Skip to main content

Advertisement

SpringerLink
Log in

Regression analysis of competing risks data via semi-parametric additive hazard model

  • Published:
Statistical Methods & Applications Aims and scope Submit manuscript

Abstract

When the subjects in a study possess different demographic and disease characteristics and are exposed to more than one types of failure, a practical problem is to assess the covariate effects on each type of failure as well as on all-cause failure. The most widely used method is to employ the Cox models on each cause-specific hazard and the all-cause hazard. It has been pointed out that this method causes the problem of internal inconsistency. To solve such a problem, the additive hazard models have been advocated. In this paper, we model each cause-specific hazard with the additive hazard model that includes both constant and time-varying covariate effects. We illustrate that the covariate effect on all-cause failure can be estimated by the sum of the effects on all competing risks. Using data from a longitudinal study on breast cancer patients, we show that the proposed method gives simple interpretation of the final results, when the primary covariate effect is constant in the additive manner on each cause-specific hazard. Based on the given additive models on the cause-specific hazards, we derive the inferences for the adjusted survival and cumulative incidence functions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aalen OO (1989) A linear regression model for the analysis of life times. Stat Med 8: 907–925

    Article  Google Scholar 

  • Andersen PK (2005) Time-dependent covariate. Encyclopedia of biostatistics 2nd. ed. 8, 5467–5471. Wiley, New York

  • Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York

    MATH  Google Scholar 

  • Beyersmann J, Schumacher M (2008) Time-dependent covariates in the proportional subdistribution hazards model for competing risks. Biostatistics 9: 765–776

    Article  Google Scholar 

  • Cheng SC, Fine JP, Wei LJ (1998) Prediction of cumulative incidence function under the proportional hazards model. Biometrics 54: 219–228

    Article  MathSciNet  MATH  Google Scholar 

  • Cortese G, Andersen PK (2010) Competing risks and time-dependent covariates. Biom J 52: 138–158

    MathSciNet  MATH  Google Scholar 

  • Cortese G, Scheike TH (2008) Dynamic regression hazards models for relative survival. Stat Med 27: 3563–3584

    Article  MathSciNet  Google Scholar 

  • Cox DR (1972) Regression models and life tables (with discussion). J Roy Stat Soc Ser B 34: 187–220

    MATH  Google Scholar 

  • Fine JP, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94: 496–509

    Article  MathSciNet  MATH  Google Scholar 

  • Gray RJ (1988) A class of K-sample tests for comparing the cumulative incidence of a competing risk. Ann Stat 16: 1141–1154

    Article  MATH  Google Scholar 

  • Klein JP, Andersen PK (2005) Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61: 223–229

    Article  MathSciNet  MATH  Google Scholar 

  • Klein JP (2006) Modelling competing risks in cancer studies. Stat Med 25: 1015–1034

    Article  MathSciNet  Google Scholar 

  • Kulathinal S, Arjas E (2006) Bayesian inference from case-cohort data with multiple end-points. Scand J Stat 33: 25–36

    Article  MathSciNet  MATH  Google Scholar 

  • Latouche A, Boisson V, Chevret S, Porcher R (2007) Misspecified regression model for the subdistribution hazard of a competing risk. Stat Med 26: 965–974

    Article  MathSciNet  Google Scholar 

  • Lin DY, Ying Z (1994) semi-parametric analysis of the additive risk model. Biometrika 81: 61–71

    Article  MathSciNet  MATH  Google Scholar 

  • Martinussen T, Scheike TH (2006) Dynamic regression models for survival data. Springer, New York

    MATH  Google Scholar 

  • McKeague IW, Sasieni PD (1994) A partly parametric additive risk model. Biometrika 81: 501–514

    Article  MathSciNet  MATH  Google Scholar 

  • Pepe MS (1991) Inference for events with dependent risks in multiple endpoint studies. J Am Stat Assoc 86: 770–778

    Article  MathSciNet  MATH  Google Scholar 

  • Ruan PK, Gray RJ (2008) Analyses of cumulative incidence functions via non-parametric multiple imputation. Stat Med 27: 5709–5724

    Article  MathSciNet  Google Scholar 

  • Scheike TH, Martinussen T (2004) Maximum likelihood estimation for Cox’s regression model under case-cohort sampling. Scand J Stat 31: 283–293

    Article  MathSciNet  MATH  Google Scholar 

  • Schaubel DE, Wei G (2007) Fitting the additive hazard model using standard statistical software. Biom J 49: 719–730

    Article  MathSciNet  Google Scholar 

  • Scheike TH, Zhang MJ (2003) Extensions and applications of the Cox-Aalen survival model. Biometrics 59: 1036–1045

    Article  MathSciNet  MATH  Google Scholar 

  • Scheike TH, Zhang MJ, Gerds TA (2008) Predicting cumulative incidence probability by direct binomial regression. Biometrika 95: 205–220

    Article  MathSciNet  MATH  Google Scholar 

  • Shen Y, Cheng SC (1999) Confidence bands for cumulative incidence curves under the additive risk model. Biometrics 55: 1093–1100

    Article  MathSciNet  MATH  Google Scholar 

  • Shu Y, Klein JP (2005) Additive hazards Markov regression models illustrated with bone marrow transplant data. Biometrika 92: 283–301

    Article  MathSciNet  MATH  Google Scholar 

  • Sun LQ, Liu JX, Sun JG, Zhang MJ (2006) Modelling the subdistribution of a competing risk. Stat Sin 16(4): 1367–1385

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics & Statistics, Georgia State University, Atlanta, GA, 30303, USA

    Xu Zhang & Haci Akcin

  2. Department of Community Health & Epidemiology, College of Medicine, University of Saskatchewan, Saskatoon, SK, S7N 5E5, Canada

    Hyun J. Lim

Authors
  1. Xu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haci Akcin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyun J. Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xu Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, X., Akcin, H. & Lim, H.J. Regression analysis of competing risks data via semi-parametric additive hazard model. Stat Methods Appl 20, 357–381 (2011). https://doi.org/10.1007/s10260-011-0161-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10260-011-0161-4

Keywords

Search

Navigation