Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection

Abstract

The conditional average treatment effect (CATE) is frequently estimated in clinical studies to refute a homogeneous treatment effect hypothesis. Under this regime, all patients making up the population experience identical benefit from a given treatment relative to a comparator. Uncovering heterogeneous treatment effects through inference about the CATE, however, requires that covariates truly modifying the treatment effect be reliably collected at baseline. CATE-based techniques will necessarily fail to detect violations when effect modifiers are omitted from the data due to, for example, resource constraints. Severe measurement error has a similar impact. Clinical decision makers can be misled as a result. To address these limitations, we prove that a practical homogeneous treatment effect hypothesis can be gauged through inference about contrasts of the potential outcomes' variances even when effect modifiers are missing from the data. We derive causal machine learning estimators of these contrasts and study their asymptotic properties. We establish that these estimators are doubly robust and asymptotically linear under mild conditions, permitting formal hypothesis testing about the treatment effect heterogeneity. Numerical experiments demonstrate that these estimators' asymptotic guarantees are approximately achieved in finite-sample randomized and observational study data alike. These inference procedures are then used to detect heterogeneous treatment effects in the re-analysis of randomized controlled trials investigating targeted temperature management in cardiac arrest patients.