References
- Clayton, D. G., and J. Cuzick. 1985. Multivariate generalizations of the proportional hazards model (with discussion). Journal of Royal Statistical Society, Series, A 148 (2):82–117. doi:https://doi.org/10.2307/2981943.
- Fan, J. J., L. Hsu, and R. L. Prentice. 2000. Dependence estimation over a finite bivariate failure region. Lifetime Data Analysis 6 (4):343–55.
- 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. doi:https://doi.org/10.1111/1467-9868.00388.
- Gelman, A., and D. B. Rubin. 1992. A single series from the Gibbs sampler provides a false sense of security. In Bayesian statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, 625–32. Oxford: Oxford University Press.
- Geweke, J. 1992. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bayesian statistics 4, eds. J. M. Bernardo, J. Berger, A. P. Dawid and A. F. M. Smith, 169–93. Oxford: Oxford University Press.
- Glidden, D. V. 1999. Checking the adequacy of the gamma frailty model for multivariate failure times. Biometrika 86 (2):381–94. doi:https://doi.org/10.1093/biomet/86.2.381.
- Hanagal, D. D. 2011. Modeling survival data using frailty models. Chapman & Hall/CRC. New York.
- Hanagal, D. D. 2017. Frailty models in public health. In Handbook of Statistics, eds. A. S. R. Srinivasa Rao, S. Pyne, and C. R. Rao, Vol. 37(B), 209–47. Amsterdam: Elsevier Publishers.
- Hanagal, D. D. 2019. Modeling survival data using frailty models. 2nd ed. Singapore: Springer Nature.
- Hanagal, D. D., and A. Pandey. 2020. Correlated inverse Gaussian frailty models for bivariate survival data. Communications in Statistics, Theory and Methods 49 (4):845–63. doi:https://doi.org/10.1080/03610926.2018.1549256.
- Hanagal, D. D., and S. M. Bhambure. 2014a. Analysis of kidney infection data using positive stable frailty models. Advances in Reliability 1:21–39.
- Hanagal, D. D., and S. M. Bhambure. 2014b. Shared inverse Gaussian frailty model based on reversed hazard rate for modeling Australian twin data. Journal of Indian Society for Probability and Statistics 15:9–37.
- Hanagal, D. D., and S. M. Bhambure. 2015. Comparison of shared gamma frailty models using Bayesian approach. Model Assisted Statistics and Applications 10:25–41. doi:https://doi.org/10.3233/MAS-140308.
- Hanagal, D. D., and S. M. Bhambure. 2016. Modeling bivariate survival data using shared inverse Gaussian frailty model. Communications in Statistics - Theory and Methods 45 (17):4969–87. doi:https://doi.org/10.1080/03610926.2014.901380.
- Hanagal, D. D., and S. M. Bhambure. 2017. Modeling Australian twin data using shared positive stable frailty models based on reversed hazard rate. Communications in Statistics - Theory and Methods 46 (8):3754–71. doi:https://doi.org/10.1080/03610926.2015.1071395.
- Hanagal, D. D., and A. D. Dabade. 2013. Modeling of inverse Gaussian frailty model for bivariate survival data. Communications in Statistics - Theory and Methods 42 (20):3744–69. doi:https://doi.org/10.1080/03610926.2011.638428.
- Hanagal, D. D., and A. T. Kamble. 2014. Bayesian estimation in shared positive stable frailty models. Journal of Data Science 13:615–40.
- Hanagal, D. D., and A. Pandey. 2014a. Inverse Gaussian shared frailty for modeling kidney infection data. Advances in Reliability 1:1–14.
- Hanagal, D. D., and A. Pandey. 2014b. Gamma shared frailty model based on reversed hazard rate for bivariate survival data. Statistics & Probability Letters 88:190–96. doi:https://doi.org/10.1016/j.spl.2014.02.008.
- Hanagal, D. D., and A. Pandey. 2015a. Gamma frailty models for bivarivate survival data. Journal of Statistical Computation and Simulation 85 (15):3172–89. doi:https://doi.org/10.1080/00949655.2014.958086.
- Hanagal, D. D., and A. Pandey. 2015b. Inverse Gaussian shared frailty models with generalized exponential and generalized inverted exponential as baseline distributions. Journal of Data Science 13 (2):569–602.
- Hanagal, D. D., and A. Pandey. 2016. Inverse Gaussian shared frailty models based on reversed hazard rate. Model Assisted Statistics and Applications 11 (2):137–51. doi:https://doi.org/10.3233/MAS-150359.
