Estimating Frailty Models via Poisson Hierarchical Generalized Linear Models

Journal of Computational and Graphical Statistics

Volumn 12, Issue 3, 2003, Pages 663-681

  Ha, Il Do ^a   Lee, Youngjo ^b  

^a Kyungsan University   (South Korea)

^b Seoul National University   (South Korea)

Author keywords

Hierarchical likelihood; Marginal likelihood; Multivariate survival data; Penalized likelihood

Indexed keywords

EID: 0141742204     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/1061860032256     Document Type: Review

References (29)

1. Aitkin, M., and Clayton, D. (1980), "The Fitting of Exponential, Weibull and Extreme Value Distributions to Complex Censored Survival Data Using GLIM," Applied Statistics, 29, 156-163.
2. Andersen, P. K., Klein, J. P., Knudsen, K., and Palacios, R. T. (1997), "Estimation of Variance in Cox's Regression Model with Shared Gamma Frailties," Biometrics, 53, 1475-1484.
3. Breslow, N. E. (1974), "Covariance Analysis of Censored Survival Data," Biometrics, 30, 89-99.
4. Clayton, D. G., and Cuzick, J. (1985), "The EM Algorithm for Cox's Regression Model Using GLIM," Applied Statistics, 34, 148-156.
5. Cox, D. R. (1972), "Regression Models and Life Tables," Journal of the Royal Statistical Society, Ser. B, 34, 187-220.
6. Cox, D. R., and Reid, N. (1987), "Parameter Orthogonality and Approximate Conditional Inference" (with discussion), Journal of the Royal Statistical Society, Ser. B, 49, 1-39.
7. Ha, I. D., and Lee, Y. (2001), "Multi-component Survival Analysis of Chronic Granulomatous Disease Data," manuscript submitted for publication.
8. Ha, I. D., Lee, Y., and Song, J.-K. (2001), "Hierarchical Likelihood Approach for Frailty Models," Biometrika, 88, 233-243.
9. _ (2002), "Hierarchical Likelihood Approach for Mixed Linear Models with Censored Data," Lifetime Data Analysis, 8, 163-176.
10. Holford, T.R. (1980), "The Analysis of Rates of Survivorship Using Log-Linear Models," Biometrics, 36, 299-305.
11. Hougaard, P. (2000), Analysis of Multivariate Survival Data, New York: Springer-Verlag.
12. Laird, N. L., and Olivier, D. (1981), "Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques," Journal of the American Statistical Association, 76, 231-240.
13. Lee, Y., and Nelder, J. A. (1996), "Hierarchical Generalized Linear Models" (with discussion), Journal of the Royal Statistical Society, Ser. B, 58, 619-678.
14. _ (2001a), "Hierarchical Generalised Linear Models: A Synthesis of Generalised Linear Models, Random-Effect Models and Structured Dispersions," Biometrika, 88, 987-1006.
15. _ (2001b), "Modelling and Analysing Correlated Non-normal Data," Statistical Modelling, 1, 7-16.
16. Manda, S. O. M. (2001), "A Comparison of Methods for Analysing a Nested Frailty Model to Child Survival in Malawi," Australian and New Zealand Journal of Statistics, 43, 7-16.
17. McGilchrist, C. A. (1993), "REML Estimation for Survival Models with Frailty," Biometrics, 49, 221-225.
18. Murphy, S. A., and van der Vaart, A. W. (2000), "On Profile Likelihood," Journal of the American Statistical Association, 95, 449-465.
19. Nelder, J. A., and Wedderburn, R. W. M. (1972), "Generalized Linear Models," Journal of the Royal Statistical Society, Ser. A, 135, 370-384.
20. Ng, E. T. M., and Cook, R. J. (2000), "A Comparison of Some Random Effect Models for Parameter Estimation in Recurrent Events," Mathematical and Computer Modelling, 32, 11-26.
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," Scandinavian Journal of Statistics, 19, 25-44.
22. Parner, E. (1998), "Asymptotic Theory for the Correlated Gamma-Frailty Model," The Annals of Statistics, 26, 181-214.
23. Pickles, A., and Crouchley, R. (1995), "A Comparison of Frailty Models for Multivariate Survival Data," Statistics in Medicine, 14, 1447-1461.
24. Ripatti, S., and Palmgren, J. (2000), "Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood," Biometrics, 56, 1016-1022.
25. Sastry, N. (1997), "A Nested Frailty Model for Survival Data, with Application to Study of Child Survival in Northeast Brazil," Journal of the American Statistical Association, 92, 426-435.
26. Therneau, T. M., and Grambsch, P. M. (2000), Modeling Survival Data: Extending the Cox Model, New York: Springer-Verlag.
27. Whitehead, J. (1980), "Fitting Cox's Regression Model to Survival Data Using GLIM," Applied Statistics, 29, 268-275.
28. Yau, K. K. W. (2001), "Multilevel Models for Survival Analysis with Random Effects," Biometrics, 57, 96-102.
29. Yau, K. K. W., and McGilchrist, C. A. (1998), "ML and REML Estimation in Survival Analysis with Time Dependent Correlated Frailty," Statistics in Medicine, 17, 1201-1213.