Applying competing risks regression models: an overview

Haller, Bernhard; Schmidt, Georg; Ulm, Kurt

doi:10.1007/s10985-012-9230-8

Published: 26 September 2012

Applying competing risks regression models: an overview

Bernhard Haller¹,
Georg Schmidt² &
Kurt Ulm¹

Lifetime Data Analysis volume 19, pages 33–58 (2013)Cite this article

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75 Citations
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Abstract

In many clinical research applications the time to occurrence of one event of interest, that may be obscured by another—so called competing—event, is investigated. Specific interventions can only have an effect on the endpoint they address or research questions might focus on risk factors for a certain outcome. Different approaches for the analysis of time-to-event data in the presence of competing risks were introduced in the last decades including some new methodologies, which are not yet frequently used in the analysis of competing risks data. Cause-specific hazard regression, subdistribution hazard regression, mixture models, vertical modelling and the analysis of time-to-event data based on pseudo-observations are described in this article and are applied to a dataset of a cohort study intended to establish risk stratification for cardiac death after myocardial infarction. Data analysts are encouraged to use the appropriate methods for their specific research questions by comparing different regression approaches in the competing risks setting regarding assumptions, methodology and interpretation of the results. Notes on application of the mentioned methods using the statistical software R are presented and extensions to the presented standard methods proposed in statistical literature are mentioned.

