  We extend the definition of the marginal causal effect to the continuous
treatment setting and develop a novel characterization of causal bias in the
framework of structural causal models. We prove that our derived bias
expression is zero if, and only if, the causal effect is identifiable via
covariate adjustment. We show that under some restrictions on the structural
equations, the causal bias can be estimated efficiently and allows for causal
regularization of predictive probabilistic models. We demonstrate the
effectiveness of our method for causal bias quantification in various settings
where (not) controlling for certain covariates would introduce causal bias.
