Front-door Versus Back-door Adjustment with Unmeasured Confounding: Bias Formulas for Front-door and Hybrid Adjustments with Application to a Job Training Program

We demonstrate that the front-door adjustment can be a useful alternative to standard covariate adjustments (i.e., back-door adjustments), even when the assumptions required for the front-door approach do not hold. We do this by providing asymptotic bias formulas for the front-door approach that can be compared directly to bias formulas for the back-door approach. In some cases, this allows the tightening of bounds on treatment effects. We also show that under one-sided noncompliance, the front-door approach does not rely on the use of control units. This finding has implications for the design of studies when treatment cannot be withheld from individuals (perhaps for ethical reasons). We illustrate these points with an application to the National Job Training Partnership Act Study.