Randomization Inference For the Always-Reporter Average Treatment Effect

TL;DR

This paper develops a robust randomization inference method for the always-reporter average treatment effect in RCTs with attrition, ensuring valid inference despite partial reporting.

Contribution

It introduces a worst-case randomization test that accounts for unobserved always-reporter status, with computational methods for different outcome types.

Findings

The proposed test is finite-sample valid under the sharp null.

It is asymptotically valid for the weak null.

Computational approaches are provided for discrete and continuous outcomes.

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.