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Review
. 2012 Jun;41(3):861-70.
doi: 10.1093/ije/dyr213. Epub 2012 Jan 9.

Competing risks in epidemiology: possibilities and pitfalls

Per Kragh Andersen  1 , Ronald B Geskus, Theo de Witte, Hein Putter
Affiliations
Review

Competing risks in epidemiology: possibilities and pitfalls

Per Kragh Andersen et al. Int J Epidemiol. 2012 Jun.

Abstract

Background: In studies of all-cause mortality, the fundamental epidemiological concepts of rate and risk are connected through a well-defined one-to-one relation. An important consequence of this relation is that regression models such as the proportional hazards model that are defined through the hazard (the rate) immediately dictate how the covariates relate to the survival function (the risk).

Methods: This introductory paper reviews the concepts of rate and risk and their one-to-one relation in all-cause mortality studies and introduces the analogous concepts of rate and risk in the context of competing risks, the cause-specific hazard and the cause-specific cumulative incidence function.

Results: The key feature of competing risks is that the one-to-one correspondence between cause-specific hazard and cumulative incidence, between rate and risk, is lost. This fact has two important implications. First, the naïve Kaplan-Meier that takes the competing events as censored observations, is biased. Secondly, the way in which covariates are associated with the cause-specific hazards may not coincide with the way these covariates are associated with the cumulative incidence. An example with relapse and non-relapse mortality as competing risks in a stem cell transplantation study is used for illustration.

Conclusion: The two implications of the loss of one-to-one correspondence between cause-specific hazard and cumulative incidence should be kept in mind when deciding on how to make inference in a competing risks situation.

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Figures

Figure 1
Figure 1
Nelson–Aalen estimates of the cumulative hazards (A) and the Kaplan–Meier estimates of the survival curves (B) for RFS for each of the five EBMT risk groups
Figure 2
Figure 2
Naïve Kaplan–Meier estimates of relapse and NRM, shown as incidence and survival curves, respectively
Figure 3
Figure 3
Cumulative incidence estimates of relapse and NRM, shown as incidence and survival curves, respectively; naïve Kaplan–Meier estimates are shown in grey
Figure 4
Figure 4
Nelson–Aalen estimates of the cumulative cause-specific hazards of (A) relapse and (B) NRM for each of the five EBMT risk groups
Figure 5
Figure 5
Model-based cumulative incidence estimates for (A) relapse and (B) NRM for each of the five EBMT risk groups
Figure 6
Figure 6
Non-parametric cumulative incidence estimates for (A) relapse and (B) NRM for each of the five EBMT risk groups
See this image and copyright information in PMC

References

    1. Rothman KJ. Epidemiology: An Introduction. New York: Oxford University Press; 2002.
    1. dos Santos Silva I. Cancer Epidemiology: Principles and Methods. Lyon, France: International Agency for Research on Cancer; 1999.
    1. Olsen J, Christensen K, Murray J, Ekbom A. An Introduction to Epidemiology for Health Professionals. New York: Springer; 2010.
    1. Rothman KJ, Greenland S. Modern Epidemiology. 2nd. Philadelphia: Lippincott-Raven;
    1. Clayton DG, Hills M. Statistical Models in Epidemiology. Oxford: Oxford University Press; 1993.

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