Robust and Agnostic Learning of Conditional Distributional Treatment Effects

Abstract

The conditional average treatment effect (CATE) is the best point prediction of individual causal effects given individual baseline covariates and can help personalize treatments. However, as CATE only reflects the (conditional) average, it can wash out potential risks and tail events, which are crucially relevant to treatment choice. In aggregate analyses, this is usually addressed by measuring distributional treatment effect (DTE), such as differences in quantiles or tail expectations between treatment groups. Hypothetically, one can similarly fit covariate-conditional quantile regressions in each treatment group and take their difference, but this would not be robust to misspecification or provide agnostic best-in-class predictions. We provide a new robust and model-agnostic methodology for learning the conditional DTE (CDTE) for a wide class of problems that includes conditional quantile treatment effects, conditional superquantile treatment effects, and conditional treatment effects on coherent risk measures given by f -divergences. Our method is based on constructing a special pseudo-outcome and regressing it on baseline covariates using any given regression learner. Our method is model-agnostic in the sense that it can provide the best projection of CDTE onto the regression model class. Our method is robust in the sense that even if we learn these nuisances nonparametrically at very slow rates, we can still learn CDTEs at rates that depend on the class complexity and even conduct inferences on linear projections of CDTEs. We investigate the performance of our proposal in simulation studies, and we demonstrate its use in a case study of 401(k) eligibility effects on wealth.

Robust Direct Learning for Causal Data Fusion

“…The partial balance property is naturally satisfied in many cases, for example, (a) the working propensity scores are correct, i.e., p a|s (X, Z s ) = p a|s (X, Z s ); (b) there are no source-specific covariates, i.e., Z s = ∅; (c) only the covariates X lead to the heterogeneity of causal effects, i.e., δ(X, Z s ) = δ(X). Case (c) holds especially when many variables predict potential outcomes but only a few has a strong modulate effect (Kallus and Oprescu, 2022).…”

“…The data splitting technique is commonly used when learning nuisance estimators (Kallus and Oprescu, 2022).…”

“…As pointed out by Kallus and Oprescu (2022), learning the conditional outcome means on two treatment arms separately and taking the difference to obtain the CATE may suffer from error accumulation, especially when the CATE function has a simpler and sparser form. This inspires us to learn the CATE function directly by modeling it as a whole.…”