Asymptotic theory for the semiparametric accelerated failure time model with missing data

Annals of Statistics

Volumn 37, Issue 5 A, 2009, Pages 2351-2376

  Nan, Bin ^a   Kalbfleisch, John D ^a   Yu, Menggang ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b INDIANA UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Accelerated failure time model; Case cohort study; Censored linear regression; Donsker class; Empirical processes; Glivenko Cantelli class; Nonpre dictable weights; Pseudo Z estimator; Rank estimating equation; Semiparametric method

Indexed keywords

EID: 69049090896     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS657     Document Type: Article

References (31)

1. BICKEL, P.J., KLAASSEN, C.A. J., RlTOV, Y. and WELLNER, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins Univ. Press, Baltimore. MR1245941
2. Borgan, O., Langholz, B., Samuelsen, S. O., Goldstein, L. andPogoda, J. (2000). Exposure stratified case-cohort designs. Lifetime Data Anal. 6 39-58. MR1767493
3. BRESLOW, N. E. and WELLNER, J. A. (2007). Weighted likelihood for semiparametric models and two-phase stratified samples, with application to Cox regression. Scand. J. Statist. 34 86-102. MR2325244
4. BUCKLEY, J. and JAMES, I. R. (1979). Linear regression with censored data. Biometrika 66 429-436.
5. CHEN, K. and Lo, S.-H. (1999). Case-cohort and case-control analysis with Cox's model. Biometrika 86 755-764. MR1741975
6. COX, D. R. (1972). Regression models and life tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187-220. MR0341758
7. FYGENSON, M. and RITOV, Y. (1994). Monotone estimating equations for censored data. Ann. Statist. 22 732-746. MR1292538
8. Hu, H. (1998). Large sample theory for pseudo-maximum likelihood estimates in semipara-metric models. Ph.D. dissertation, Dept. Statistics, Univ. Washington.
9. Huang, Y. (2002). Calibration regression of censored lifetime medical cost. J. Amer. Statist. Assoc. 97 318-327. MR1947289
10. JIN, Z., Ying, Z. and WEI, L. J. (2001). A simple resampling method by perturbing the minimand. Biometrika 88 381-390. MR1844838
11. KALBFLEISCH, J. D. and LAWLESS, J. F. (1988). Likelihood analysis of multi-state models for disease incidence and mortality. Stat. Med. 7 149-160.
12. KALBFLEISCH, J. D. and PRENTICE, R. L. (2002). The Statistical Analysis of Failure Time Data, 2nd ed. Wiley, New York. MR1924807
13. KULICH, M. and LIN, D. Y. (2004). Improving the efficiency of relative-risk estimation in case-cohort studies. J. Amer. Statist. Assoc. 99 832-844. MR2090916
14. LITTLE, R.J.A. and RUBIN, D. B. (2002). Statistical Analysis with Missing Data, 2nd ed. Wiley, Hoboken, NJ. MR1925014
15. NAN B. WELLNER J. A. (2006). Semiparametric pseudo Z-estimation with applications. Technical report, Dept. Biostatistics, Univ. Michigan.
16. Nan, B., Yu, M. and Kalbfleisch, J. D. (2006). Censored linear regression for case-cohort studies. Biometrika 93 747-762. MR2285069
17. Parzen, M. I., Wei, L.J. and Ying, Z. (1994). A resampling method based on pivotal estimating functions. Biometrika 81 341-350. MR1294895
18. Pierce, D. A. (1982). The asymptotic effect of substituting estimators for parameters in certain types of statistics. Ann. Statist. 10 475-478. MR0653522
19. Prentice, R. L. (1986). A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika 73 1-11.
20. Pugh, M., Robins, J., Lipsitz, S. and Harrington, D. (1994). Inference in the Cox proportional hazards model with missing covariates. Technical Report 758Z, Harvard School of Public Health, Boston, MA.
21. Ritov, Y. (1990). Estimation in a linear regression model with censored data. Ann. Statist. 18 303-328. MR1041395
22. Robins, J.M., Rotnitzky, A. and Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. J. Amer. Statist. Assoc. 89 846-866. MR1294730
23. Self, S. G. and Prentice, R. L. (1988). Asymptotic distribution theory and efficiency results for case-cohort studies. Ann. Statist. 16 64-81. MR0924857
24. Stute, W. (1993). Consistent estimation under random censorship when covariables are available. J. Multivariate Anal. 45 89-103. MR1222607
25. Stute, W. (1996). Distributional convergence under random censorship when covariables are present. Scand. J. Statist. 23 461-471. MR1439707 (Pubitemid 126407691)
26. Tsiatis, A. A. (1990). Estimating regression parameters using linear rank tests for censored ata. Ann. Statist. 18 354-372. MR1041397
27. van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York. MR1385671
28. van der Vaart, A.W. and Wellner, J. A. (2000). Preservation theorems for Glivenko- Cantelli and uniform Glivenko-Cantelli classes. In High Dimensional Probability II (E. Gine, D. Mason and J. A. Wellner, eds.) 115-134. Birkhauser, Boston. MR1857319
29. Wei, L.J., Ying, Z.L. and Lin, D. Y. (1990). Linear regression analysis for censored survival data based on rank tests. Biometrika 77 845-851. MR1086694
30. Ying, Z. (1993). A large sample study of rank estimation for censored regression data. Ann. Statist. 21 76-99. MR1212167
31. Yu, M. and Nan, B. (2006). A hybrid Newton-type method for censored survival data using double weights in linear models. Lifetime Data Anal. 12 345-364. MR2328581