Which practical interventions does the do-operator refer to in causal inference? Illustration on the example of obesity and cancer

• Published in: arXiv.org 2019-01
• Main Authors: Etievant, Lola, Viallon, Vivian
• Format: Article
• Language: English
• Subjects: Intervention; Obesity
• ISSN: 2331-8422

For exposures \(X\) like obesity, no precise and unambiguous definition exists for the hypothetical intervention \(do(X = x_0)\). This has raised concerns about the relevance of causal effects estimated from observational studies for such exposures. Under the framework of structural causal models, we study how the effect of \(do(X = x_0)\) relates to the effect of interventions on causes of \(X\). We show that for interventions focusing on causes of \(X\) that affect the outcome through \(X\) only, the effect of \(do(X = x_0)\) equals the effect of the considered intervention. On the other hand, for interventions on causes \(W\) of \(X\) that affect the outcome not only through \(X\), we show that the effect of \(do(X = x_0)\) only partly captures the effect of the intervention. In particular, under simple causal models (e.g., linear models with no interaction), the effect of \(do(X = x_0)\) can be seen as an indirect effect of the intervention on \(W\).