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References

Allignol A, Schumacher M, Wanner C, Drechsler C, Beyersmann J (2011) Understanding competing risks: a simulation point of view. BMC Med Res Methodol 11:86. doi:10.1186/1471-2288-11-86
Andersen PK, Keiding N (2012) Interpretability and importance of functionals in competing risks and multistate models. Stat Med 31: 1074–1088. doi:10.1002/sim.4385
MathSciNet Article Google Scholar
Andersen PK, Perme MP (2010) Pseudo-observations in survival analysis. Stat Methods Med Res 19: 71–99. doi:10.1177/0962280209105020
MathSciNet Article Google Scholar
Andersen PK, Klein JP, Rosthøj S (2003) Generalised linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika 90: 15–27. doi:10.1093/biomet/90.1.15
MathSciNet MATH Article Google Scholar
Bakoyannis G, Touloumi G (2011) Practical methods for competing risks data: a review. Stat Methods Med Res. doi:10.1177/0962280210394479
Barthel P, Schneider R, Bauer A, Ulm K, Schmitt C, Schömig A, Schmidt G (2003) Risk stratification after acute myocardial infarction by heart rate turbulence. Circulation 108: 1221–1226. doi:10.1161/01.CIR.0000088783.34082.89
Article Google Scholar
Bauer A, Kantelhardt JW, Barthel P, Schneider R, Makikallio T, Ulm K, Hnatkova K, Schömig A, Huikuri H, Bunde A, Malik M, Schmidt G (2006) Declaration capacity of heart rate as a predictor of mortality after myocardial infarction: cohort study. Lancet 367: 1674–1681. doi:10.1016/S0140-6736(06)68735-7
Article Google Scholar
Bauer A, Barthel P, Schneider R, Ulm K, Müller A, Joeining A, Stich R, Kiviniemi A, Hnatkova K, Huikuri H, Schömig A, Malik M, Schmidt G (2009) Improved stratification of autonomic regulation for risk prediction in post-infarction patients with preserved left ventricular function (isar-risk). Eur Heart J 30: 576–583. doi:10.1093/eurheartj/ehn540
Article Google Scholar
Belot A, Abrahamowicz M, Remontet L, Giorgi R (2010) Flexible modeling of competing risks in survival analysis. Stat Med 29(23): 2453–2468. doi:10.1002/sim.4005
MathSciNet Google Scholar
Beyersmann J, Schumacher M (2007) Letter to the editor: Misspecified regression model for the subdistribution hazard of a competing risk. Stat Med 26: 1649–1652. doi:10.1002/sim.2727
MathSciNet Article Google Scholar
Beyersmann J, Dettenkofer M, Bertz H, Schumacher M (2007) A competing risks analysis of bloodstream infection after stem-cell transplantation using subdistribution hazards and cause-specific hazards. Stat Med 26: 5360–5369. doi:10.1002/sim.3006
MathSciNet Article Google Scholar
Beyersmann J, Latouche A, Buchholz A, Schumacher M (2009) Simulating competing risks data in survival analysis. Stat Med 28(6): 956–971. doi:10.1002/sim.3516
MathSciNet Article Google Scholar
Beyersmann J, Schumacher M, Allignol A (2012) Competing risks and multistate models with R. Springer, New York
MATH Book Google Scholar
Cox DR (1972) Regression models and life-tables. J R Stat Soc Ser B 34: 187–220. doi:10.2307/2985181
MATH Google Scholar
Cox C, Chu H, Schneider MF, Muñoz A (2007) Tutorial in biostatistics: parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat Med 26: 4352–4374. doi:10.1002/sim.2836
MathSciNet Article Google Scholar
Crowder MJ (2001) Classical competing risks. Chapman & Hall/CRC, Boca Raton
MATH Book Google Scholar
Dignam JJ, Kocherginsky MN (2008) Choice and interpretation of statistical tests used when competing risks are present. J Clin Oncol 26(24): 4027–4034. doi:10.1200/JCO.2007.12.9866
Article Google Scholar
Efron B, Tibshirani RJ (1994) An introduction to the bootstrap. Chapman and Hall/CRC, London
Google Scholar
Escarela G, Bowater RJ (2008) Fitting a semi-parametric mixture model for competing risks in survival data. Commun Stat 37: 277–293. doi:10.1080/03610920701649134
MathSciNet MATH Article Google Scholar
Fahrmeir L, Tutz G (2001) Multivariate statistical modelling based on generalized linear models. Springer, New York
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. doi:10.2307/2670170
MathSciNet MATH Article Google Scholar
Friedman M (1982) Piecewise exponential models for survival data with covariates. Ann Stat 10: 101–113
MATH Article Google Scholar
Grambauer N, Schumacher M, Beyersmann J (2010) Proportional subdistribution hazards modeling offers a summary analysis, even if misspecified. Stat Med 29: 875–884. doi:10.1002/sim.3786
MathSciNet Article Google Scholar
Gray R (1988) A class of k-sample tests for comparing the cumulative incidence function in the presence of a competing risk. Ann Stat 16: 1141–1154. doi:10.2307/2241622
MATH Article Google Scholar
Gray B (2010) cmprsk: Subdistribution analysis of competing risks. URL http://CRAN.R-project.org/package=cmprsk, R package version 2.2-1
Hastie TJ (1997) Generalized additive models. Chapman & Hall/CRC, New York
Google Scholar
Højsgaard S, Halekoh U, Yan J (2005) The R package geepack for generalized estimating equations. J Stat Softw 15:1–11. http://CRAN.R-project.org/package=survival, R package version 2.36-5
Google Scholar
Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data. Wiley, Hoboken
MATH Book Google Scholar
Kaplan EL, Meier P (1958) Non-parametric estimation from incomplete observations. J Am Stat Assoc 53: 457–481
MathSciNet MATH Article Google Scholar
Klein JP (2010) Competing risks. WIREs Comput Stat 2: 333–339. doi:10.1002/wics.83
Article 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. doi:10.1111/j.0006-341X.2005.031209.x
MathSciNet MATH Article Google Scholar
Klein JP, Moeschberger ML (2003) Survival analysis—techniques for censored and truncated data. Springer, New York
MATH Google Scholar
