Front-door Versus Back-door Adjustment with Unmeasured Confounding: Bias Formulas for Front-door and Hybrid Adjustments


In this paper, we develop bias formulas for front-door estimates and front-door/back- door hybrid estimates of average treatment effects under general patterns of measured and unmeasured confounding. These bias formulas allow for sensitivity analysis, and also allow for comparisons of the bias resulting from standard back-door covariate ad- justments (also known as direct adjustment and standardization). We also present these bias comparisons in two special cases: linear structural equation models and nonrandomized program evaluations with one-sided noncompliance. These compar- isons demonstrate that there are broad classes of applications for which the front-door or hybrid adjustments will be preferred to the back-door adjustments. We illustrate this point with an application to the National JTPA (Job Training Partnership Act) Study, showing that by using information on enrollment in addition to pre-treatment covariates, the front-door approach provides estimates that are closer to the experi- mental benchmark than the back-door approach.

Last updated on 02/25/2014