Treatment Effects in Extreme Regimes

TL;DR

This work addresses measuring treatment effects in distribution tails by introducing extreme treatment effects (ETE) and conditional extreme treatment effects (CETE) defined through differences in the tail shape parameter $\xi$ of the generalized extreme value ($GEV$) distributions for potential outcomes. It develops identifiability under a tail unconfoundedness assumption, and introduces a likelihood-based CETE/ETE estimator that uses covariate-dependent $GEV$ parameters and a practical $\varepsilon$-max-sampler to cope with scarce tail data. The authors prove consistency and asymptotic normality for the estimators and validate the approach on synthetic and semi-synthetic datasets, showing accurate tail-index estimation and superior performance over naive baselines. The methodology provides a principled way to quantify extreme risks of interventions, enabling decision-making that accounts for worst-case tail behavior and enabling personalized risk assessment in critical applications.

Abstract

Understanding treatment effects in extreme regimes is important for characterizing risks associated with different interventions. This is hindered by the unavailability of counterfactual outcomes and the rarity and difficulty of collecting extreme data in practice. To address this issue, we propose a new framework based on extreme value theory for estimating treatment effects in extreme regimes. We quantify these effects using variations in tail decay rates of potential outcomes in the presence and absence of treatments. We establish algorithms for calculating these quantities and develop related theoretical results. We demonstrate the efficacy of our approach on various standard synthetic and semi-synthetic datasets.

Figures (9)

• Figure 1: Illustration of what the ETE represents. The control group has faster decaying tails with a shape parameter of $0.5$ whereas the treatment group has a shape parameter of $1.5$ with slowly decaying tails. Yet, the treatment group has a lower mean. Hence, ETE $=1$, while the ATE is negative.
• Figure 2: Convergence of different Extreme Treatment Effect (ETE) estimators over increasing sample sizes, showcasing the performance of the Naive Estimator and Proposed Estimator compared to the True ETE. The error bars represent the variability in the estimates across different simulations.
• Figure 3: From left to right, the figures represent the estimation of the individual tail parameter under the control condition, the tail parameter under the treatment condition, and the Conditional Extreme Treatment Effect (CETE) using our proposed method.
• Figure 4: Different conditional outcomes for different treatment groups. The goal of our method is to estimate the difference in the shape parameters of these limiting GEVs.
• Figure 5: Experiments For Conditional GEV Performance as a function of $N$ and $D$

Theorems & Definitions (21)

• Definition 2.1: Causal Identifiability
• Definition 2.5
• Theorem 2.6: Fisher–Tippett–Gnedenko
• Definition 3.1: ETE and CETE
• Definition 3.2
• Remark 3.3
• Remark 3.4: Expected Number of Events
• Proposition 3.6
• Definition 3.7: CETE Estimator
• Definition 3.8: ETE Estimator