Shared frailty model based on reversed hazard rate for left censored data

References

• Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. N., Csaki, F., eds. Second International Symposium on Information Theory. Budapest: Academiai Kiado, pp. 267–281.
   Google Scholar
• Andersen, P. K., Borgan, O., Gill, R. D., Keiding, N. (1993). Statistical Methods Based on Counting Processes. New York: Springer Verlag.
   Google Scholar
• Barlow, R. E., Marshal, A. W., Proschan, F. (1963). Properties of the probability distribution with monotone hazard rate. Annals of Mathematical Statistics 34:375–389.
   Google Scholar
• Block, H. W., Savits, T. H., Singh, H. (1998). On the reversed hazard rate function. Probability in the Engineering and Informational Sciences 12:69–90.
   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 65:141–151.
   Google Scholar
• Clayton, D. G., Cuzick, J. (1985). Multivariate generalizations of the proportional hazards model (with discussion). Journal of Royal Statistical Society, Series A 148:82–117.
   Google Scholar
• Duchateau, L., Janssen, P. (2008). The Frailty Model. New York: Springer.
   Google Scholar
• Duffy, D. L., Martin, N. G., Mathews, J. D. (1990). Appendectomy in Australian twins. Australian Journal of Human Genetics 47(3):590–592.
   Google Scholar
• Gelman, A., Rubin, D. B. (1992). A single series from the Gibbs sampler provides a false sense of security. In: Bernardo, J. M., Berger, J. O., Dawid, A. P., Smith, A. F. M., eds. Bayesian Statistics. Vol. 4. Oxford University Press: Oxford, pp. 625–632.
   Google Scholar
• Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo, J. M., Berger, J., Dawid, A. P., Smith, A. F. M., eds. Bayesian Statistics. Vol. 4. Oxford: Oxford University Press, pp. 169–193
   Google Scholar
• Gleeja, V. L. (2008). Department Modelling and Analysis of Bivariate Lifetime Data using Reversed Hazard Rates. Ph. D. dissertation, India: Cochin University of Science and Technology.
   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., Dabade, A. D. (2013). Bayesian estimation of parameters and comparison of shared gamma frailty models. Communications in Statistics, Simulation & Computation 42(4):910–931.
   Google Scholar
• Hougaard, P. (1987). Modelling Multivariate Survival. Scandinavian Journal of Statistics 14(4):291–304.
   Google Scholar
• Ibrahim, J. G., Ming-Hui, C., Sinha, D. (2001). Bayesian Survival Analysis. Springer Verlag: New York.
   Google Scholar
• Jeffreys, H. (1961). Theory of Probability. 3rd ed. New York: Oxford University Press.
   Google Scholar
• Kass, R. E., Raftery, A. E. (1995). Bayes factor. Journal of the American Statistical Association 90(430):773–795.
   Google Scholar
• Kheiri, S., Kimber, A., Meshkani, M. R. (2007). Bayesian analysis of an inverse Gaussian correlated frailty model. Computational Statistics and Data Analysis 51:5317–5326.
   Google Scholar
• Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. 2nd ed. John Wiley and Sons: New Jersey.
   Google Scholar
• Nelsen, R. B. (2006). An Introduction to Copulas. 2nd ed. Springer: New York.
   Google Scholar
• Nielsen, G. G., Gill, R. D., Andersen, P. K., Sorensen, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics 19:25–43.
   Google Scholar
• Raftery, A. E. (1994). Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models. Technical Report 255. Seattle, WA: Department of Statistics, University of Washington.
   Google Scholar
• Sahu, S. K., Dey, D. K., Aslanidou, H., Sinha, D. (1997). A Weibull regression model with gamma frailties for multivariate survival data. Life Time Data Analysis 3:123–137.
   Google Scholar
• Sankaran, P. G., Gleeja, V. L. (2006). On bivariate reversed hazard rates. Journal of Japan Statistical Society 10:181–198.
   Google Scholar
• Sankaran, P. G., Gleeja, V. L. (2011). On proportional reversed hazards frailty models. Metron 69:151–173.
   Google Scholar
• Santos, C. A., Achcar, J. A. (2010). A Bayesian analysis for multivariate survival data in the presence of covariates. Journal of Statistical Theory and Applications 9:233–253.
   Google Scholar
• Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6(2):461–464.
   Google Scholar
• Shaked, M., Shantikumar, J. G. (1994). Stochastic Orders and Their Applications. New York: Academic Press.
   Google Scholar
• Spiegelhalter, D. J., Best, N. G., Carlin, B. P., Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of Royal Statistical Society, B. 64(4):583–639.
   Google Scholar
• Vaupel, J. W. (1991a). Relatives’ risks: Frailty models of life history data. Theoretical Population Biology 37(1):220–234.
   Google Scholar
• Vaupel, J. W. (1991b). Kindred lifetimes: Frailty models in population genetics. In: Adams, J., et al., eds. Convergent Questions in Genetics and Demography. Oxford University Press: Oxford, pp. 155–170.
   Google Scholar
• Vaupel, J. W., Manton, K. G., Stallaed, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16:439–454.
   Google Scholar
• Vaupel, J. W., Yashin, A. I., Hauge, M., Harvald, B., Holm, N., Liang, X. (1991). Survival analysis in genetics: Danish twins data applied to gerontological question. In: Klein, J. P., Goel, P. K., eds. Survival Analysis: State of the Art. Kluwer Academic Publisher: Dordecht, pp. 121–138.
   Google Scholar
• Vaupel, J. W., Yashin, A. I., Hauge, M., Harvald, B., Holm, N., Liang, X. (1992). Strategies of modelling genetics in survival analysis. What can we learn from twins data? Paper presented on PAA meeting in Denver, CO, 30 April–2 May.
   Google Scholar