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Model-assisted inference for dynamic causal effects in staggered rollout cluster randomized experiments

Xinyuan Chen, Fan Li

Abstract

Staggered rollout cluster randomized experiments (SR-CREs) involve sequential treatment adoption across clusters, requiring analysis methods that address a general class of dynamic causal effects, anticipation, and non-ignorable cluster-period sizes. Without imposing any outcome modeling assumptions, we study regression estimators using individual data, cluster-period averages, and scaled cluster-period totals, with and without covariate adjustment from a design-based perspective. We establish consistency and asymptotic normality of each estimator under a randomization-based framework and prove that the associated variance estimators are asymptotically conservative in the Löwner ordering. Furthermore, we conduct a unified efficiency comparison of the estimators and provide recommendations. We highlight the efficiency advantage of using estimators based on scaled cluster-period totals with covariate adjustment over their counterparts using individual-level data and cluster-period averages. Our results rigorously justify linear regression estimators as model-assisted methods to address an entire class of dynamic causal effects in SR-CREs.

Model-assisted inference for dynamic causal effects in staggered rollout cluster randomized experiments

Abstract

Staggered rollout cluster randomized experiments (SR-CREs) involve sequential treatment adoption across clusters, requiring analysis methods that address a general class of dynamic causal effects, anticipation, and non-ignorable cluster-period sizes. Without imposing any outcome modeling assumptions, we study regression estimators using individual data, cluster-period averages, and scaled cluster-period totals, with and without covariate adjustment from a design-based perspective. We establish consistency and asymptotic normality of each estimator under a randomization-based framework and prove that the associated variance estimators are asymptotically conservative in the Löwner ordering. Furthermore, we conduct a unified efficiency comparison of the estimators and provide recommendations. We highlight the efficiency advantage of using estimators based on scaled cluster-period totals with covariate adjustment over their counterparts using individual-level data and cluster-period averages. Our results rigorously justify linear regression estimators as model-assisted methods to address an entire class of dynamic causal effects in SR-CREs.

Paper Structure

This paper contains 24 sections, 11 theorems, 27 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Staggered rollout cluster randomized experiments
  3. Identification assumptions
  4. Dynamic causal effect estimands
  5. Regression-based causal effects estimators
  6. Preliminaries
  7. Estimators using individual-level data
  8. Without covariates
  9. With covariates
  10. Estimators using cluster-level data
  11. Using cluster-period averages
  12. Using scaled cluster-period totals
  13. Generalization to summary estimands
  14. Comparisons and recommendations
  15. Estimators using individual-level data and cluster-period averages
  16. ...and 9 more sections

Key Result

Theorem 1

Under Assumptions asp:sutva and asp:rand, and regularity conditions (C1) and (C2) in Section S2 of the Online Supplement, for $a<a'\in\mathcal{A}$, $\widehat{\bm{\tau}}_{j,\mathrm{I}}(a,a')=\bm{\tau}(a,a')+\bm{o}_\mathbb{P}(1)$; if we further assume $\max_i\pi_{ij\cdot}=o(I^{-2/3})$ for $j=1,\ldots,

Figures (3)

  • Figure 1: An example schematic of an SR-CRE with $I=\sum_{a\in\mathcal{A}} I(a)$ clusters and $J=5$ rollout periods. There are six possible treatment adoption times, $\mathcal{A}=\{1,2,3,4,5,\infty\}$. Each row represents a subset of all clusters with a unique treatment adoption time. Each period is of equal length, and we include in each cell all cluster-period sizes ($N_{ij}$) for clusters included in that row during that period. A white cell indicates the control condition, and a shaded cell indicates the treatment condition.
  • Figure 2: Relative bias, coverage percentages of 95% CIs, and empirical standard errors for $\tau_1(1,\infty)$ from simulation studies I and II.
  • Figure 3: Relative bias, coverage percentages of 95% CIs, and empirical standard errors for $\mathrm{OWTE}^{cal}$ from simulation studies I and II.

Theorems & Definitions (12)

  • Theorem 1
  • Theorem 2
  • Corollary 1
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Remark 1
  • Proposition 1
  • Proposition 2
  • ...and 2 more