Klein J, Gerster M, Andersen P, Tarima S, Perme M (2008) SAS and R functions to compute pseudo- values for censored data regression. Comput Methods Prog Biomed 89(3): 289–300. doi:10.1016/j.cmpb.2007.11.017
Article Google Scholar
Koller MT, Raatz H, Steyerberg EW, Wolbers M (2012) Competing risks and the clinical community: irrelevance or ignorance. Stat Med 31: 1089–1097
MathSciNet Article Google Scholar
Larson MG, Dinse GE (1985) A mixture model for the regression analysis of competing risks data. J R Stat Soc Ser C 34: 201–211
MathSciNet 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(5): 965–974. doi:10.1002/sim.2600
MathSciNet Article Google Scholar
Lau B, Cole SR, Moore SR, Gange SJ (2008) Evaluating competing adverse and beneficial outcomes using a mixture model. Stat Med 27: 4313–4327. doi:10.1002/sim.3293
MathSciNet Article Google Scholar
Lau B, Cole SR, Gange SJ (2009) Competing risk regression models for epidemiologic data. Am J Epidemiol 170: 244–256. doi:10.1093/aje/kwp107
Article Google Scholar
Lau B, Cole S, Gange S (2011) Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time-dependent hazards and delayed entry. Stat Med 30: 654–665. doi:10.1002/sim.4123
MathSciNet Article Google Scholar
Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73: 13–22. doi:10.1093/biomet/73.1.13
MathSciNet MATH Article Google Scholar
Lunn M, McNeil D (1995) Applying Cox regression to competing risks. Biometrics 51: 524–532. doi:10.2307/2532940
Article Google Scholar
McLachlan GJ, Krishnan T (1997) The EM algorithm and extensions. Wiley, New York
MATH Google Scholar
Miller RG (1974) The Jackknife—a review. Biometrika 6(1): 1–15. doi:0.1093/-biomet/61.1.1
Google Scholar
Ng GK, McLachlan GJ (2003) An em-based semi-parametric mixture model approach to the regression analysis of competing-risks data. Stat Med 22: 1097–1111. doi:10.1002/sim.1371
Article Google Scholar
Nicolaie MA, Houwelingen HC, Putter H (2010) Vertical modeling: a pattern mixture approach for competing risks modeling. Stat Med 29: 1190–1205. doi:10.1002/sim.3844
MathSciNet Google Scholar
Perme MP, Andersen PK (2008) Checking hazard regression models using pseudo-observations. Stat Med 27: 5309–5328. doi:10.1002/sim.3401
MathSciNet Article Google Scholar
Pintilie M (2006) Competing risks: a practical perspective. Wiley, Chichester
MATH Google Scholar
Prentice R, Kalbfleisch J, Peterson A, Flournoy N, Farewell V, Breslow N (1978) The analysis of failure times in the presence of competing risks. Biometrics 34: 541–554. doi:10.2307/2530374
MATH Article Google Scholar
Putter H, Fiocco M, Geskus RB (2007) Tutorial in biostatistics: competing risks and multi-state models. Stat Med 26(11): 2389–2430. doi:10.1002/sim.2712
MathSciNet Article Google Scholar
R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/, ISBN 3-900051-07-0
Robins J, Rotnitzky A (1992) Recovery of information and adjustment for dependent censoring using surrogate markers. In: Jewell N, Dietz K, Farewell V (eds) AIDS epidemiology—methodological issues. Birkhäuser, Boston, pp 24–33
Google Scholar
Scheike TH, Zhang MJJ (2008) Flexible competing risks regression modeling and goodness-of-fit. Lifetime Data Anal 14: 464–483. doi:10.1007/s10985-008-9094-0
MathSciNet MATH Article Google Scholar
Schemper M, Smith T (1996) A note on quantifying follow-up in studies of failure time. Lancet 17: 343–346
Google Scholar
Schoenfeld D (1982) Partial residuals for the proportional hazards regression model. Biometrika 69(1): 239–241. doi:10.1093/biomet/69.1.239
Article Google Scholar
Sun Y, Hyun S, Gilbert P (2008) testing and estimation of time-varying cause-specific hazard ratios with covariate adjustment. Biometrics 64: 1070–1079. doi:10.1111/j.1541-0420.2008.01012.x
MathSciNet MATH Article Google Scholar
Tai BC, Wee J, Machin D (2011) Analysis and design of randomised clinical trials involving competing risks endpoints. Trials 12: 127. doi:10.1186/1745-6215-12-127
Article Google Scholar
Therneau T (2011) Survival: survival analysis, including penalised likelihood. http://CRAN.R-project.org/package=survival, R package version 2.36-5
Therneau TM, Grambsch PM (2000) Modeling survival data: extending the Cox model (statistics for biology and health). Springer, New York
MATH Google Scholar
Tsiatis A (1975) A nonidentifiability aspect of the problem of competing risks. Proc Natl Acad Sci USA 72(1):20–22
Google Scholar
Urbanek S (2011) multicore: parallel processing of R code on machines with multiple cores or CPUs. http://CRAN.R-project.org/package=multicore, R package version 0.1-5

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Institut für Medizinische Statistik und Epidemiologie der Technischen Universität München, Ismaninger Straße 22, 81675, Munich, Germany
Bernhard Haller & Kurt Ulm
1. Medizinische Klinik und Poliklinik der Technischen Universität München, Munich, Germany
Georg Schmidt

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Bernhard Haller
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Georg Schmidt
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Kurt Ulm
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Correspondence to Bernhard Haller.

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Haller, B., Schmidt, G. & Ulm, K. Applying competing risks regression models: an overview. Lifetime Data Anal 19, 33–58 (2013). https://doi.org/10.1007/s10985-012-9230-8

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Received: 07 February 2012
Accepted: 10 September 2012
Published: 26 September 2012
Issue Date: January 2013
DOI: https://doi.org/10.1007/s10985-012-9230-8

Keywords

Competing risks
Cause-specific hazard
Subdistribution hazard
Mixture model
Vertical modelling
Pseudo-observation approach