An efficient estimator for proportional hazards models with frailties

Scandinavian Journal of Statistics

Volumn 23, Issue 1, 1996, Pages 13-26

  Chang, I Shou ^a   Hsiung, Chao A ^b  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

^b INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Asymptotic distribution; Asymptotic efficiency; Proportional hazards models; Regular estimators; Time dependent frailties

Indexed keywords

EID: 0030536010     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. Andersen, E. B. (1970). Asymptotic properties of conditional maximum-likelihood estimators. J. Roy. Statist. Soc. Sci. B 32, 283-301.
2. Andersen, P. K. & Gill, R. D. (1982). Cox's regression model for counting processes: a large sample study. Ann. Statist. 10, 1100-1120.
3. Andersen, P. K., Borgan, Ø., Gill, R. D. & Keiding, N. (1993). Statistical models based on counting processes. Springer Verlag, New York.
4. Begun, J. M., Hall, W. J., Huang, W. & Wellner, J. A. (1983). Information and asymptotic efficiency in parametric-nonparametric models. Ann. Statist., 11, 432-453.
5. Bickel, P. J. (1993). Estimation in semiparametric models. To appear in Proceedings of international conference for multivariate analysis (ed. C. R. Rao). Elsevier/North Holland, Amsterdam.
6. Billingsley, P. (1968). Convergence of probability measures. Wiley, New York.
7. Brémaud, P. (1981). Point processes and queues, martingale dynamics. Springer Verlag, New York.
8. Chang, I. S. & Hsiung, C. A. (1991a). Applications of estimating function theory to replicates of generalized proportional hazards models. In Estimating functions (ed. V. P. Godambe), 23-33. Oxford University Press, Oxford.
9. Chang, I. S. & Hsiung, C. A. (1991b). An E-ancillarity projection property of Cox's partial score function. Ann. Statist. 19, 1651-1660.
10. Chang, I. S. & Hsiung, C. A. (1994). Information and asymptotic efficiency in some generalized proportional hazards models for counting processes. Ann. Statist. 22, 1275-1298.
11. Clayton, D. & Cuzick, J. (1985). Multivariate generalizations of the proportional hazards model (with discussion). J. Roy. Statist. Soc. Ser. A 148, 82-117.
12. Cox, D. R. (1972). Regression models and life tables (with discussion). J. Roy. Statist. Soc. Ser. 34, 187-220.
13. Freireich, E. J., Gehan, E., Frei, E., Schroeder, L. R., Wolman, I. J., Anbari, R., Burgert, E. O., Mills, S. D., Pinkel, D., Selawry, O. S., Moon, J. H., Gendel, B. R., Spurr, C. L., Storrs, R., Haurani, F., Hoogstraten, B. & Lee, S. (1963). The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: a model for evaluation of other potentially useful therapy. Blood 21, 699-716.
14. Godambe, V. P. & Thompson, M. E. (1989). An extension of quasi-likelihood estimation (with discussion). J. Statist. Plan. Infer. 22, 137-172.
15. Gross, S. T. & Huber, C. (1987). Matched pair experiments: Cox and maximum likelihood estimation. Scand. J. Statist. 14, 27-41.
16. Holt, J. D. & Prentice, R. L. (1974). Survival analysis in twin studies and matched pair experiments. Biometrika 61, 17-30.
17. Lindsay, B. G. (1983). Efficiency of the conditional score in a mixture setting. Ann. Statist. 11, 486-497.
18. Murphy, S. A. (1994). Consistency in a proportional hazards model incorporating a random effect. Ann. Statist. 22, 712-731.
19. Nielsen, G. G., Gill, R. D., Andersen, P. K. & Sørensen, T. I. A. (1992). A counting process approach to maximum likelihood estimation in frailty models. Scand. J. Statist. 19, 25-43.
20. Oakes, D. (1989). Bivariate survival models induced by frailties J. Amer. Statist. Assoc. 84, 487-493.
21. Parthasarathy, K. R. (1967). Probability measures on metric spaces. Academic Press, New York.
22. Robbins, H. (1988). The u, v method of estimation. In Statistical decision theory and related topics IV (eds. S. S. Gupta & J. O. Berger), Vol. 1, 265-270. Springer Verlag, New York.
23. Rudin, W. (1987). Real and complex analysis, 3rd edn. McGraw-Hill, New York.
24. Small, C. G. & McLeish, D. L. (1989). Projection as a method for increasing sensitivity and eliminating nuisance parameters. Biometrika 76, 693-703.
25. Vaupel, J. W. (1990). Relatives' risks: frailty models of life history data. Theoret. Populat. Biol. 37, 220-234.
26. Wild, C. J. (1983). Failure time models with matched data. Biometrika 70, 633-641.