  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 $W$.

Methodology