Parameter estimation in regression for long-term survival rate from censored data

Journal of Statistical Planning and Inference

Volumn 99, Issue 2, 2001, Pages 211-222

  Subramanian, Sundarraman ^a  

^a UNIVERSITY OF MAINE   (United States)

Author keywords

62N02; Conditional Kaplan Meier estimator; Counting process; Cox proportional hazards; Cumulative hazard function; Martingale; Newton Raphson method; Primary 62N01; Secondary 62E20

Indexed keywords

EID: 0037706356     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(01)00084-2     Document Type: Article

References (15)

1. Andersen P.K., Borgan O., Gill D.R., Keiding N. Statistical Models Based on Counting Processes. 1993;Springer, New York.
2. Andersen P.K., Gill R.D. Cox's regression model for counting processes: a large sample study. Ann. Statist. 10:1982;1100-1120.
3. Chang M.N., Yang G. Strong consistency of a nonparametric estimator of the survival function with doubly censored data. Ann. Statist. 15:1987;1536-1547.
4. Cox D.R. Regression models and life-tables (with Discussion). J. R. Statist. Soc. B. 34:1972;187-202.
5. Dabrowska D.M. Uniform consistency of the kernel conditional Kaplan-Meier estimate. Ann. Statist. 17:1989;1157-1167.
6. Efron, B., 1967. Two sample problem with censored data. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. IV. Prentice-Hall, Engelwood Cliffs, NJ, pp. 831-853.
7. Gill R.D. Censoring and Stochastic Integrals. 1980;Mathematisch Centrum, Amsterdam.
8. Groeneboom P., Wellner J.A. Information Bounds and Nonparametric Maximum Likelihood Estimation. 1992;Birkhauser Verlag, Basel.
9. Jung S. Regression analysis for long-term survival rate. Biometrika. 83:1996;227-232.
10. Laird N.M. Missing information principle. Encycl. Statist. Sci. 5:1985;548-552.
11. McCullagh P., Nelder J.A. Generalized Linear Models. 2nd Edition:1989;Chapman & Hall, London.
12. Orchard, T., Woodbury, M.A., 1972. A missing information principle: theory and applications. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics Probability, Vol. 1, pp. 697-715.
13. Robins J.M., Ritov Y. Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Statist. Med. 16:1997;285-319.
14. Shorack G.R., Wellner J.A. Empirical Processes with Applications to Statistics. 1986;Wiley, New York.
15. Ying Z., Jung S., Wei L.J. Survival analysis with median regression models. J. Amer. Statist. Assoc. 90:1995;178-184.