Skip to main content
Log in

A Bootstrap Approach to Nonparametric Regression for Right Censored Data

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

In this paper a two-stage bootstrap method is proposed for nonparametric regression with right censored data. The method is applied to construct confidence intervals and bands for a conditional survival function. Its asymptotic validity is established using counting process techniques and martingale central limit theory. The performance of the bootstrap method is investigated in a Monte Carlo study. An illustration is given using a real data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Akritas, M. (1986). Bootstrapping the Kaplan-Meier estimator, J. Amer. Statist. Assoc., 81, 1032-1039.

    Google Scholar 

  • Andersen, P. K. and Gill, R. D. (1982). Cox's regression model for counting processes: A large sample study, Ann. Statist., 10, 1100-1120.

    Google Scholar 

  • Beran, R. (1981). Nonparametric regression with randomly censored survival data, Tech. Report, Department of Statistics, University of California, Berkeley.

    Google Scholar 

  • Burr, D. (1994). A comparison of certain bootstrap confidence intervals in the Cox model, J. Amer. Statist. Assoc., 89, 1290-1302.

    Google Scholar 

  • Cao, R. and González-Manteiga, W. (1993). Bootstrap methods in regression smoothing, J. Nonparametr. Statist., 2, 379-388.

    Google Scholar 

  • Chung, K. L. (1974). A Course in Probability Theory, 2nd ed., Academic Press, New York.

    Google Scholar 

  • Dabrowska, D. M. (1987). Nonparametric regression with censored survival time data, Scand. J. Statist., 14, 181-197.

    Google Scholar 

  • Dabrowska, D. M. (1989). Uniform consistency of the Kernel conditional Kaplan-Meier estimate, Ann. Statist., 7, 1-26.

    Google Scholar 

  • Dabrowska, D. M. (1992). Variable bandwidth conditional Kaplan-Meier estimate, Scand. J. Statist., 19, 351-361.

    Google Scholar 

  • Efron, B. (1979). Bootstrap methods: Another look at the jackknife, Ann. Statist., 7, 1-26.

    Google Scholar 

  • Efron, B. (1981). Censored data and the bootstrap, J. Amer. Statist. Assoc., 76, 312-319.

    Google Scholar 

  • Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Monogr. Statist. Appl. Probab., No. 57, Chapman & Hall, London.

    Google Scholar 

  • Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis, Wiley, New York.

    Google Scholar 

  • Freedman, D. A. (1981). Bootstrapping regression models, Ann. Statist., 6, 1218-1228.

    Google Scholar 

  • Gill, R. D. (1980). Censoring and stochastic integrals, Mathematical Centre Tracts, 124, Mathematical Centre, Amsterdam.

    Google Scholar 

  • Hall, P. (1992). The Bootstrap and Edgeworth Expansion, Springer, New York.

    Google Scholar 

  • Hall, W. J. and Wellner, J. A. (1980). Confidence bands for a survival curve from censored data, Biometrika, 67, 133-143.

    Google Scholar 

  • Härdle, W. and Bowman, A. W. (1988). Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands, J. Amer. Statist. Assoc., 83, 102-110.

    Google Scholar 

  • Härdle, W. and Marron, J. S. (1991). Bootstrap simultaneous error bars for nonparametric regression, Ann. Statist., 19, 778-796.

    Google Scholar 

  • Hjort, N. L. (1985). Bootstrapping Cox's regression model, Tech. Report, No. 241, Department of Statistics, Stanford University, California.

    Google Scholar 

  • Li, G. (1997). Optimal rate local smoothing in a multiplicative intensity counting process model, Journal of Mathematical Methods of Statistics, 6, 224-244.

    Google Scholar 

  • Li, G. and Datta, S. (1999). A bootstrap approach to nonparametric regression for right censored data, Tech. Report, Sta 99-8, Department of Statistics, University of Georgia, Athens.

    Google Scholar 

  • Li, G. and Doss, H. (1995). An approach to nonparametric regression for life history data using local linear fitting, Ann. Statist., 23, 787-823.

    Google Scholar 

  • Lo, S. H. and Singh, K. (1986). The product-limit estimator and the bootstrap: Some asymptotic representations, Probab. Theory Related Fields, 71, 455-465.

    Google Scholar 

  • McKeague, I. W. and Utikal, K. J. (1990). Inference for a nonlinear counting process regression model, Ann. Statist., 18, 1172-1187.

    Google Scholar 

  • Nadaraya, E. A. (1970). Remarks on nonparametric estimates for density functions and regression curves, Theory Probab. Appl., 15, 134-137.

    Google Scholar 

  • Rao, B. L. S. Prakasa (1983). Nonparametric Functional Estimation, Academic Press, New York.

    Google Scholar 

  • Van Keilegom, I. and Veraverbeke, N. (1997). Weak convergence of the bootstrapped conditional Kaplan-Meier process and its quantile process, Comm. Statist. Theory Methods, 26, 853-869.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Li, G., Datta, S. A Bootstrap Approach to Nonparametric Regression for Right Censored Data. Annals of the Institute of Statistical Mathematics 53, 708–729 (2001). https://doi.org/10.1023/A:1014644700806

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014644700806

Navigation