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Randomization Inference For the Always-Reporter Average Treatment Effect

Haoge Chang, Zeyang Yu

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.

Randomization Inference For the Always-Reporter Average Treatment Effect

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.

Paper Structure

This paper contains 46 sections, 35 theorems, 267 equations, 2 tables, 17 algorithms.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Setup, Dataset and Statistical Framework
  4. Notation and Identification Assumptions
  5. Experimental Design and Data Generating Process
  6. Problem Statement
  7. Statistical Procedure
  8. Assign units to principal reporting strata
  9. Refine sets of always-reporters with pretesting
  10. Test Statistics
  11. The Studentized-Hajek Statistic
  12. The Chi-square Statistics
  13. Statistical Guarantees
  14. Randomization-based Procedures
  15. Asymptotic-Distribution-Based Procedures
  16. ...and 31 more sections

Key Result

Theorem 4.2

Consider the statistical procedure in Algorithm alg:inf with test statistics $\mathcal{T}_n^0$, $\mathcal{T}_n^1$ and $\mathcal{T}_n^2$ defined in (eqn:t0), (eqn:t1), and (eqn:t2). Fix a significance level $\alpha\in(0,0.25]$ and a pre-testing level $\beta\in [0,\alpha)$. Let $\Theta^s_n$ be the par Fix $\delta <1$, $s\in(0,1]$, $r \in (0,1/2]$, and $B > 0$. Let $\Theta^w_n(\delta,s,r,B)$ be the p

Theorems & Definitions (70)

  • Remark 3.1
  • Remark 4.1
  • Theorem 4.2
  • Remark 4.3
  • Theorem 4.4
  • Remark 4.5
  • Lemma 5.1
  • Lemma 5.2
  • Theorem 5.3
  • Theorem A.1
  • ...and 60 more