Skip to main content
SpringerLink
Log in

Connecting Threshold Regression and Accelerated Failure Time Models

  • Conference paper
  • First Online:
Risk Assessment and Evaluation of Predictions

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 215))

  • 1931 Accesses

Abstract

The accelerated failure time model is one of the most commonly used alternative methods to the Cox proportional hazards model when the proportional hazards assumption is violated. Threshold regression is a relatively new alternative model for analyzing time-to-event data with non-proportional hazards. It is based on first-hitting-time models, where the time-to-event data can be modeled as the time at which the stochastic process of interest first hits a boundary or threshold state. This paper compares threshold regression and accelerated failure time models and demonstrates the situations when the accelerated failure time model becomes a special case of the threshold regression model. Three illustrative examples from clinical studies are provided.

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 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Aalen, O.O., Borgan, Ø., Gjessing, H.K.: Survival and Event History Analysis: A Process Point of View. Springer, New York (2008)

    Book  Google Scholar 

  2. Betensky, R.A., Rabinowitz, D., Tsiatis, A.A.: Computationally simple accelerated failure time regression for interval censored data. Biometrika 88, 703–711 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Breslow, N.E., Edler, L., Breger, J.: A two-sample censored-data rank test for acceleration. Biometrics 40, 1049–1062 (1984)

    Article  MATH  Google Scholar 

  4. Buckley, I.V., James, I.: Linear regression with censored data. Biometrika 66, 429–436 (1979)

    Article  MATH  Google Scholar 

  5. Duchesne, T., Lawless, J.: Alternative time scales and failure time models. Lifetime Data Anal. 6, 157–179 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Duchesne, T., Rosenthal, J.S.: On the collapsibility of lifetime regression models. Adv. Appl. Probab. 35, 755–772 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fleming, T.R., O’Fallon, J.R., O’Brien, P.C., Harrington D.P.: Modified Kolmogorov-Smirnov test procedures with application to arbitrarily right-censored data. Biometrics 36, 607–625 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fygenson, M., Ritov, Y.: Monotone estimating equations for censored data. Ann. Stat. 22, 732–746 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gill, R.D., Schumacher, M.: A simple test of the proportional Hazards assumption. Biometrika 74, 289–300 (1987)

    Article  MATH  Google Scholar 

  10. Hess, K.R.: Graphical methods for assessing violations of the proportional hazards assumption in Cox regression. Stat. Med. 14, 1707–1723 (1995)

    Article  Google Scholar 

  11. Huang, J., Harrington, D.P.: Operating characteristics of partial least squares in right-censored data analysis and its application in predicting the change of HIV-I RNA. In: Nikulin, M., Commenges, D., Huber, C. (eds.) Probability, Statistics, and Modelling in Public Health, pp. 202–230. Springer, New York (2005)

    Google Scholar 

  12. Jin, Z., Lin, D.Y., Wei, L.J., Ying, Z.: Rank-based inference for the accelerated failure time model. Biometrika 90, 341–353 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jin, Z., Lin, D.Y., Ying, Z.: On least-squares regression with censored data. Biometrika 93, 147–161 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kalbfleisch, J.D., Prentice, R.L.: The Statistical Analysis of Failure Time Data, 2nd edn. Wiley, New York (2002)

    Book  MATH  Google Scholar 

  15. Klein, J.P., Moeschberger, M.L.: Survival Analysis: Techniques for Censored and Truncated Data, 2nd edn. Springer, New York (2003)

    Google Scholar 

  16. Kordonsky, K.B., Gertsbakh, I.: Multiple time scales and the lifetime coefficient of variation: engineering applications. Lifetime Data Anal. 3, 139–156 (1997)

    Article  MATH  Google Scholar 

  17. Lai, T.L., Ying, Z.: Large sample theory of a modified Buckley-James estimator for regression analysis with censored data. Ann. Stat. 19, 1370–1402 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lawless, J.F.: Statistical Models and Methods for Lifetime Data, 2nd edn. Wiley, New York (2003)

