Partially linear additive hazards regression with varying coefficients

Journal of the American Statistical Association

Volumn 103, Issue 483, 2008, Pages 1200-1213

  Yin, Guosheng ^a   Li, Hui ^b   Zeng, Donglin ^c  

^a UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

^b BEIJING NORMAL UNIVERSITY   (China)

^c University of North Carolina at Chapel Hill   (United States)

Author keywords

Asymptotic normality; Censored data; Estimating equation; Kernel function; Local polynomial; Semiparametric estimation; Varying coefficient model

Indexed keywords

EID: 54949146866     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214508000000463     Document Type: Article

References (41)

1. Aalen, O. O. (1989), "A Linear Regression Model for the Analysis of Lifetimes," Statistics in Medicine, 8, 907-925.
2. Andersen, P., and Gill, R. (1982), "Cox's Regression Model for Counting Processes: A Large Sample Study," The Annals of Statistics, 10, 1100-1120.
3. Ang, P.-T., Buzdar, A. U., Smith, T. L., Kau, S., and Hortobagyi, G. N. (1989), "Analysis of Dose Intensity in Doxorubicin-Containing Adjuvant Chemotherapy in Stage II and III Breast Carcinoma," Journal of Clinical Oncology, 7, 1677-1684.
4. Bickel, P. J., and Rosenblatt, M. (1973), "On Some Global Measures of the Deviations of Density Function Estimates," The Annals of Statistics, 1, 1071-1095.
5. Cai, Z., and Sun, Y. (2003), "Local Linear Estimation for Time-Dependent Coefficients in Cox's Regression Models," Scandinavian Journal of Statistics, 30, 93-111.
6. Cai, Z., Fan, J., and Li, R. (2000), "Efficient Estimation and Inference for Varying-Coefficient Models," Journal of the American Statistical Association, 95, 888-902.
7. Chen, S., and Zhou, L. (2006), "Local Partial Likelihood Estimation in Proportional Hazards Regression," The Annals of Statistics, 35, 888-916.
8. Chiang, C.-T., Rice, J. A., and Wu, C. O. (2001), "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, 96, 605-619.
9. Cox, D. R. (1972), "Regression Models and Life Tables" (with discussion), Journal of the Royal Statistical Society, Ser. B, 34, 187-220.
10. Dabrowska, D. M. (1997), "Smoothed Cox Regression," The Annals of Statistics, 25, 1510-1540.
11. Efron, B., and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, London: Chapman & Hall.
12. Fan, J., and Chen, J. (1999), "One-Step Local Quasi-Likelihood Estimation," Journal of Royal Statistical Society, Ser. B, 61, 927-943.
13. Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman & Hall.
14. Fan, J., Gijbels, I., and King, M. (1997), "Local Likelihood and Local Partial Likelihood in Hazard Regression," The Annals of Statistics, 25, 1661-1690.
15. Fan, J., Lin, H. Z., and Zhou, Y. (2006), "Local Partial Likelihood Estimation for Lifetime Data," The Annals of Statistics, 34, 290-325.
16. Fleming, T., and Harrington, D. (1991), Counting Processes and Survival Analysis, New York: Wiley.
17. Gamerman, D. (1991), "Dynamic Bayesian Methods for Survival Data," Applied Statistics, 40, 63-79.
18. Hastie, T., and Tibshirani, R. (1993), "Varying-Coefficient Models," Journal of the Royal Statistical Society, Ser. B, 55, 757-796.
19. Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L.-P. (1998), "Nonparametric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data," Biometrika, 85, 809-822.
20. Huang, J. Z., Wu, C. O., and Zhou, L. (2002), "Varying-Coefficient Models and Basis Function Approximations for the Analysis of Repeated Measurements," Biometrika, 89, 111-128.
21. Huffer, F. W., and McKeague, I. W. (1991), "Weighted Least Squares Estimation for Aalen's Additive Risk Model," Journal of the American Statistical Association, 86, 114-129.
22. Kalbfleisch, J. D., and Prentice, R. L. (2002), The Statistical Analysis of Failure Time Data (2nd ed.), New York: Wiley.
23. Kosorok, M. R. (2008), Introduction to Empirical Processes and Semiparametric Inference, New York: Springer.
24. Lin, D. Y., and Ying, Z. (1994), "Semiparametric Analysis of the Additive Risk Model," Biometrika, 81, 61-71.
25. Lin, D. Y., Fleming, T. R., and Wei, L. J. (1994), "Confidence Bands for Survival Curves Under the Proportional Hazards Model," Biometrika, 81, 73-81.
26. Martinussen, T., and Scheike, T. H. (2006), Dynamic Regression Models for Survival Data, New York: Springer-Verlag.
27. Martinussen, T., Scheike, T. H., and Skovgaard, I. M. (2002), "Efficient Estimation of Fixed and Time-Varying Covariate Effects in Multiplicative Intensity Models," Scandinavian Journal of Statistics, 29, 57-74.
28. Marzec, L., and Marzec, P. (1997), "On Fitting Cox's Regression Model With Time-Dependent Coefficients," Biometrika, 84, 901-908.
29. McKeague, I. W., and Sasieni, P. (1994), "A Partly Parametric Additive Risk Model," Biometrika, 81, 501-514.
30. Murphy, S. (1993), "Testing for a Time-Dependent Coefficient in Cox's Regression Model," Scandinavian Journal of Statistics, 20, 35-50.
31. Murphy, S., and Sen, P. (1991), "Time-Dependent Coefficients in a Cox-Type Regression Model," Stochastic Processes and Their Applications, 39, 153-180.
32. Nielsen, J. P., and Linton, O. (1995), "Kernel Estimation in a Nonparametric Marker Dependent Hazard Estimation," The Annals of Statistics, 5, 1735-1748.
33. Nielsen, J. P., and Tanggaard, C. (2001), "Simple Boundary and Bias-Correction Kernel Hazard Estimation," Scandinavian Journal of Statistics, 28, 695-724.
34. Peng, L., and Huang, Y. (2007), "Survival Analysis With Temporal Covariate Effects," Biometrika, 94, 719-733.
35. Sun, Y., and Wu, H. (2005), "Semiparametric Time-Varying Coefficients Regression Model for Longitudinal Data," Scandinavian Journal of Statistics, 32, 21-47.
36. Tian, L., Zucker, D., and Wei, L. J. (2005), "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, 100, 172-183.
37. van der Vaart, A. (1998), Asymptotic Statistics, Cambridge, U.K.: Cambridge University Press.
38. van der Vaart, A., and Wellner, J. (1996), Weak Convergence and Empirical Processes, New York: Springer-Verlag.
39. Yandell, B. S. (1983), "Nonparametric Inference for Rates With Censored Survival Data," The Annals of Statistics, 11, 1119-1135.
40. Zhang, D. (2004), "Generalized Linear Mixed Models With Varying Coefficients for Longitudinal Data," Biometrics, 60, 8-15.
41. Zucker, D., and Karr, A. (1990), "Nonparametric Survival Analysis With Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach," The Annals of Statistics, 18, 329-353.