Skip to main content
SpringerLink
Log in

Statistical Inference for Two-Sample and Regression Models with Heterogeneity Effect: A Collected-Sample Perspective

  • Conference paper
Probability, Statistics and Modelling in Public Health

Summary

Heterogeneity effect is an important issue in the analysis of clinical trials, survival data, and epidemiological cohort studies. This article reviews the works of inference for heterogeneity effect from a series of works by Hsieh who used the empirical process approach, and relevant works by Bagdonavičius, Nikulin, and coworkers. This includes two-sample models and Cox-type relative risk regression models. Heterogeneity property over the covariate space as well as non-constancy property are discussed for several models. In survival analysis, the log-relative risk as a function of time and of the covariates are plotted to present the heterogeneity property of Hsieh’s and Bagdonavicius and Nikulin’s hazards regression models.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersen, P. K., Borgan, Ø., Gill, R. D., and Keiding, N.: Statistical Models Based on Counting Processes. Springer-Verlag, New York (1993)

    Google Scholar 

  2. Bagdonavičius, V., Hafdi, M. A., and Nikulin, M.: Analysis of survival data with cross-effects of survival functions. Biostatistics, 5 415–425 (2004)

    Google Scholar 

  3. Bagdonavičius, V. and Nikulin, M.: Generalized proportional hazards model based on modified partial likelihood. Lifetime Data Analysis, 5 329–350 (1999)

    MathSciNet  Google Scholar 

  4. Bagdonavičius, V. and Nikulin, M.: Accelerated Life Models. Chapman and Hall/CRC, London (2002)

    Google Scholar 

  5. Bagdonavičius, V. and Nikulin, M.: Semiparametric analysis of survival data with multiple crossing of survival functions. Preprint 0304, IFR “Public Health”, University Victor Segalen Bordeaux 2, France (2004)

    Google Scholar 

  6. Bagdonavičius, V., Nikulin, M., Levuliene, R., and Zdorova, O.: Tests for homogeneity of survival distributions against nonlocation alternatives and statistical analysis of chemo and radio therapy data of the Gastrointestinal Tumor Study Group. Lifetime Data Analysis, to appear (2005)

    Google Scholar 

  7. Bickel, P. J., Klaasen, C. A., Ritov, Y., and Wellner, J. A.: Efficient and Adaptive Inference in Semiparametric Models., Johns Hopkins University Press, Baltimore (1993)

    Google Scholar 

  8. Cox, D. R.: Regression models and life-tables (with discussion). Journal of the Royal Statistical Society, Series B, 34 187–220 (1972)

    MATH  Google Scholar 

  9. Csörgő, M.: Quantile Processes with Statistical Applications. SIAM, Philadelphia (1983)

    Google Scholar 

  10. Gore, S. M., Pocock, S. J., and Kerr, G. R.: Regression models and non-proportional hazards in the analysis of breast cancer survival. Applied Statistics, 33 176–195 (1984)

    Google Scholar 

  11. Heller, G.: The Cox proportional hazards model with a partly linear relative risk function. Lifetime Data Analysis, 7 255–277 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hsieh, F.: The empirical process approach for semiparametric two-sample models with heterogeneous treatment effect. Journal of the Royal Statistical Society, Series B, 57 735–748 (1995)

    MATH  MathSciNet  Google Scholar 

  13. Hsieh, F.: Empirical process approach in a two-sample locationscale model with censored data. The Annals of Statistics, 24 2705–2719 (1996a)

    MATH  MathSciNet  Google Scholar 

  14. Hsieh, F.: Nonparametric and semiparametric estimation of the receiver operating characteristic curve. The Annals of Statistics, 24 25–40 (1996b)

    MATH  MathSciNet  Google Scholar 

  15. Hsieh, F.: A transformation model for two survival curves: an empirical process approach. Biometrika, 83 519–528 (1996c)

    Article  MATH  MathSciNet  Google Scholar 

  16. Hsieh, F.: On heteroscedastic Cox’s regression models and its applications. Journal of the Royal Statistical Society, Series B, 63 63–79 (2001)

    MATH  MathSciNet  Google Scholar 

  17. Martinussen, T., Scheike, T. H., and Skovgaard, Ib. M.: Efficient estimation of fixed and time-varying covariate effects in multiplicative intensity models. Scandinavian Journal of Statistics, 28 58–74 (2001)

    Article  Google Scholar 

  18. Murphy, S. A.: Testing for a time-dependent coefficient in Cox’s regression model. Scandinavian Journal of Statistics, 20 35–50 (1993)

    MATH  MathSciNet  Google Scholar 

  19. Murphy, S. A. and Sen, P. K.: Time dependent coefficients in a Cox-type regression model. Stochastic Processes and Their Applications, 39 153–180 (1991)

    Article  MathSciNet  Google Scholar 

  20. Nielsen, J. P., Linton, O., and Bickel, P. J.: On a semiparametric survival model with flexible covariate effect. The Annals of Statistics, 26 215–241 (1998)

    MathSciNet  Google Scholar 

  21. Sasieni, P.: Non-orthogonal projections and their application to calculating the information in a partly linear Cox model. Scandinavian Journal of Statistics, 19 215–233 (1992a)

    MATH  MathSciNet  Google Scholar 

  22. Sasieni, P.: Information bounds for the conditional hazard ratio in a nested family of regression models. Journal of the Royal Statistical Society, Series B, 54 627–635 (1992b)

    MathSciNet  Google Scholar 

  23. Valsecchi, M. G., Silvestri, D., and Sasieni, P.: Evaluation of long-term survival: use of diagnostics and robust estimators with Cox’s proportional hazards model. Statistics in Medicine, 15 2763–2780 (1996)

    Article  Google Scholar 

  24. Wu, H.-D. I.: Effect of model misspecification when omitting heterogeneity. In: Nikulin, M. S., Balakrishnan, N., Limnios, N., and Mesbah, M. (eds) Parametric and Semiparametric models with applications to reliability, survival analysis, and quality of life, 239–250. Birkhauser, Boston (2004a)

    Google Scholar 

  25. Wu, H.-D. I.: A partial score test for difference among heterogeneous populations. Preprint, China Medical University, TAIWAN. (Under revision in Lifetime Data Analysis.) (2004b)

    Google Scholar 

  26. Wu, H.-D. I. and Hsieh, F.: Heterogeneity and varying effect in hazards regression. Preprint, China Medical University, TAIWAN (2004)

    Google Scholar 

  27. Wu, H.-D. I., Hsieh, F., and Chen, C.-H.: Validation of a heteroscedastic hazards regression model. Lifetime Data Analysis, 8 21–34 (2002)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Public Health, China Medical University, 91 Hsueh-Shih Rd., Taichung, 404, Taiwan

    Hong-Dar Isaac Wu

Authors
  1. Hong-Dar Isaac Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université Victor Segalin Bordeaux 2, France

    Mikhail Nikulin  & Daniel Commenges  & 

  2. V. Steklov Mathematical Institute, Saint Petersburg, Russia

    Mikhail Nikulin

  3. Université René Descartes, Paris, France

    Catherine Huber

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, Inc.

About this paper

Cite this paper

Wu, HD.I. (2006). Statistical Inference for Two-Sample and Regression Models with Heterogeneity Effect: A Collected-Sample Perspective. In: Nikulin, M., Commenges, D., Huber, C. (eds) Probability, Statistics and Modelling in Public Health. Springer, Boston, MA. https://doi.org/10.1007/0-387-26023-4_31

Download citation

Publish with us

Policies and ethics

Search

Navigation