A version of the EM algorithm for proportional hazard model with random effects

Biometrical Journal

Volumn 47, Issue 6, 2005, Pages 847-862

  Abrahantes, José Certiñas ^a   Burzykowski, Tomasz ^a  

^a HASSELT UNIVERSITY   (Belgium)

Author keywords

EM algorithm; Frailty model; Laplace approximation; Multivariate failure time data

Indexed keywords

HAZARDS; LAPLACE TRANSFORMS; RANDOM PROCESSES;

EM ALGORITHMS; ESTIMATION OF PARAMETERS; FAILURE TIME DATA; FRAILTY MODELS; INTENSIVE RESEARCH; LAPLACE'S APPROXIMATION; MULTIVARIATE FAILURE-TIME DATA; PRACTICAL PROBLEMS; PROPORTIONAL HAZARD MODELS; RANDOM EFFECTS;

APPROXIMATION ALGORITHMS;

EID: 29844457158     PISSN: 03233847     EISSN: None     Source Type: Journal    
DOI: 10.1002/bimj.200410141     Document Type: Article

References (32)

1. Bleistein, N. and Handelsman, R. A. (1986). Asymptotic Expansions of Integrals. Dover, New York.
2. Clahsen, P. C., van de Velde, C. J., Julien, J. P., Floiras, J. L., Delozier, T., Mignolet, F. Y., and Sahmoud, T. M. (1996). Improved local control and disease-free survival after preoperative chemotherapy for early-stage breast cancer. A European Organization for Research and Treatment of Cancer breast cancer cooperative group study. Journal of Clinical Oncology 14, 745-753.
3. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1997). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society B 39, 1-38.
4. Duchateau, L., Janssen, P., Lindsey, P., Legrand, C., Nguti, R., and Sylvester, R. (2002). The shared frailty model and the power for heterogeneity tests in multicenter trials. Computational Statistics and Data Analysis 40, 603-620.
5. Evans, M. and Swartz, T. (2000). Approximating Integrals via Monte Carlo and Deterministic Methods. Oxford University Press, Oxford.
6. Ferreira, A., and Garcia, N. L. (2002). Simulation study for misspecifications on a frailty model. Brazilian Journal of Probability and Statistics 15, 121-134.
7. Gray, R. J. (1995). Tests for variation over groups in survival data. Journal of the American Statistical Association 90, 198-203.
8. Johansen, S. (1993). An extension of Cox's regression model. International Statistical Review 51, 258-262.
9. Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, Vol. 1. Houghton Mifflin, Boston.
10. Kass, R. E., Tierney, L., and Kadane J. B. (1990). The validity of posterior expansions based on Laplace's method. Bayesian and likelihood methods in statistics and econometrics (ed. S. Geisser, J. S. Hodges, S. J. Press and A. Zellner). Elsevier Science North Holland, Amsterdam, 473-488.
11. Klein, J. P. (1992). Semiparametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics 48, 795-806.
12. Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society B 44, 190-200.
13. McGilchrist, C. A. and Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics 47, 461-466.
14. McGilchrist, C. A. (1993). REML estimation for survival models with frailty. Biometrics 49, 221-225.
15. McGilchrist, C. A. (1994). Estimation in generalized mixed models. Journal of the Royal Statistical Society B 56, 61-69.
16. Murray, J. D. (1984). Asymptotic Analysis. Springer-Verlag, New York.
17. Murphy, S. A. (1995). Asymptotic theory for the frailty model. Annals of Statistics 23, 182-198.
18. Nielsen, G. G., Gill, R. D., Andersen, P. K., and Sorensen, T. I. A (1992). A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics 19, 25-43.
19. Parner, E. (1998). Asymptotic theory for the correlated gamma-frailty model. Annals of Statistics 26, 183-214.
20. Ripatti, S. and Palmgren, J. (2000). Estimation of multivariate frailty models using penalized partial likelihood. Biometrics 56, 1016-1022.
21. Ripatti, S., Larsen, K., and Palmgren, J. (2002). Maximum likelihood inference for multivariate frailty models using an automated Monte Carlo EM algorithm. Lifetime Data Analysis 8, 349-360.
22. Therneau, T. and Grambsch, P. M. (2000). Modeling Survival Data: Extending the Cox model. Springer-Verlag, New York.
23. Therneau, T., Grambsch, P. M., and Shane Pankratz, V. (2000). Penalized survival models and frailty. Technical Report (June 2000).
24. Therneau, T. (2003). On mixed effect Cox models, sparse matrices, and modelling data from large pedigree. Technical Report (July 2003).
25. Vaida, F. (2004). Parameter convergence for EM and MM Algorithms. Statistica Sinica, to appear.
26. Vaida, F. and Xu, R. (2000). Proportional hazards model with random effects. Statistics in Medicine 19, 3309-3324.
27. Wong, R. (1989). Asymptotic Approximations of Integrals. Academic Press, San Diego.
28. Wu, C.-F. J. (1983). On the convergency properties of the EM algorithm. Annals of Statistics 11, 95-103.
29. Xue, X. (1998). Multivariate survival data under bivariate frailty: an estimating equation approach. Biometrics 54, 1631-1637.
30. Xue, X. and Brookmeyer, R. (1996). Bivariate frailty model for the analysis of multivariate survival time. Lifetime Data Analysis 2, 277-289.
31. Xue, X. and Ding, Y. (1999). Assessing heterogeneity and correlation of paired failure times with the bivariate frailty model. Statistics in Medicine 18, 907-918.
32. Yamaguchi, T. and Ohashi, Y. (1999). Investigating centre effects in a multi-centre clinical trial of superficial bladder cancer. Statistics in Medicine 18, 1961-1971.