Which Covariates to Adjust for? Specification-robust Causal Inference in Observational Studies

TL;DR

This paper introduces a robust method for causal inference in observational studies that provides valid estimates even when multiple covariate adjustment sets are plausible, by reweighting the population to ensure credible inference.

Contribution

It proposes a specification-robust procedure that yields a single point estimate and confidence interval valid under at least one correct adjustment set, addressing conflicts among different covariate adjustments.

Findings

Provides tighter confidence intervals than existing methods

Maintains nominal coverage across various adjustment sets

Demonstrates effectiveness on synthetic and real data

Abstract

In observational causal inference, domain knowledge often leaves multiple covariate adjustments plausible, yet which sets satisfy ignorability is untestable. Different adjustment sets can yield conflicting estimates of the average treatment effect, and standard remedies (adjusting for their union or intersection, or reporting the union or convex hull of confidence intervals) can fail or produce intervals whose width does not vanish with sample size. We propose a specification-robust procedure that returns a single point estimate and a confidence interval that is valid as long as at least one candidate adjustment set is valid and has width shrinking at the parametric $n^{-1/2}$ rate. Our approach mirrors how trimming and overlap weighting handle overlap violations:~We shift the target to a reweighted population, closest in KL-divergence to the original population, for which credible, specification-robust inference is feasible. We also provide diagnostic plots to assess the population shift and an extension to protect any function of the covariates used for reweighting, similar to calipers in matching. Synthetic and real-data examples demonstrate that our procedure provides substantially tighter confidence intervals than the convex hull while maintaining nominal coverage.