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Causal Inference in the Face of Competing Events

  • Epidemiologic Methods (P Howards, Section Editor)
  • Published:
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Abstract

Purpose of Review

Epidemiologists frequently must handle competing events, which prevent the event of interest from occurring. We review considerations for handling competing events when interpreting results causally.

Recent Findings

When interpreting statistical associations as causal effects, we recommend following a causal inference “roadmap” as one would in an analysis without competing events. There are, however, special considerations to be made for competing events when choosing the causal estimand that best answers the question of interest, selecting the statistical estimand (e.g., the cause-specific or subdistribution) that will target that causal estimand, and assessing whether causal identification conditions (e.g., conditional exchangeability, positivity, and consistency) have been sufficiently met.

Summary

When doing causal inference in the competing events setting, it is critical to first ascertain the relevant question and the causal estimand that best answers it, with the choice often being between estimands that do and do not eliminate competing events.

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References

Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

  1. Lau B, Cole SR, Gange SJ. Competing risk regression models for epidemiologic data. Am J Epidemiol. 2009;170(2):244–56. https://doi.org/10.1093/aje/kwp107.

    Article  PubMed  PubMed Central  Google Scholar 

  2. Andersen PK, Abildstrom SZ, Rosthoj S. Competing risks as a multi-state model. Stat Methods Med Res. 2002;11(2):203–15. https://doi.org/10.1191/0962280202sm281ra.

    Article  PubMed  Google Scholar 

  3. Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data, second edition. Wiley series in probability and statistics. Hoboken: John Wiley & Sons, Inc.; 2002.

    Google Scholar 

  4. Hernan MA, Robins JM. Causal inference: what if. Chapman & Hall/CRC: Boca Raton; 2020.

    Google Scholar 

  5. Petersen ML, van der Laan MJ. Causal models and learning from data: integrating causal modeling and statistical estimation. Epidemiology. 2014;25(3):418–26. https://doi.org/10.1097/EDE.0000000000000078.

    Article  PubMed  PubMed Central  Google Scholar 

  6. Ahern J. Start with the “C-word,” follow the roadmap for causal inference. Am J Public Health. 2018;108(5):621. https://doi.org/10.2105/AJPH.2018.304358.

    Article  PubMed  PubMed Central  Google Scholar 

  7. Andersen PK, Geskus RB, de Witte T, Putter H. Competing risks in epidemiology: possibilities and pitfalls. Int J Epidemiol. 2012;41(3):861–70. https://doi.org/10.1093/ije/dyr213.

    Article  PubMed  PubMed Central  Google Scholar 

  8. Schisterman EF, Silver RM, Perkins NJ, Mumford SL, Whitcomb BW, Stanford JB, et al. A randomised trial to evaluate the effects of low-dose aspirin in gestation and reproduction: design and baseline characteristics. Paediatr Perinat Epidemiol. 2013;27(6):598–609. https://doi.org/10.1111/ppe.12088.

    Article  PubMed  Google Scholar 

  9. •• Cole SR, Hudgens MG, Brookhart MA, Westreich D. Risk. Am J Epidemiol. 2015;181(4):246–50. https://doi.org/10.1093/aje/kwv001. This paper was the first to extend the potential outcomes framework to competing risk settings and is an excellent deep-dive into this fundamental measure of outcome occurrence. (Although we recognize that this paper is more than 3 years old, it is a key citation.).

  10. • Cole SR, Lau B, Eron JJ, Brookhart MA, Kitahata MM, Martin JN, et al. Estimation of the standardized risk difference and ratio in a competing risks framework: application to injection drug use and progression to AIDS after initiation of antiretroviral therapy. Am J Epidemiol. 2015;181(4):238–45. https://doi.org/10.1093/aje/kwu122. This companion paper to Risk discusses many of the same topics but in the context of a practical application. Lesko.

  11. •• Lesko CR, Lau B. Bias due to confounders for the exposure-competing risk relationship. Epidemiology. 2017;28(1):20–7. https://doi.org/10.1097/EDE.0000000000000565. This highly approachable paper uses simulation to demonstrate important concepts related to controlling for confounding when there are competing events and was the first paper to show that we ought to control for confounders of the exposure-competing event relationship.

  12. •• Young JG, Stensrud MJ, Tchetgen Tchetgen EJ, Hernan MA. A causal framework for classical statistical estimands in failure-time settings with competing events. Stat Med. 2020;39:1199–236. https://doi.org/10.1002/sim.8471. While more technical than the current paper, this work covers essentially all important topics related to estimating causal effects when there are competing events.

  13. Sarfati D, Blakely T, Pearce N. Measuring cancer survival in populations: relative survival vs cancer-specific survival. Int J Epidemiol. 2010;39(2):598–610. https://doi.org/10.1093/ije/dyp392.

