Checking for the gamma frailty distribution under the marginal proportional hazards frailty model

Statistica Sinica

Volumn 14, Issue 1, 2004, Pages 249-267

  Cui, Sufang ^a,c   Sun, Yanqing ^b  

^a Transamerica Occid Life Insurance ^*  (United States)

^b UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

^c Transamerica Occid Life Insurance   (United States)

Author keywords

Correlated failure times; Posterior expectations; Tests

Indexed keywords

EID: 1842539312     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. Aalen, O. O. (1988). Heterogeneity in survival analysis. Statist. Medicine 7, 1121-1137.
2. Aalen, O. O. (1990). Modeling heterogeneity in survival analysis by the compound Poisson distribution. Technical Report, Section of Medical Statistics, University of Oslo.
3. Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York.
4. Billingsley, P. (1995). Probability and Measure. Wiley, New York.
5. Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 85, 141-151.
6. Clayton, D. G. and Cuzick, J. (1985). Multivariate generalizations of the proportional hazards model (with Discussion). J. Roy. Statist. Soc. Ser. A 148, 82-117.
7. Clayton, D. G. (1991). A Monte Carlo method for Bayesian inference in frailty models. Biometrics 47, 467-485.
8. Glidden, D. V. (1999). Checking the adequacy of the gamma frailty model for multivariate failure times. Biometrika 86, 381-393.
9. Glidden, D. V. and Self, S. G. (1999). Semiparametric likelihood estimation in the Clayton-Oakes failure time model. Scand. J. Statist. 26, 363-372.
10. Glidden, D. V. (2000). A two-stage estimator of the dependence parameter for the Clayton-Oakes Model. Lifetime Data Anal. 6, 141-156.
11. Hougaard, P. (1986a). A class of multivariate failure time distributions. Biometrika 73, 671-678.
12. Hougaard, P. (1986b). Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387-396.
13. Hougaard, P. (1987). Modeling multivariate survival. Scand. J. Statist. 14, 291-304.
14. Lin, D. Y., Wei, L. J. and Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 80, 557-572.
15. Lin, D. Y. (1994). Cox regression analysis of multivariate failure time data: the marginal approach. Statist. Medicine 13, 2233-2247.
16. Mantel, N., Bohidar, N. R. and Ciminera, J. L. (1977). Mantel-Haenszel analysis of litter-matched time-to-response data, with modifications for recovery of interlitter information. Cancer Research 37, 3863-3868.
17. Mantel, N. and Ciminera, J. L. (1979). Use of logrank scores in the analysis of litter matched data on time to tumor appearance. Cancer Research 39, 4308-4315.
18. McKeague, I. W. and Zhang, M. J. (1994). Identification of nonlinear time series from first order cumulative characteristics. Ann. Statist. 22, 495-514
19. Murphy, S. A. (1994). Consistency in a proportional hazards model incorporating a random effect. Ann. Statist. 22, 712-731.
20. Murphy, S. A. (1995). Asymptotic theory for the frailty model. Ann. Statist. 23, 182-198.
21. Nielsen, G. G., Gill, R. D., Andersen, P. K. and Sørensen, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist. 19, 25-43.
22. Oakes, D. (1982). A model for association in bivariate survival data. J. Roy. Statist. Soc. Ser. B 44, 414-422.
23. Oakes, D. (1986). Semiparametric inference in a model for association in bivariate survival data. Biometrika 73, 353-361.
24. Oakes, D. (1989). Bivariate survival models induced by frailties. J. Amer. Statist. Assoc. 84, 487-493.
25. Pollard, D. (1984). Convergence of Stochastic Processes. Springer, New York.
26. Pulver, A. E. and Liang, K. Y. (1991). Estimating effects of proband characteristics and familial risk: II. the association between age at onset and familial risk in the Maryland schizophrenia sample. Genetic Epidemiology 8, 339-350.
27. Shih, J. H. and Louis, T. A. (1995a). Inference on the association parameter in copula models for bivariate survival data. Biometrics 51, 1384-1399.
28. Shih, J. H. and Louis, T. A. (1995b). Assessing gamma frailty models for clustered failure time data. Lifetime Data Anal. 1, 205-220.
29. Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.
30. Spiekerman, C. F. and Lin, D. Y. (1996). Checking the marginal Cox model for correlated failure time data. Biometrika 88, 143-156.
31. Spiekerman, C. F. and Lin, D. Y. (1998). Marginal regression models for multivariate failure time data. J. Amer. Statist. Assoc. 93, 1164-1175.
32. Van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York.
33. Vaupel, J. W., Manton, K. G. and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16, 439-454.
34. Vaupel, J. W. (1990). Kindred lifetimes: frailty models in population genetics. In Convergent Issues in Genetics and Demography (Edited by J. Adams, A. Hermalin, D. Lam and P. Smouse). Oxford University Press, Oxford.
35. Wei, L. J., Lin, D. Y. and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J. Amer. Statist. Assoc. 84, 1065-1073.