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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Rethinking the Win Ratio: A Causal Framework for Hierarch...
Mathieu Even, Julie Josse · 2025-01-28 · via math.ST updates on arXiv.org

Quantifying causal effects in the presence of complex and multivariate outcomes remains a key challenge in treatment evaluation. For hierarchical multivariate outcomes, the FDA recommends the Win Ratio and Generalized Pairwise Comparisons approaches \citep{Pocock2011winratio,Buyse2010}. However, commonly used estimators can yield treatment recommendations that target a population-level estimand (the probability that a randomly sampled patient under treatment fares better than another randomly sampled patient under control), which can contradict conclusions drawn from an ideal estimand (the probability that an individual would fare better with treatment than without), especially in heterogeneous populations. This discrepancy arises from the non-identifiability of the latter estimand and underscores both the influence of the chosen causal measure on the resulting conclusions and the necessity of articulating the underlying causal framework with clarity. We propose a novel, individual-level yet identifiable causal effect measure that more closely approximates the ideal individual-level estimand. We show that computing the Win Ratio or Net Benefit via nearest-neighbor pairing between treated and control patients, which can be seen as an extreme form of stratification, yields an estimator of our new causal measure in both randomized controlled trials and observational settings. We then develop a distributional regression framework, alongside semiparametric efficient estimators. Our methods are simple to implement and readily applicable in practice. We evaluate the proposed approach through simulations and apply it to the CRASH-3 trial \citep{crash3}, a major study assessing the effects of tranexamic acid in patients with traumatic brain injury.