• Etsuji Suzuki, Hirokazu Komatsu, Takashi Yorifuji, Eiji Yamamoto, Hiroyuki Doi, and Toshihide Tsuda.
• Department of Epidemiology, Okayama University Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Shikata-cho, Kita-ku, Okayama, Japan. etsuji-s@cc.okayama-u.ac.jp
• Nihon Eiseigaku Zasshi. 2009 Sep 1;64(4):796-805.

AbstractConfounding is frequently a primary concern in epidemiological studies. With the increasing complexity of hypothesized relationships among exposures, outcomes, and covariates, it becomes very difficult to present these hypotheses lucidly and comprehensively. Graphical models are of great benefit in this regard. In this article, we focuse on directed acyclic graphs (DAGs), and review their value for confounder selection, categorization of potential biases, and hypothesis specification. We also discuss the importance of considering causal structures before selecting the covariates to be included in a statistical model and the potential biases introduced by inappropriately adjusting statistical models for covariates. DAGs are nonparametric and qualitative tools for visualizing research hypotheses regarding an exposure, an outcome, and covariates. Causal structures represented in DAGs will rarely be perfectly "correct" owing to the uncertainty about the underlying causal relationships. Nevertheless, to the extent that using DAGs forces greater clarity about causal assumptions, we are able to consider key sources of bias and uncertainty when interpreting study results. In summary, in this article, we review the following three points. (1) Although researchers have not adopted a consistent definition of confounders, using DAGs and the rules of d-separation we are able to identify clearly which variables we must condition on or adjust for in order to test a causal hypothesis under a set of causal assumptions. (2) We also show that DAGs should accurately correspond to research hypotheses of interest. To obtain a valid causal interpretation, research hypotheses should be defined explicitly from the perspective of a counterfactual model before drawing DAGs. A proper interpretation of the coefficients of a statistical model for addressing a specific research hypothesis relies on an accurate specification of a causal DAG reflecting the underlying causal structure. Unless DAGs correspond to research hypotheses, we cannot reliably reach proper conclusions testing the research hypotheses. Finally, (3) we have briefly reviewed other approaches to causal inference, and illustrate how these models are connected.

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