title: A counterfactual approach to bias and effect modification in terms of response types.
abstract: BACKGROUND
  The counterfactual approach provides a clear and coherent framework to think about a variety of important concepts related to causation. Meanwhile, directed acyclic graphs have been used as causal diagrams in epidemiologic research to visually summarize hypothetical relations among variables of interest, providing a clear understanding of underlying causal structures of bias and effect modification. In this study, the authors aim to further clarify the concepts of bias (confounding bias and selection bias) and effect modification in the counterfactual framework.
  
  
  METHODS
  The authors show how theoretical data frequencies can be described by using unobservable response types both in observational studies and in randomized controlled trials. By using the descriptions of data frequencies, the authors show epidemiologic measures in terms of response types, demonstrating significant distinctions between association measures and effect measures. These descriptions also demonstrate sufficient conditions to estimate effect measures in observational studies. To illustrate the ideas, the authors show how directed acyclic graphs can be extended by integrating response types and observed variables.
  
  
  RESULTS
  This study shows a hitherto unrecognized sufficient condition to estimate effect measures in observational studies by adjusting for confounding bias. The present findings would provide a further understanding of the assumption of conditional exchangeability, clarifying the link between the assumptions for making causal inferences in observational studies and the counterfactual approach. The extension of directed acyclic graphs using response types maintains the integrity of the original directed acyclic graphs, which allows one to understand the underlying causal structure discussed in this study.
  
  
  CONCLUSIONS
  The present findings highlight that analytic adjustment for confounders in observational studies has consequences quite different from those of physical control in randomized controlled trials. In particular, the present findings would be of great use when demonstrating the inherent distinctions between observational studies and randomized controlled trials.
authors.affiliation: Department of Epidemiology, Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Okayama University, 2-5-1 Shikata-cho, Kita-ku, Okayama 700-8558, Japan. etsuji-s@cc.okayama-u.ac.jp.
authors.forename: Etsuji
authors.initials: E
authors.lastname: Suzuki
authors.forename: Toshiharu
authors.initials: T
authors.lastname: Mitsuhashi
authors.forename: Toshihide
authors.initials: T
authors.lastname: Tsuda
authors.forename: Eiji
authors.initials: E
authors.lastname: Yamamoto
mesh_terms: D000465:Algorithms; D015986:Confounding Factors, Epidemiologic; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D064887:Observational Studies as Topic; D015588:Observer Variation; D011897:Random Allocation; D016032:Randomized Controlled Trials as Topic; D015983:Selection Bias; D016896:Treatment Outcome
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