Randomization Inference For the Always-Reporter Treatment Effect

2026-03-25

AI Summary

This study addresses inference on the average treatment effect among “always-reporters”—units whose outcomes would be observed under either treatment assignment—in randomized experiments with missing data. The authors propose a worst-case randomization test that maximizes the p-value over all always-reporter configurations compatible with the observed data, augmented by a pre-screening step to exclude implausible configurations. This approach establishes the first finite-sample valid inference framework for this setting: it guarantees exact validity under sharp null hypotheses and asymptotic validity under weak nulls. Efficient computation is achieved through studentized Hájek statistics and chi-square–type test statistics, leveraging exact enumeration for discrete outcomes and integer programming–based bounding algorithms for continuous outcomes, thereby enabling reliable and computationally feasible inference.

Technology Category

Reasoning under Uncertainty: CausalityKnowledge Representation and Reasoning: PreferencesMachine Learning: Calibration & Uncertainty Quantification

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSecurity and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

This article studies randomization inference for treatment effects in randomized controlled trials with attrition, where outcomes are observed for only a subset of units. We assume monotonicity in reporting behavior as in \cite{lee2009training} and focus on the average treatment effect for always-reporters (AR-ATE), defined as units whose outcomes are observed under both treatment and control. Because always-reporter status is only partially revealed by observed assignment and response patterns, we propose a worst-case randomization test that maximizes the randomization p-value over all always-reporter configurations consistent with the data, with an optional pretest to prune implausible configurations. Using studentized Hajek- and chi-square-type statistics, we show the resulting procedure is finite-sample valid for the sharp null and asymptotically valid for the weak null. We also discuss computational implementations for discrete outcomes and integer-programming-based bounds for continuous outcomes.

Problem

• randomization inference
• attrition
• always-reporter
• treatment effect
• monotonicity

Innovation

• randomization inference
• always-reporter treatment effect
• attrition
• worst-case p-value
• finite-sample validity