Efficient estimation from right-censored data when failure indicators are missing at random

Annals of Statistics

Volumn 26, Issue 1, 1998, Pages 164-182

  Van Der Laan, Mark J ^a   McKeague, Ian W ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Bivariate censorship; Incomplete data; Influence curve; Kaplan Meier estimator; Self consistency

Indexed keywords

EID: 0032373940     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1030563981     Document Type: Article

References (26)

1. BICKEL, P. J., KLAASSEN, C. A. J., RITOV, Y. and WELLNER, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins Univ. Press.
2. BIJLSMA, F. (1994). Mortality among young people: causes and background. Nederl. Tijdschr. Geneeskd. 138 2439-2443. (In Dutch.)
3. DINSE, G. E. (1982). Nonparametric estimation for partially-complete time and type of failure data. Biometrics 38 417-431.
4. EFRON, B. (1967). The two sample problem with censored data. Proc. Fifth Berkeley Symp. Math. Statist. Probab. 4 831-853.
5. GIJBELS, I., LIN, D. Y. and YING, Z. (1993). Non-and semi-parametric analysis of failure time data with missing failure indicators. Preprint.
6. GILL, R. D. (1989). Non-and semi-parametric maximum likelihood estimators and the von Mises method (part 1). Scand. J. Statist. 16 97-124.
7. GILL, R. D. and JOHANSEN, S. (1990). A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18 1501-1555.
8. GILL, R. D., VAN DER LAAN, M. J. and ROBINS, J. M. (1997). Coarsening at random. In Proceedings of the First Seattle Symposium on Biostatistics (D.-Y. Lin, ed.). Springer, New York.
9. GILL, R. D., VAN DER LAAN, M. J. and WELLNER, J. A. (1995). Inefficient estimators of the bivariate survival function for three models. Ann. Inst. H. Poincaré Probab. Statist. 31 545-597.
10. HEITJAN, D. F. and RUBIN, D. B. (1991). Ignorability and coarse data. Ann. Statist. 19 2244-2253.
11. JACOBSEN, M. and KEIDING, N. (1995). Coarsening at random in general sample spaces and random censoring in continuous time. Ann. Statist. 23 774-786.
12. KAPLAN, E. L. and MEIER, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 457-481.
13. LAPIDUS, G., BRADDOCK, M., SCHWARTZ, R., BANCO, L. and JACOBS, L. (1994). Accuracy of fatal motorcycle-injury reporting on death certificates. Accid. Anal. Prev. 26 535-542.
14. LITTLE, R. J. A. and RUBIN, D. B. (1987). Statistical Analysis with Missing Data. Wiley, New York.
15. Lo, S.-H. (1991). Estimating a survival function with incomplete cause-of-death data. J. Multivariate Anal. 39 217-235.
16. MCKEAGUE, I. W. and SUBRAMANIAN, S. (1996). Product-limit estimators and Cox regression with missing censoring information. Scand. J. Statist. To appear.
17. NEWEY, W. K. (1990). Semiparametric efficiency bounds. J. Appl. Econometrics 5 99-135.
18. O'SULLIVAN, F. (1986). A statistical perspective on ill-posed inverse problems. Statist. Sci. 1 502-527.
19. PRUITT, R. C. (1991). On negative mass assigned by the bivariate Kaplan-Meier estimator. Ann. Statist. 19 443-453.
20. ROBINS, J. M. and RITOV, Y. (1997). Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Statistics in Medicine 16 285-319.
21. ROBINS, J. M. and ROTNITZKY, A. (1992). Recovery of information and adjustment for dependent censoring using surrogate markers. In AIDS Epidemiology-Methodological Issues (N. Jewell, K. Dietz and V. Farewell, eds.) 279-331. Birkhäuser, Boston.
22. RUBIN, D. B. (1976). Inference and missing data. Biometrika 63 581-590.
23. VAN DER LAAN, M. J. (1996a). Efficient and inefficient estimation in semiparametric models. CWI Tract 114. Centre of Computer Science and Mathematics, Amsterdam.
24. VAN DER LAAN, M. J. (1996b). Efficient estimation in the bivariate censoring model and repairing NPMLE. Ann. Statist. 24 596-627.
25. VAN DER VAART, A. W. (1991). Efficiency and Hadamard differentiable functionals. Scand. J. Statist. 18 63-75.
26. WELLNER, J. A. (1982). Asymptotic optimality of the product limit estimator. Ann. Statist. 10 595-602.