Skip to main content
Log in

Inference for outcome probabilities in multi-state models

  • Published:
Lifetime Data Analysis Aims and scope Submit manuscript

Abstract

In bone marrow transplantation studies, patients are followed over time and a number of events may be observed. These include both ultimate events like death and relapse and transient events like graft versus host disease and graft recovery. Such studies, therefore, lend themselves for using an analytic approach based on multi-state models. We will give a review of such methods with emphasis on regression models for both transition intensities and transition- and state occupation probabilities. Both semi-parametric models, like the Cox regression model, and parametric models based on piecewise constant intensities will be discussed.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

  • Andersen PK, Hansen LS, Keiding N (1991) Non- and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process. Scand J Stat 18: 153–67

    MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Andersen PK, Keiding N (2002) Multi-state models for event history analysis. Stat Methods Med Res 11: 91–15

    Article  MATH  Google Scholar 

  • Andersen PK, Klein JP (2007) Regression analysis for multistate models based on a pseudo-value approach, with applications to bone marrow transplantation studies. Scand J Stat 34: 3–6

    Article  MATH  MathSciNet  Google Scholar 

  • Cheng SC, Fine JP, Wei LJ (1998) Prediction of cumulative incidence function under the proportional hazards model. Biometrics 54: 219–28

    Article  MATH  MathSciNet  Google Scholar 

  • Commenges D (1999) Multi-state models in epidemiology. Lifetime Data Anal 5: 315–27

    Article  MATH  MathSciNet  Google Scholar 

  • Commenges D (2002) Inference for multi-state models from interval-censored data. Stat Methods Med Res 11: 167–82

    Article  MATH  Google Scholar 

  • Cook RJ, Lawless JF (2007) The statistical analysis of recurrent events. Springer-Verlag, New York

    MATH  Google Scholar 

  • Datta S, Satten GA (2001) Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. Stat Probab Lett 55: 403–11

    Article  MATH  MathSciNet  Google Scholar 

  • Fine JP (2001) Regression modeling of competing crude failure probabilities. Biostatistics 2: 85–7

    Article  MATH  Google Scholar 

  • Fine JP, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94: 496–09

    Article  MATH  MathSciNet  Google Scholar 

  • Frydman H (1992) A non-parametric estimation procedure for a periodically observed three-state Markov process, with application to AIDS. J R Stat Soc Ser B 54: 853–66

    MATH  MathSciNet  Google Scholar 

  • Frydman H (1995) Nonparametric estimation of a Markov ‘illness-death’ process from interval-censored observations, with application to diabetes survival data. Biometrika 82: 773–89

    MATH  MathSciNet  Google Scholar 

  • Graw F, Gerds TA, Schumacher M (2008) On pseudo-values for regression analysis in multi-state models, manuscript

  • Hougaard P (1999) Multi-state models: a review. Lifetime Data Anal 5: 239–64

    Article  MATH  MathSciNet  Google Scholar 

  • Kay RA (1986) Markov model for analysing cancer markers and disease states in survival models. Biometrics 42: 855–65

    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: 223–29

    Article  MATH  MathSciNet  Google Scholar 

  • Klein JP, Shu Y (2002) Multi-state models for bone marrow transplantation studies. Stat Methods Med Res 11: 117–39

    Article  MATH  Google Scholar 

  • Lin DY, Wei LJ, Yang I, Ying ZL (2000) Semiparametric regression for the mean and rate functions of recurrent events. J R Stat Soc Ser B 62: 711–30

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Meira-Machado L, Una-Álvarez J, Cadarso-Suárez C (2006) Nonparametric estimation of transition probabilities in a non-Markov illness-death model. Lifetime Data Anal 12: 325–44

    Article  MathSciNet  Google Scholar 

  • Meira-Machado L, Una-Ávarez J, Cadarso-Suárez C, Andersen PK (2009) Multi-state models for the analysis of time to event data. Stat Methods Med Res 18 (to appear)

  • Pepe MS (1991) Inference for events with dependent risks in multiple endpoint studies. J Am Stat Assoc 86: 770–78

    Article  MATH  MathSciNet  Google Scholar 

  • Putter H, Fiocco M, Geskus RB (2007) Tutorial in biostatistics: competing risks and multi-state models. Stat Med 26: 2389–430

    Article  MathSciNet  Google Scholar 

  • Scheike TH, Zhang MJ (2003) Extensions and applications of the Cox-Aalen survival model. Biometrics 59: 1036–045

    Article  MATH  MathSciNet  Google Scholar 

  • Scheike TH, Zhang MJ (2007) Direct modelling of regression effects for transition probabilities in multistate models. Scand J Stat 34: 17–2

    Article  MathSciNet  Google Scholar 

  • Shen Y, Cheng SC (1999) Confidence bands for cumulative incidence curves under the additive risk model. Biometrics 55: 1093–100

    Article  MATH  MathSciNet  Google Scholar 

  • Shu Y, Klein JP (2005) Additive hazards Markov regression models illustrated with bone marrow transplant data. Biometrika 92: 283–01

    Article  MATH  MathSciNet  Google Scholar 

  • Shu Y, Klein JP, Zhang MJ (2007) Asymptotic theory for the Cox semi-Markov illness-death model. Lifetime Data Anal 13: 91–17

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Per Kragh Andersen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andersen, P.K., Pohar Perme, M. Inference for outcome probabilities in multi-state models. Lifetime Data Anal 14, 405–431 (2008). https://doi.org/10.1007/s10985-008-9097-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10985-008-9097-x

Keywords

Navigation