Causal Stability Selection

TL;DR

This paper introduces causal stability selection, a method for identifying effect modifiers in causal inference with finite-sample false discovery control, applicable to various estimators and validated on real data.

Contribution

It proposes a novel algorithm combining cross-fitting and stability selection that provides explicit bounds on false positives in effect modifier discovery.

Findings

The method controls the expected number of false discoveries.

Convergence of estimated selection probabilities to oracle values is proven.

Demonstrated on oncology trial and maternal smoking data.

Abstract

Identifying covariates that modify treatment effects is a central problem in causal inference. Yet existing data-adaptive procedures do not provide finite-sample control over the expected number of false discoveries, risking spurious findings that fail to replicate. We introduce causal stability selection, an algorithm that combines cross-fitted estimation of conditional average treatment effects with integrated path stability selection. The method accommodates arbitrary treatment effect estimators and arbitrary base selectors, and produces a selection set with an explicit, non-asymptotic bound on the expected number of false positives. Under standard causal identifying assumptions and regularity conditions on the base selector, we prove that the estimated selection probabilities converge to their oracle counterparts at the rate of the underlying treatment effect estimator. This establishes a direct connection between treatment effect estimation and effect modifier discovery. We illustrate the method on a randomized trial in oncology and on observational data on maternal smoking and infant birthweight.