Estimation of the mean function with panel count data using monotone polynomial splines

Biometrika

Volumn 94, Issue 3, 2007, Pages 705-718

  Lu, Minggen ^a   Zhang, Ying ^a   Huang, Jian ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Counting process; Empirical process; Isotonic regression; Maximum likelihood estimator; Maximum pseudolikelihood estimator; Monotone polynomial spline; Monte Carlo

Indexed keywords

EID: 34548528995     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asm057     Document Type: Article

References (29)

1. ANDERSON, J. A. & SENTHILSELVAN, A. (1980). Smooth estimates for the hazard function. J. R Statist. Soc. B 42, 322-7.
2. ANDREWS, D. F. & HERZBERG, A. M. (1985). Data; A Collection of Problems from Many Fields for the Student and Research Worker. New York: Spring-Verlag.
3. DE BOOR, C. (2001). A Practical Guide to Splines. New York: Spring-Verlag.
4. BYAR, D. P. (1980). The Veterans administration study of chemoprophylaxis for recurrent stage I bladder tumours: comparisons of placebo, pyridoxine, and topical thiotepa. In Bladder Tumors and Other Topics in Urological Oncology, Ed. M. Macaluso, P. H. Smith and F. Edsmyr, pp. 363-70. New York: Plenum.
5. BYAR, D. P., BLACKARD, C. & THE VETERANS ADMINISTRATION COOPERATIVE UROLOGICAL RESEARCH GROUP. (1977). Comparisons of placebo, pyridoxine, and topical thiotepa in preventing recurrence of stage I bladder cancer. Urology 10, 556-61.
6. CAI, T. & BETENSKY, R. A. (2003). Hazard regression for interval-censored data with penalized spline. Biometrics 59, 570-9.
7. HUANG, J. (1999). Efficient estimation of the partly linear additive Cox model. Ann. Statist. 27, 1536-63.
8. JAMSHIDIAN, M. (2004). On algorithms for restricted maximum likelihood estimation. Comp. Statist. Data Anal. 45, 137-57.
9. JONGBLOED, G. (1998). The iterative convex minorant algorithm for nonparametric estimation. J. Comp. Graph. Statist. 7, 310-21.
10. KALBFLEISCH, J. D. & LAWLESS, J. F. (1985). The analysis of panel count data under a Markov assumption. J. Am. Statist. Assoc. 80, 863-71.
11. KOOPERBERG, C., STONE, C. J. & TRUONG, Y. K. (1995). Hazard regression. J. Am. Statist. Assoc. 90, 78-94.
12. LEE, E. W. & KIM, M. Y. (1998). The analysis of correlated panel count data using a continuous-time Markov model. Biometrics 54, 1638-44.
13. RAMSAY, J. O. (1988). Monotone regression splines in action. Statist. Sci. 3, 425-41.
14. ROSEN, J. B. (1960). The gradient projection method for nonlinear programming. J. SIAM 8, 181-217.
15. ROSENBERG, P. S. (1995). Hazard function estimation using B-splines. Biometrics 51, 874-87.
16. SCHUMAKER, L. (1981). Spline Functions: Basic Theory. New York: Wiley.
17. SHEN, X. & WONG, W. H. (1994). Convergence rate of sieve estimates. Ann. Statist. 22, 580-615.
18. STONE, C. J. (1986). The dimensionality reduction principle for generalized additive models. Ann. Statist. 14, 590-606.
19. SUN, J. & KALBFLEISCH, J. D. (1995). Estimation of the mean function of point processes based on panel count data. Statist. Sinica. 5, 279-90.
20. SUN, J. & WEI, L. J. (2000). Regression analysis of panel count data with covariate-dependent observation and censoring times. J. R Statist. Soc. B 62, 293-302.
21. THALL, P. F. (1988). Mixed Poisson likelihood regression models for longitudinal interval count data. Biometrics 44, 197-209.
22. THALL, P. F. & LACHIN, J. M. (1988). Analysis of recurrent events: nonparametric methods for random-interval count data. J. Am. Statist. Assoc. 83, 339-47.
23. VAN DER VAART, A. W. & WELLNER, J. A. (1996). Weak Convergence and Empirical Processes with Application to Statistics. New York: Springer-Verlag.
24. 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.
25. WELLNER, J. A. & ZHANG, Y. (2000). Two estimators of the mean of a counting process with panel count data. Ann. Statist. 28, 779-814.
26. WHITTEMORE, A. S. & KELLER, J. B. (1986). Survival estimation using splines. Biometrics 42, 495-506.
27. ZHANG, Y. (2002). A semiparametric pseudolikelihood estimation method for panel count data. Biometrika 89, 39-48.
28. ZHANG, Y. & JAMSHIDIAN, M. (2004). On algorithms for NPMLE of the failure function with censored data. J. Comp. Graph. Statist. 13, 123-40.
29. ZHOU, S., SHEN, X. & WOLFE, D. A. (1998). Local asymptotics for regression splines and confidence regions. Ann. Statist. 26, 1760-82.