Efficient estimation of semiparametric transformation models for counting processes

Biometrika

Volumn 93, Issue 3, 2006, Pages 627-640

  Zeng, Donglin ^a   Lin, D Y ^a  

^a IL   (United States)

Author keywords

Censoring; Intensity; Linear transformation model; Nonparametric likelihood; Proportional hazards; Proportional odds; Recurrent events; Semiparametric efficiency; Survival data; Time varying covariate

Indexed keywords

EID: 33750189876     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/93.3.627     Document Type: Article

References (26)

1. AKAIKE, H. (1985). Prediction and entropy. In A Celebration of Statistics, Ed. A. C. Atkinson and S. E. Fienberg, pp. 1-24. New York: Springer-Verlag.
2. ANDERSEN, P. K. & GILL, R. D. (1982). Cox's regression model for counting processes: a large sample study. Ann. Statist. 10, 1100-20.
3. ANDERSEN, P. K., BORGAN, Ø., GILL, R. D. & KEIDING, N. (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag.
4. BENNETT, S. (1983). Analysis of survival data by the proportional odds model. Statist. Med. 2, 273-7.
5. BICKEL, P. J., KLAASSEN, C. A. J., RITOV, Y. & WELLNER, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Baltimore: Johns Hopkins University Press.
6. BYAR, D. P. (1980). The Veterans Administration study of chemoprophylaxis for recurrent stage I bladder tumors: comparisons of placebo, pyridoxine, and topical thiotepa. In Bladder T umors and Other Topics in Urological Oncology, Ed. M. Pavone-Macaluso, P. H. Smith and F. Edsmyn, pp. 363-70. New York: Plenum.
7. CHEN, K., JIN, Z. & YING, Z. (2002). Semiparametric analysis of transformation models with censored data. Biometrika 89, 659-68.
8. CHENG, S. C., WEI, L. J., & YING, Z. (1995). Analysis of transformation models with censored data. Biometrika 82, 835-45.
9. CHENG, S. C., WEI, L. J., & YING, Z. (1997). Prediction of survival probabilities with semi-parametric transformation models. J. Am. Statist. Assoc. 92, 227-35.
10. COLEMAN, T. F. & LI, Y. (1994). On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds. Math. Prog. 67, 189-224.
11. COLEMAN, T. F. & LI, Y. (1996). An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optimiz. 6, 418-45.
12. COX, D. R. (1972). Regression models and life-tables (with Discussion). J. R. Statist. Soc. B 34, 187-220.
13. COX, D. R. (1975). Partial likelihood. Biometrika 62, 269-76.
14. DABROWSKA, D. M. & DOKSUM, K. A. (1988). Partial likelihood in transformation models with censored data. Scand. J. Statist. 18, 1-23.
15. LIN, D. Y., WEI, L. J., & YING, Z. (2001). Semiparametric transformation models for point processes. J. Am. Statist. Assoc. 96, 620-8.
16. MURPHY, S. A. (1994). Consistency in a proportional hazards model incorporating a random effect. Ann. Statist. 22, 712-31.
17. MURPHY, S. A. (1995). Asymptotic theory for the frailty model. Ann. Statist. 23, 182-98.
18. MURPHY, S. A. & VAN DER VAART, A. W. (2000). On the profile likelihood. J. Am. Statist. Assoc. 95, 449-65.
19. MURPHY, S. A., ROSSINI, A. J. & VAN DER VAART, A. W. (1997). Maximal likelihood estimation in the proportional odds model. J. Am. Statist. Assoc. 92, 968-76.
20. PARNER, E. (1998). Asymptotic theory for the correlated gamma-frailty models. Ann. Statist. 26, 183-214.
21. PETTITT, A. N. (1984). Proportional odds models for survival data and estimates using ranks. Appl. Statist. 33, 169-75.
22. PRENTICE, R. L. (1973). Exponential survivals with censoring and explanatory variables. Biometrika 60, 278-88.
23. SCHARFSTEIN, D. O., TSIATIS, A. A. & GILBERT, P. B. (1998). Semiparametric efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data. Lifetime Data Anal. 4, 355-91.
24. THERNEAU, T. M. & GRAMBSCH, P. M. (2000). Modeling Survival Data: Extending the Cox Model. New York: Springer.
25. VAN DER VAART, A. W. & WELLNER, J. A. (1996). Weak Convergence and Empirical Processes. New York: Springer-Varlag.
26. WEI, L. J., LIN, D. Y. & WEISSFELD, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J. Am. Statist. Assoc. 84, 1065-73.