Conditional Front-door Adjustment for Heterogeneous Treatment Assignment Effect Estimation Under Non-compliance

Winston Chen, Trenton Chang, Jenna Wiens

Abstract: Estimates of heterogeneous treatment assignment effects are valuable when making treatment decisions. Under the presence of non-compliance (e.g., patients do not adhere to their assigned treatment), the standard backdoor adjustment (SBD) and the conditional frond-door adjustment (CFD) can both recover unbiased estimates of the treatment assignment effects. Therefore, which is more suitable depends on their estimation variance. From existing literature, it is unclear which of the two produces lower-variance estimates. In this work, we demonstrate theoretically and empirically that CFD yields lower-variance estimates than SBD when the true effect of treatment assignment is small. Additionally, since CFD requires estimating multiple nuisance parameters, we introduce LobsterNet, a multi-task neural network that implements CFD with joint modeling. Empirically, LobsterNet reduces estimation error across several semi-synthetic and real-world datasets compared to baselines. Our findings suggest CFD with shared nuisance parameter modeling can improve treatment assignment effect estimation under non-compliance.