    Article  PubMed  Google Scholar 

  14. Thompson CA, Zhang ZF, Arah OA. Competing risk bias to explain the inverse relationship between smoking and malignant melanoma. Eur J Epidemiol. 2013;28(7):557–67. https://doi.org/10.1007/s10654-013-9812-0.

    Article  PubMed  Google Scholar 

  15. Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed. Philadelphia: Lippincott Williams & Wilkins; 2008.

    Google Scholar 

  16. Cole SR, Edwards JK, Naimi AI, Munoz A. Hidden imputations and the Kaplan-Meier estimator. Am J Epidemiol. 2020. https://doi.org/10.1093/aje/kwaa086.

  17. Hernan MA. The hazards of hazard ratios. Epidemiology. 2010;21(1):13–5. https://doi.org/10.1097/EDE.0b013e3181c1ea43.

    Article  PubMed  PubMed Central  Google Scholar 

  18. Aalen OO, Johansen S. An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scand J Stat. 1978;5(3):141–50.

    Google Scholar 

  19. Geskus RB. Data analysis with competing risks and intermediate states. Chapman & Hall/CRC Biostatistics Series. Boca Raton: CRC Press; 2015.

    Book  Google Scholar 

  20. Collett D. Competing risks. Modelling survival data in medical research. 3rd ed. Boca Raton: CRC Press; 2015. p. 405–28.

    Book  Google Scholar 

  21. Fine JP, Gray RJ. A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc. 1999;94(446):496–509. https://doi.org/10.1080/01621459.1999.10474144.

    Article  Google Scholar 

  22. Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data. New York: Wiley; 1980.

    Google Scholar 

  23. Ishwaran H, Gerds TA, Kogalur UB, Moore RD, Gange SJ, Lau BM. Random survival forests for competing risks. Biostatistics. 2014;15(4):757–73. https://doi.org/10.1093/biostatistics/kxu010.

    Article  PubMed  PubMed Central  Google Scholar 

  24. Lau B, Cole SR, Gange SJ. Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time-dependent hazards and delayed entry. Stat Med. 2011;30(6):654–65. https://doi.org/10.1002/sim.4123.

    Article  PubMed  Google Scholar 

  25. Gerds TA, Scheike TH, Andersen PK. Absolute risk regression for competing risks: interpretation, link functions, and prediction. Stat Med. 2012;31(29):3921–30. https://doi.org/10.1002/sim.5459.

    Article  PubMed  PubMed Central  Google Scholar 

  26. Binder N, Gerds TA, Andersen PK. Pseudo-observations for competing risks with covariate dependent censoring. Lifetime Data Anal. 2014;20(2):303–15. https://doi.org/10.1007/s10985-013-9247-7.

    Article  PubMed  Google Scholar 

  27. Neophytou AM, Picciotto S, Brown DM, Gallagher LE, Checkoway H, Eisen EA, et al. Estimating counterfactual risk under hypothetical interventions in the presence of competing events: crystalline silica exposure and mortality from 2 causes of death. Am J Epidemiol. 2018;187(9):1942–50. https://doi.org/10.1093/aje/kwy077.

    Article  PubMed  PubMed Central  Google Scholar 

  28. Cole SR, Richardson DB, Chu H, Naimi AI. Analysis of occupational asbestos exposure and lung cancer mortality using the g formula. Am J Epidemiol. 2013;177(9):989–96. https://doi.org/10.1093/aje/kws343.

    Article  PubMed  PubMed Central  Google Scholar 

  29. Cortese G, Andersen PK. Competing risks and time-dependent covariates. Biom J. 2010;52(1):138–58. https://doi.org/10.1002/bimj.200900076.

    Article  PubMed  Google Scholar 

  30. Cortese G, Gerds TA, Andersen PK. Comparing predictions among competing risks models with time-dependent covariates. Stat Med. 2013;32(18):3089–101. https://doi.org/10.1002/sim.5773.

    Article  PubMed  PubMed Central  Google Scholar 

  31. Robins JM, Wasserman L. On the impossibility of inferring causation from association without background knowledge. In: Glymour C, Cooper G, editors. Computation, causation, and discovery. Cambridge: AAAI Press/The MIT Press; 1999. p. 305–21.

    Google Scholar 

  32. Lau B, Lesko C. Missingness in the setting of competing risks: from missing values to missing potential outcomes. Curr Epidemiol Rep. 2018;5(2):153–9. https://doi.org/10.1007/s40471-018-0142-3.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Nevo D, Nishihara R, Ogino S, Wang M. The competing risks cox model with auxiliary case covariates under weaker missing-at-random cause of failure. Lifetime Data Anal. 2018;24(3):425–42. https://doi.org/10.1007/s10985-017-9401-8.

    Article  PubMed  Google Scholar 

  34. Bakoyannis G, Siannis F, Touloumi G. Modelling competing risks data with missing cause of failure. Stat Med. 2010;29(30):3172–85. https://doi.org/10.1002/sim.4133.

