Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

References

• Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrox, B.N., Caski, F., eds. Second International Symposium on Information Theory(pp. 267–281) Budapest: Akademiai Kiado.
   Google Scholar
• Barlow, R.E., Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. New York: Holt, Rinehart & Winston.
   Google Scholar
• Bolstad, W.M., Manda, S.O. (2001). Investigating child mortality in malawi using family and community random effects: A Bayesian Analysis. J. Am. Stat. Assoc. 96:12–19.
   Web of Science ®Google Scholar
• Brooks, S.P., Gelman, A. (1998). Alternative methods for monitoring convergence of iterative simulations. J. Comput. Graphical Stat. 7:434–455.
   Web of Science ®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. Biometrika 65:141–151.
   Web of Science ®Google Scholar
• Cox, D.R., Oakes, D. (1984). Analysis of Survival Data. New York: Chapman and Hall.
   Google Scholar
• Fleming, T.R., Harrington, D.P. (1991). Counting Processes and Survival Analysis. New York: Wiley.
   Google Scholar
• Freund, J.E. (1961). A bivariate extension of exponential distribution. J. Am. Stat. Assoc. 56:971–977.
   Web of Science ®Google Scholar
• Geweke, J. (1992). Evaluating the accuracy of sampling based approaches to calculating posterior moments. In: Bernardo, J.M., Berger, J.O., Dawiv, A.P., Smith, A. F.M., eds., Bayesian Statistics, 4.Oxford, UK: Clarendon Press.
   Google Scholar
• Hanagal, D.D. (1992a). Some inference results in bivariate exponential distributions based on censored samples. Commun. Statist. Theory Meth. 21:1273–1295.
   Web of Science ®Google Scholar
• Hanagal, D.D. (1992b). Some inference results in modified freund’s bivariate exponential distribution. Biometrical J. 34(6):745–756.
   Web of Science ®Google Scholar
• Hanagal, D.D., Kale, B.K. (1991a). Large sample tests of independence for absolutely continuous bivariate exponential distribution. Commun. Statist. Theory Meth. A20:1301–1313.
   Web of Science ®Google Scholar
• Hanagal, D.D., Kale, B.K. (1991b). Large sample tests of λ3 in the bivariate exponential distribution. Stat. Prob. Lett. 12(4):311–313.
   Web of Science ®Google Scholar
• Hanagal, D.D., Kale, B.K. (1992). Large sample tests for testing symmetry and independence in bivariate exponential models. Commun. Statist. Theory Meth. 21(9):2625–2643.
   Web of Science ®Google Scholar
• Huster, W.J., Brookmeyer, R., Self, S.G. (1989). Modelling paired survival data with covariates. Biometrics 45:145–156.
   PubMed Web of Science ®Google Scholar
• Ibrahim, J.G., Ming-Hui, Chen, Sinha, D. (2001). Bayesian Survival Analysis. New York: Springer Verlag.
   Google Scholar
• Kheiri, S., Kimber, A., (2007). Bayesian analysis of an inverse gaussian correlated frailty model. Computat. Stati. Data Anal. 51:5317–5326.
   Web of Science ®Google Scholar
• Korsgaard, I.R., Madsen, P., Jensen, J. (1998). Bayesian inference in the semiparametric log-normal frailty model using gibbs sampling. Genetics, Selection, Evolution 30:241–256.
   Web of Science ®Google Scholar
• Kotz, S., Balakrishnan, N., Johnson, N.L. (2000). Continuous Multivariate Distributions. Models and Applications. New York: John Wiley and Sons.
   Google Scholar
• Marshall, A.W., Olkin, I. (1967). A multivariate exponential distribution. J. Am. Stat. Assoc. 62:30–44.
   Web of Science ®Google Scholar
• Pena, E.A., (1990). Bayes estimation for the Marshall–Olkin exponential distribution. J. R. Stat. Soc., B, 52(2):379–389.
   Google Scholar
• Proschan, F., Sullo, P. (1974). Estimating the parameters of bivariate exponential distributions in several sampling situations. In: Proschan, I., Serfling, R.J., eds., Reliability and Biometry. (pp. 423–440) Philadelphia: SIAM.
   Google Scholar
• Sahu, S.K., Dey, D.K. (2000). A comparison of frailty and other models for bivariate survival data. Lifetime Data Analysis 6:207–228.
   PubMed Web of Science ®Google Scholar
• Sahu, S.K., Dey, D.K., Aslanidou, H., Sinha, D. (1997). A weibull regression model with gamma frailties for multivariate survival data. Lifetime Data Anal. 3:123–137.
   PubMedGoogle Scholar
• Santos, C.A., Jorge, A.A. (2010). A Bayesian analysis for multivariate survival data in the presence of covariates. J. Stat. Theory and Applications 9:233–253.
   Google Scholar
• Schwarz, G.E. (1978). Estimating the dimension of a model. Ann. Stat. 6(2):461–464.
   Web of Science ®Google Scholar
• Spiegelhalter, D., Best, N., Carlin, B., Linde, A. V.D. (2002). Bayesian measures of model complexity and Fit. J. Roy. Stati. Soc. Ser. B 64:583–639.
   Google Scholar
• Therneau, T., Grambsch, P. (2000). Modeling Survival Data: Extending the Cox Model. Berlin: Springer.
   Google Scholar
• Xue, X., Ding, Y. (1999). Assessing heterogeneity and correlation of paired failure times with the bivariate frailty model. Stat. Med. 18:907–918.
   PubMed Web of Science ®Google Scholar