Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection

The conditional average treatment effect (CATE) is frequently estimated to refute the homogeneous treatment effect assumption. Under this assumption, all units making up the population under study experience identical benefit from a given treatment. 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. To address these limitations, we prove that the homogeneous treatment effect assumption can be gauged through inference about contrasts of the potential outcomes' variances. 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 homogeneous treatment effect assumption even when effect modifiers are missing or mismeasured. Numerical experiments demonstrate that these estimators' asymptotic guarantees are approximately achieved in experimental and observational 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.