• Jenkinson, A. F. 1955. The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quarterly Journal of the Royal Meteorological Society 81 (348):158–71. doi:10.1002/qj.49708134804.
   Web of Science ®Google Scholar
• Kass, R. A., and A. E. Raftery. 1995. Bayes’ factor. Journal of the American Statistical Association 90 (430):773–95. doi:10.1080/01621459.1995.10476572.
   Web of Science ®Google Scholar
• Kheiri, S., A. Kimber, and M. R. Meshkani. 2007. Bayesian analysis of an inverse Gaussian correlated frailty model. Computational Statistics and Data Analysis 51 (11):5317–26. doi:10.1016/j.csda.2006.09.026.
   Web of Science ®Google Scholar
• McGilchrist, C. A., and C. W. Aisbett. 1991. Regression with frailty in survival analysis. Biometrics 47 (2):461–6.
   PubMed Web of Science ®Google Scholar
• Nielsen, G. G., R. D. Gill, P. K. Andersen, and T. I. A. Sorensen. 1992. A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics 19:25–43.
   Web of Science ®Google Scholar
• Oakes, D. 1982. A model for association in bivariate survival data. Journal of the Royal Statistical Society, B (Methodological) 44:414–22.
   Web of Science ®Google Scholar
• Oakes, D. 1989. Bivariate survival models induced by frailties. Journal of the American Statistical Association 84 (406):487–93. doi:10.1080/01621459.1989.10478795.
   Web of Science ®Google Scholar
• Qiou, Z., N. Ravishanker, and D. K. Dey. 1999. Multivariate survival analysis with positive stable frailties. Biometrics 55 (2):637–44.
   PubMed Web of Science ®Google Scholar
• Sahu, S. K., D. K. Dey, H. Aslanidou, and D. Sinha. 1997. A weibull regression model with gamma frailties for multivariate survival data. Lifetime Data Analysis 3 (2):123–37.
   PubMedGoogle Scholar
• Santos, C. A., and J. A. Achcar. 2010. A Bayesian analysis for multivariate survival data in the presence of covariates. Journal of Statistical Theory and Applications 9:233–53.
   Google Scholar
• Shih, J. H. 1998. A goodness-of-fit test for association in a bivariate survival model. Biometrika 85 (1):189–200. doi:10.1093/biomet/85.1.189.
   Web of Science ®Google Scholar
• Vaupel, J. W., K. G. Manton, and E. Stallard. 1979. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16 (3):439–54.
   PubMed Web of Science ®Google Scholar
• Vaupel, J. W. 1991a. Relatives’ risks: Frailty models of life history data. Theoretical Population Biology 37 (1):220–34. doi:10.1016/0040-5809(90)90037-V.
   Web of Science ®Google Scholar
• Vaupel, J. W. 1991b. Kindred lifetimes: Frailty models in population genetics: In Convergent questions in genetics and demography, ed. J. Adams, 155–170. Oxford: Oxford University Press.
   Google Scholar
• Vaupel, J. W., A. I. Yashin, M. Hauge, B. Harvald, N. Holm, and X. Liang. 1991. Survival analysis in genetics: Danish twins data applied to gerontological question. In Survival analysis: State of the art, ed. J. P. Klein and P. K. Goel, 121–138. Dordrecht: Kluwer Academic Publisher.
   Google Scholar
• Vaupel, J. W., A. I. Yashin, M. Hauge, B. Harvald, N. Holm, and X. Liang. 1992. Strategies of modelling genetics in survival analysis. What can we learn from twins data. Paper presented on PAA meeting in Denver, CO, April 30–May 2, 1992.
   Google Scholar