European Journal of Epidemiology

, Volume 21, Issue 12, pp 847–853 | Cite as

On the relationship of sufficient component cause models with potential outcome (counterfactual) models



The sufficient-component cause (SSC) model provides a useful, concise method to conceptualize and organize ideas concerning biologic effects and interactions of multiple factors. Another type of model, the potential outcome or counterfactual models, has also proved useful in epidemiology, providing insights into definitions of effects, exchangeability and confounding, and selection bias. Prior work has shown important links between these two types of models. Here, we show additional connections between the two types of models. We first review basic concepts for both the SSC model and the potential outcome models. We then indicate additional similarities between them, and derive a quantitative link. Our results show that the SSC model actually corresponds to a unique response pattern in a particular potential outcome model. Recognition of the links between the two models should allow greater insight into use of each model, and allow the strengths of both models to be used jointly.


Causality Sufficient-component cause Counterfactual Exchangeability Interaction Confounding 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We would like to acknowledge the helpful comments of Dr. Kenneth Rothman. After having written several drafts of the manuscript, we became aware that Dr. James Robins had independently developed some of the same results, with a manuscript in preparation.


  1. 1.
    Rothman KJ, Greenland S (2005) Causation and causal inference in epidemiology Am J Public Health 95(Supp 1): S144–S150PubMedCrossRefGoogle Scholar
  2. 2.
    Rothman KJ (1976) Causes Am J Epidemiol 104: 587–592PubMedGoogle Scholar
  3. 3.
    Rothman KJ, Greenland S (1998) Causation and causal inference. In: Rothman KJ, Greenland S (eds). Modern Epidemiology. Philadelphia, PA: Lippincott, pp. 7–28Google Scholar
  4. 4.
    Greenland S, Rothman KJ (1998) Concepts of Interaction. In: Rothman KJ, Greenland S (eds). Modern Epidemiology. Philadelphia, PA: Lippincott, pp. 329–342Google Scholar
  5. 5.
    Kupper LL, Hogan MD (1978) Interaction in epidemiologic studies Am J Epidemiol 108: 447–453PubMedGoogle Scholar
  6. 6.
    Greenland S, Brumback B (2002) An overview of relations among causal modeling methods Int J Epidemiol 312: 1030–1037CrossRefGoogle Scholar
  7. 7.
    Greenland S, Robins JM (1986) Identifiability, exchangeability, and epidemiological confounding Int J Epidemiol 15(3):413–419PubMedCrossRefGoogle Scholar
  8. 8.
    Hernán MA, Hernandez-Diaz S, Robins JM (2004) A structural approach to selection bias Epidemiology 15: 615–625PubMedCrossRefGoogle Scholar
  9. 9.
    Greenland S, Poole C (1988) Invariants and noninvariants in the concept of interdependent effects Scand J Work Environ Health 14: 125–129PubMedGoogle Scholar
  10. 10.
    Koopman JS (1977) Causal models and sources of interaction Am J Epidemiol 106: 439–444PubMedGoogle Scholar
  11. 11.
    Siemiatycki J, Thomas DC (1981) Biological models and statistical interactions: an example from multistage carcinogenesis Int J Epidemiol 10: 382–387CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Emory University, Rollins School of Public HealthAtlantaUSA
  2. 2.Emory University, Rollins School of Public HealthAtlantaUSA

Personalised recommendations