Estimation of controlled direct effects

When regression models adjust for mediators on the causal path from exposure to outcome, the regression coefficient of exposure is commonly viewed as a measure of the direct exposure effect. This interpretation can be misleading, even with a randomly assigned exposure. This is because adjustment for post-exposure measurements introduces bias whenever their association with the outcome is confounded by more than just the exposure. By the same token, adjustment for such confounders stays problematic when these are themselves affected by the exposure. Robins accommodated this by introducing linear structural nested direct effect models with direct effect parameters that can be estimated by using inverse probability weighting by a conditional distribution of the mediator. The resulting estimators are consistent, but inefficient, and can be extremely unstable when the mediator is absolutely continuous. We develop direct effect estimators which are not only more efficient but also consistent under a less demanding model for a conditional expectation of the outcome. We find that the one estimator which avoids inverse probability weighting altogether performs best. This estimator is intuitive, computationally straightforward and, as demonstrated by simulation, competes extremely well with ordinary least squares estimators in settings where standard regression is valid.