Estimation in the Cox model with missing covariate data

Journal of Nonparametric Statistics

Volumn 14, Issue 3, 2002, Pages 223-247

  Pons, Odile ^a  

^a CEMAGREF   (France)

Author keywords

Asymptotic distribution; Censored data; Cox model; Missing data; Nonparametric estimation

Indexed keywords

EID: 0036626308     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485250212379     Document Type: Article

References (25)

1. P.K. Andersen, O. Borgan, R.D. Gill and N. Keiding. Statistical models based on counting processes. Springer-Verlag, New York, 1993.
2. P.K. Andersen and R.D. Gill. Cox's regression model for counting processes: a large sample study. Ann. Statist. 10, (1982), 1100-1120.
3. J.M. Begun, W.J. Hall, W.-M. Huang and J.A. Wellner. Information and asymptotic efficiency in parametric-nonparametric models. Ann. Statist. 11, (1983), 432-452.
4. P.J. Bickel, C.A. Klassen, Y. Ritov and J.A. Wellner. Efficient and adaptive estimation in semiparametric models. Johns Hopkins University Press, Baltimore, 1993.
5. P. Billingsley. Convergence of probability measures. Wiley, New York, 1968.
6. N.E. Breslow. Discussion of the paper by D.R. Cox. J. Roy. Statist. Soc. Ser. B. 34, (1972), 216-217.
7. N.E. Breslow and J.J. Crowley. A large sample study of the life table and product limit estimates under random censorship. Ann. Statist. 2, (1974), 437-453.
8. R.J. Carroll, R.K. Knickerbocker and C.Y. Wang. Dimension reduction in semi-parametric regression model with errors in covariates. Ann. Statist. 23, (1995), 161-181.
9. H.Y. Chen and R.J. Little. Proportional hazards regression with missing covariates. J. Amer. Statist. Assoc. 94, (1999), 896-908.
10. D.R. Cox. Regression model and life tables (with discussion). J. Roy. Statist. Soc. Ser. B. 34, (1972), 187-220.
11. R.D. Gill. Non- and semi-parametric maximum likelihood estimators and the von Mises method. Scand. J. Statist. 16, (1989), 97-128.
12. W. Hoeffding. A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19, (1948), 293-325.
13. P. Hu, A.A. Tsiatis and M. Davidian. Estimating the parameters in the Cox model when covariate variables are measured with error. Biometrics. 54, (1998), 1407-1419.
14. J. Jacob. Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales. Z. Wahrsch. verw. Gebiete. 31, (1975), 235-254.
15. D.Y. Lin and Z. Ying. Cox regression with incomplete covariate measurements. J. Amer. Statist. Assoc. 88, (1993), 1341-1349.
16. M.C. Paik and W.Y. Tsai. On using the Cox proportional hazards model with missing covariates. Biometrika. 84, (1997), 579-593.
17. M.S. Pepe and T.R. Fleming. A nonparametric method for dealing with mismeasured covariate data. J. Amer. Statist. Assoc. 86, (1991), 108-113.
18. O. Pons. Estimation dans un modèle de Cox avec une covariable partiellement observée. Séminaire de l'Université Paris V, Paris, 2000.
19. O. Pons and M. Visser. A non-stationary Cox model. Scand. J. Statist., 27, (2000), 619-639.
20. R.L. Prentice. A case-cohort design for epidemiological cohort studies and diseases prevention trials. Biometrika. 73, (1986), 1-11.
21. J.M. Robins, A. Rotnitzki and L.P. Zhao. Estimation of regression coefficients when some regressors are not always observed. J. Amer. Statist. Assoc. 89, (1994), 846-866.
22. R.J. Serfling. Approximation theorems of mathematical statistics. Wiley, New York, 1980.
23. G.R. Shorack and J.A. Wellner. Empirical processes. Wiley, New York, 1986.
24. A.A. Tsiatis. A large sample study of Cox's regression model. Ann. Statist. 9, (1981), 93-108.
25. H.B. Zhou and M.S. Pepe. Auxiliary covariate data in failure time regression. Biometrika. 82, (1995), 139-149.