    MATH  Google Scholar 

  19. Lawless, J., Crowder, M.: Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Anal. 10, 213–227 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lee, M.-L.T., Whitmore, G.A.: Threshold regression for survival analysis: modeling event times by a stochastic process reaching a boundary. Stat. Sci. 21, 501–513 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lee, M.-L.T., Whitmore, G.A.: Proportional hazards and threshold regression: their theoretical and practical connections. Lifetime Data Anal. 16, 196–214 (2010)

    Article  MathSciNet  Google Scholar 

  22. Lee, M.-L.T., Whitmore, G.A., Laden, F., Hart, J.E., Garshick, E.: Assessing lung cancer risk in railroad workers using a first hitting time regression model. Environmetrics 15, 501–512 (2004)

    Article  Google Scholar 

  23. Lee, M.-L.T., Whitmore, G.A., Laden, F., Hart, J.E., Garshick, E.: A case-control study relating railroad worker mortality to diesel exhaust exposure using a threshold regression model. J. Stat. Plan. Inferences 139, 1633–1642 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Murphy, S.A., Van der Vaart, A.W., Wellner, J.A.: Current status regression. Math. Method. Stat. 8, 407–425 (1999)

    MATH  Google Scholar 

  25. Nahman, N.S., Middendorf, D.F., Bay, W.H., McElligott, R., Powell, S., Anderson, J.: Modification of the percutaneous approach to peritoneal dialysis catheter placement under peritoneoscopic visualization: clinical results in 78 patients. J. Am. Soc. Nephrol. 3, 103–107 (1992)

    Google Scholar 

  26. Oakes, D.: Multiple time scales in survival analysis. Lifetime Data Anal. 1, 7–18 (1995)

    Article  MATH  Google Scholar 

  27. Ritov, Y.: Estimation in linear regression model with censored data. Ann. Stat. 18, 303–328 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  28. Shen, X.: Linear regression with current status data. J. Am. Stat. Assoc. 95, 842–852 (2000)

    Article  MATH  Google Scholar 

  29. Tian, L., Cai, T.: On the accelerated failure time model for current status and interval censored data. Biometrika 93, 329–342 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  30. Tsiatis, A.A.: Estimating regression parameters using linear rank tests for censored data. Ann. Stat. 18, 354–372 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wei, L.J., Ying, Z., Lin, D.Y.: Linear regression analysis of censored survival data based on rank tests. Biometrika 77, 845–851 (1990)

    Article  MathSciNet  Google Scholar 

  32. Yamaguchi, K.: Accelerate failure-time regression models with a regression model of surviving fraction: an application to the analysis of “permanent employment” in Japan. J. Am. Stat. Assoc. 87, 284–292 (1992)

    Google Scholar 

  33. Ying, Z.: A large sample study of rank estimation for censored regression data. Ann. Stat. 21, 76–99 (1993)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported in part by CDC/NIOSH grant OH008649 (Lee).

Author information

Authors and Affiliations

  1. University of Maryland, College Park, MD, USA

    Xin He

  2. McGill University, Montreal, QC, Canada

    G. A. Whitmore

Authors
  1. Xin He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. A. Whitmore
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xin He .

Editor information

Editors and Affiliations

  1. University of Maryland, College Park, Maryland, USA

    Mei-Ling Ting Lee

  2. National Cancer Institute Div. Cancer Epidemiology & Genetics, Bethesda, Maryland, USA

    Mitchell Gail

  3. National Cancer Institute, Bethesda, Maryland, USA

    Ruth Pfeiffer

  4. Centers for Disease Control and Prevention, Atlanta, Georgia, USA

    Glen Satten

  5. Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts, USA

    Tianxi Cai

  6. Department of Mathematics, Imperial College London, London, United Kingdom

    Axel Gandy

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this paper

Cite this paper

He, X., Whitmore, G.A. (2013). Connecting Threshold Regression and Accelerated Failure Time Models. In: Lee, ML., Gail, M., Pfeiffer, R., Satten, G., Cai, T., Gandy, A. (eds) Risk Assessment and Evaluation of Predictions. Lecture Notes in Statistics, vol 215. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8981-8_3

Download citation

Publish with us

Policies and ethics

Search

Navigation