The Annals of Statistics

Towards a general asymptotic theory for Cox model with staggered entry

Yannis Bilias, Minggao Gu, and Zhiliang Ying

Full-text: Open access

Abstract

A general asymptotic theory is established for the two-parameter Cox score process with staggered entry data. It extends in several directions the existing theory developed by Sellke and Siegmund, Slud and Gu and Lai. An essential tool employed here is a modern empirical process theory, as elucidated in a recent monograph by Pollard.

Article information

Source
Ann. Statist., Volume 25, Number 2 (1997), 662-682.

Dates
First available in Project Euclid: 12 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031833668

Digital Object Identifier
doi:10.1214/aos/1031833668

Mathematical Reviews number (MathSciNet)
MR1439318

Zentralblatt MATH identifier
0923.62085

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62E20: Asymptotic distribution theory 62J05: Linear regression

Keywords
Proportional hazards regression partial likelihood score staggered entry empirical processes functional central limit theorem pseudodimension manageability random fields

Citation

Bilias, Yannis; Gu, Minggao; Ying, Zhiliang. Towards a general asymptotic theory for Cox model with staggered entry. Ann. Statist. 25 (1997), no. 2, 662--682. doi:10.1214/aos/1031833668. https://projecteuclid.org/euclid.aos/1031833668


Export citation

References

  • ANDERSEN, P. K., BORGAN, Ø., GILL, R. D. and KEIDING, N. 1993. Statistical Models Based on Counting Processes. Springer, New York. Z.
  • ANDERSEN, P. K. and GILL, R. D. 1982. Cox's regression model for counting processes: a large sample study. Ann. Statist. 10 1100 1120. Z. Z.
  • COX, D. R. 1972. Regression models and life-tables with discussion. J. Roy. Statist. Soc. Ser. B 34 187 220.
  • COX, D. R. 1975. Partial likelihood. Biometrika 62 269 276. Z.
  • GILL, R. D. and SCHUMACHER, M. 1987. A simple test of the proportional hazards assumption. Biometrika 74 289 300. Z.
  • GOFFMAN, C. 1965. Calculus of Several Variables. Harper and Row, New York. Z.
  • GU, M. G. and LAI, T. L. 1991. Weak convergence of time-sequential censored rank statistics with applications to sequential testing in clinical trials. Ann. Statist. 19 1403 1433. Z.
  • GU, M. G. and YING, Z. 1995. Group sequential methods for survival data using partial likelihood score processes with covariate adjustment. Statist. Sinica 5 793 804. Z.
  • KALBFLEISCH, J. D., LAWLESS, J. F. and ROBINSON, J. A. 1991. Methods for the analysis and prediction of warranty claims. Technometrics 33 273 285. Z.
  • LAI, T. L. and YING, Z. 1988. Stochastic integral of empirical-ty pe processes with applications to censored regression. J. Multivariate Anal. 27 334 358. Z.
  • LIN, D. Y. 1991. Goodness-of-fit analysis for the Cox regression model based on a class of parameter estimators. J. Amer. Statist. Assoc. 86 725 728. Z.
  • LIN, D. Y., SHEN, L., YING, Z. and BRESLOW, N. 1996. Group sequential designs for monitoring survival probabilities. Biometrics 52 1033 1041. Z.
  • POLLARD, D. 1990. Empirical Processes: Theory and Applications. IMS, Hay ward, CA. Z.
  • SELLKE, T. and SIEGMUND, D. 1983. Sequential analysis of the proportional hazards model. Biometrika 70 315 326. Z.
  • SLUD, E. V. 1984. Sequential linear rank tests for two-sample censored survival data. Ann. Statist. 12 551 571. Z.
  • SLUD, E. and WEI, L. J. 1982. Two-sample repeated significance tests based on the modified Wilcoxon statistic. J. Amer. Statist. Assoc. 77 862 868. Z.
  • TSIATIS, A. A., ROSNER, G. L. and TRITCHLER, D. L. 1985. Group sequential tests with censored survival data adjusting for covariates. Biometrika 72 365 373.
  • IOWA STATE UNIVERSITY MONTREAL, QUEBEC
  • AMES, IOWA 50011 CANADA H3A 2K6
  • HILL CENTER, BUSCH CAMPUS RUTGERS UNIVERSITY
  • PISCATAWAY, NEW JERSEY 08855 E-MAIL: zying@stat.rutgers.edu