    Article  PubMed  Google Scholar 

  35. Lu K, Tsiatis AA. Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure. Biometrics. 2001;57(4):1191–7. https://doi.org/10.1111/j.0006-341x.2001.01191.x.

    Article  CAS  PubMed  Google Scholar 

  36. Lau B, Cole SR, Moore RD, Gange SJ. Evaluating competing adverse and beneficial outcomes using a mixture model. Stat Med. 2008;27(21):4313–27. https://doi.org/10.1002/sim.3293.

    Article  PubMed  PubMed Central  Google Scholar 

  37. Nicolaie MA, van Houwelingen HC, Putter H. Vertical modelling: analysis of competing risks data with missing causes of failure. Stat Methods Med Res. 2015;24(6):891–908. https://doi.org/10.1177/0962280211432067.

    Article  CAS  PubMed  Google Scholar 

  38. VanderWeele TJ. Concerning the consistency assumption in causal inference. Epidemiology. 2009;20(6):880–3. https://doi.org/10.1097/EDE.0b013e3181bd5638.

    Article  PubMed  Google Scholar 

  39. Grambauer N, Schumacher M, Dettenkofer M, Beyersmann J. Incidence densities in a competing events analysis. Am J Epidemiol. 2010;172(9):1077–84. https://doi.org/10.1093/aje/kwq246.

    Article  PubMed  Google Scholar 

  40. Edwards JK, Cole SR, Chu H, Olshan AF, Richardson DB. Accounting for outcome misclassification in estimates of the effect of occupational asbestos exposure on lung cancer death. Am J Epidemiol. 2014;179(5):641–7. https://doi.org/10.1093/aje/kwt309.

    Article  PubMed  Google Scholar 

  41. Keil AP, Mooney SJ, Jonsson Funk M, Cole SR, Edwards JK, Westreich D. Resolving an apparent paradox in doubly robust estimators. Am J Epidemiol. 2018;187(4):891–2. https://doi.org/10.1093/aje/kwx385.

    Article  PubMed  PubMed Central  Google Scholar 

  42. Karn MN. An inquiry into various death-rates and the comparative influence of certain diseases on the duration of life. Ann Eugenics. 1931;4(3–4):279–302.

    Article  Google Scholar 

  43. Prentice RL, Kalbfleisch JD, Peterson AV Jr, Flournoy N, Farewell VT, Breslow NE. The analysis of failure times in the presence of competing risks. Biometrics. 1978;34(4):541–54.

    Article  CAS  PubMed  Google Scholar 

  44. Pintilie M. Competing risks: a practical perspective. Statistics in practice. Chichester: John Wiley & Sons, Ltd.; 2006.

    Book  Google Scholar 

  45. Austin PC, Fine JP. Practical recommendations for reporting Fine-Gray model analyses for competing risk data. Stat Med. 2017;36(27):4391–400. https://doi.org/10.1002/sim.7501.

    Article  PubMed  PubMed Central  Google Scholar 

  46. Westreich D, Edwards JK, Rogawski ET, Hudgens MG, Stuart EA, Cole SR. Causal impact: epidemiological approaches for a public health of consequence. Am J Public Health. 2016;106(6):1011–2. https://doi.org/10.2105/AJPH.2016.303226.

    Article  PubMed  PubMed Central  Google Scholar 

  47. Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Stat Med. 2007;26(11):2389–430. https://doi.org/10.1002/sim.2712.

    Article  CAS  PubMed  Google Scholar 

  48. Andersen PK, Keiding N. Interpretability and importance of functionals in competing risks and multistate models. Stat Med. 2012;31(11–12):1074–88. https://doi.org/10.1002/sim.4385.

    Article  PubMed  Google Scholar 

  49. Latouche A, Allignol A, Beyersmann J, Labopin M, Fine JP. A competing risks analysis should report results on all cause-specific hazards and cumulative incidence functions. J Clin Epidemiol. 2013;66(6):648–53. https://doi.org/10.1016/j.jclinepi.2012.09.017.

    Article  PubMed  Google Scholar 

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Funding

This work was supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development grant R01 HD093602 and National Institutes of Health grant K01 AA028193.

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Authors and Affiliations

  1. Department of Epidemiology, Graduate School of Public Health, University of Pittsburgh, 130 DeSoto Street, Pittsburgh, PA, 15261, USA

    Jacqueline E. Rudolph & Ashley I. Naimi

  2. Department of Epidemiology, Johns Hopkins School of Public Health, 615 N. Wolfe Street, Baltimore, MD, 21205, USA

    Catherine R. Lesko

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  1. Jacqueline E. Rudolph
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Correspondence to Jacqueline E. Rudolph.

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Rudolph, J.E., Lesko, C.R. & Naimi, A.I. Causal Inference in the Face of Competing Events. Curr Epidemiol Rep 7, 125–131 (2020). https://doi.org/10.1007/s40471-020-00240-7

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