- Hanagal, D. D., and A. Pandey. 2017. Correlated gamma frailty models for bivariate survival data based on reversed hazard rate. International Journal of Data Science 2 (4):301–24. doi:https://doi.org/10.1504/IJDS.2017.088102.
- Hanagal, D. D., A. Pandey, and A. Ganguly. 2017b. Correlated gamma frailty models for bivariate survival data. Communications in Statistics - Simulation and Computation 3627–44. doi:https://doi.org/10.1080/03610918.2015.1085559.
- Hanagal, D. D., A. Pandey, and P. G. Sankaran. 2017a. Shared frailty model based on reversed hazard rate for left censoring data. Communications in Statistics - Simulation and Computation 46 (1):230–43. doi:https://doi.org/10.1080/03610918.2014.960092.
- Hanagal, D. D., and R. Sharma. 2013. Modeling heterogeneity for bivariate survival data by shared gamma frailty regression model. Model Assisted Statistics and Applications 8 (2):85–102. doi:https://doi.org/10.3233/MAS-130259.
- Hanagal, D. D., and R. Sharma. 2015a. Bayesian inference in Marshall-Olkin bivariate exponential shared gamma frailty regression model under random censoring. Communications in Statistics - Theory and Methods 44 (1):24–47. doi:https://doi.org/10.1080/03610926.2012.732182.
- Hanagal, D. D., and R. Sharma. 2015b. Comparison of frailty models for acute leukaemia data under Gompertz baseline distribution. Communications in Statistics - Theory and Methods 44 (7):1338–50. doi:https://doi.org/10.1080/03610926.2013.769600.
- Hanagal, D. D., and R. Sharma. 2015c. Analysis of bivariate survival data using shared inverse Gaussian frailty model. Communications in Statistics - Theory and Methods 44 (7):1351–80. doi:https://doi.org/10.1080/03610926.2013.768663.
- Hougaard, P. 1986. Survival models for heterogeneous populations derived from stable distributions. Biometrika 73 (2):387–96. doi:https://doi.org/10.1093/biomet/73.2.387.
- Hougaard, P. 2000. Analysis of multivariate survival data. Springer: New York.
- Iachine, I. A. 1995a. Correlated frailty concept in the analysis of bivariate survival data. Bachelor project, Department of Mathematics and Computer Science, Odense University, Denmark.
- Iachine, I. A. 1995b. Parameter estimation in the bivariate correlated frailty model with observed covariates via the EM-algorithm. Working Paper Series: Population Studies of Aging 16, CHS, Odense University, Denmark.
- Ibrahim, J. G., C. Ming-Hui, and D. Sinha. 2001. Bayesian survival analysis. New York: Springer, Verlag.
- Kheiri, S., A. Kimber, and M. R. Meshkani. 2007. Bayesian analysis of an inverse Gaussian correlated frailty model. Computational Statistics & Data Analysis 51 (11):5317–26. doi:https://doi.org/10.1016/j.csda.2006.09.026.
- McGilchrist, C. A., and C. W. Aisbett. 1991. Regression with frailty in survival analysis. Biometrics 47 (2):461–66. doi:https://doi.org/10.2307/2532138.
- Oakes, D. 1989. Bivariate survival models induced by frailties. Journal of the American Statistical Association. 84 (406):487–93. doi:https://doi.org/10.1080/01621459.1989.10478795.
- Pickles, A., R. Crouchley, E. Simonoff, L. Eaves, J. Meyer, M. Rutter, J. Hewitt, and J. Silberg. 1994. Survival models for developmental genetic data: Age of onset of puberty and antisocial behavior in twins. Genetic Epidemiology 11 (2):155–70. doi:https://doi.org/10.1002/gepi.1370110206.
- 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. doi:https://doi.org/10.1023/A:1009605117713.
- 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.
- Shih, J. H. 1998. A goodness-of-fit test for association in a bivariate survival model. Biometrika 85 (1):189–200. doi:https://doi.org/10.1093/biomet/85.1.189.
- 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. doi:https://doi.org/10.2307/2061224.
- Wienke, A. 2011. Frailty models in survival analysis. New York: Chapman & Hall/CRC.
- Yashin, A. I., J. W. Vaupel, and I. A. Iachine. 1993. Correlated individual frailty: An advantageous approach to survival analysis of bivariate data. Working Paper. Population Studies of Aging 7, Odense University. Odense.
- Yashin, A. I., J. W. Vaupel, and I. A. Iachine. 1995. Correlated individual frailty: An advantageous approach to survival analysis of bivariate data. Mathematical Population Studies 5 (2):145–59. doi:https://doi.org/10.1080/08898489509525394.