Efficient estimation in a non-proportional hazards model in survival analysis

Scandinavian Journal of Statistics

Volumn 23, Issue 1, 1996, Pages 49-61

  Vonta, Filia ^a  

^a NONE

Author keywords

Asymptotic distribution; Consistency; Efficiency; Non proportional hazards model; Regression

Indexed keywords

EID: 0030535019     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Andersen, P. K. & Gill, R. D. (1982). Cox's regression model for counting processes: a large sample study. Ann. Statist. 10, 1100-1120.
2. Begun, J. M., Hall, W. J., Huang, W. M. & Wellner, J. A. (1983). Information and asymptotic efficiency in parametric-nonparametric models. Ann. Statist. 11, 432-452.
3. Clayton, D. & Cuzick, J. (1985). Multivariate generalizations of the proportional hazards model (with discussion). J. Roy. Statist. Soc. Ser. A 148, 82-117.
4. Clayton, D. & Cuzick, J. (1986). The semiparametric Pareto model for regression analysis of survival times. Papers on Semiparametric Models. MS-R8614, 19-31. Centrum voor Wiskunde en Informatica, Amsterdam.
5. Cox, D. R. (1972). Regression models and life tables. J. Roy. Statist. Soc. Ser. B 34, 187-202.
6. Cox, D. R. (1975). Partial likelihood. Biometrika 62, 269-276.
7. Efron, B. (1977). The efficiency of Cox's likelihood function for censored data. J. Amer. Statist. Assoc. 72, 557-565.
8. Fernholz, L. T. (1983). von Mises calculus for statistical functionals. Lecture Notes in Statistics 19, Springer, New York.
9. Gill, R. D. (1989). Non- and semi-parametric maximum likelihood estimators and the von Mises method (Part I). Scand. J. Statist. 16, 97-128.
10. Hougaard, P. (1984). Life table methods for heterogeneous populations: distributions describing the heterogeneity. Biometrika 71, 75-83.
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). Modelling multivariate survival. Scand. J. Statist, 14, 291-304.
14. Huber, P. J. (1967). The behavior of maximum likelihood estimates under non-standard conditions. Proc. Fifth Berkeley Sympos. Math. Statist. Probab. 1, 221-233.
15. Jennrich, R. I. (1969). Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40, 633-643.
16. Johansen, S. (1983). An extension of Cox's regression model. Int. Statist. Rev. 51, 165-174.
17. Oakes, D. (1977). The asymptotic information in censored survival data. Biometrika 64, 441-448.
18. Peto, R. & Peto, J. (1972). Asymptotically efficient rank invariant test procedures (with discussion). J. Roy. Statist. Soc. Ser. A 135, 185-207.
19. Rao, C. R. (1973). Linear statistical inference and its applications, 2nd edn. Wiley, New York.
20. Reeds, J. A. (1976). On the definition of von Mises functionals. Research Report S-44, Department of Statistics, University of Harvard.
21. Slud, E. V. (1982). Consistency and efficiency of inferences with the partial likelihood. Biometrika 69, 547-552.
22. Tsiatis, A. A. (1981). A large sample study of Cox's regression model. Ann. Statist. 9, 93-108.
23. Vaupel, J. W. (1990a). Kindred lifetimes: frailty models in population genetics. In Convergent issues in genetics and demography (eds J. Adams, A. Hermalin, D Lam and P. Smouse), Oxford University Press, Oxford.
24. Vaupel, J. W. (1990b). Relatives' risks: frailty models of life history data. Theor. Pop. Biol. 37, 220-234.
25. Vonta, F. (1992). Efficient estimation of a structural parameter in a nonproportional hazards model in the two-sample problem. PhD dissertation, University of Maryland.
26. Vonta, F. (1993). Efficient estimation in a nonproportional hazards model in survival analysis. Technical Report 14/93, Department of Mathematics and Statistics, University of Cyprus.
27. Vonta, F. (1994). An algorithmic procedure for efficient estimation in a nonproportional hazards model. Preprint.
28. Wong, W. H. (1986). Theory of partial likelihood. Ann. Statist. 14, 88-123.