Nonparametric Estimation of the Average Causal Effect using the Front-door Criterion

Ana P. L. Cavalcante, Rafael Izbicki, Rafael Bassi Stern

Keywords: Causal inference, Front-door Criterion, Nonparametric Estimation, Average Causal Effect, Continuous Treatment

TL;DR: We propose three nonparametric methods for estimating the average causal effect when the front-door criterion holds, Frontdoor-CDE, Frontdoor-Odds and Frontdoor-S, the latter of which is applicable to continuous treatments.

Abstract:

Existing estimators for the average causal effect that are based on the front-door criterion are largely parametric or semiparametric, relying on restrictive assumptions that may not hold in practice.
To address this gap, we propose three nonparametric methods,
Frontdoor-CDE, Frontdoor-Odds and Frontdoor-S,
the latter of which is applicable to continuous treatments.
Specifically, when unobservable confounders prevent the identification of the causal effect of $X$ on $Y$ through the backdoor criterion, the front-door criterion allows identification through mediators, $\mathbb{W}$. Our approach estimates either conditional densities, conditional odds ratios, or conditional density ratios, using these quantities to re-weight instances and identify the causal effect. We establish that under mild nonparametric assumptions, all proposed estimators converge to the true causal effect. In the binary treatment case, simulation studies reveal that Frontdoor-CDE and Frontdoor-Odds outperform parametric methods when model assumptions are violated, while remaining competitive when assumptions hold. For continuous treatments, Frontdoor-S demonstrates consistency and the ability to capture complex data structures.

Submission Number: 11