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

TL;DR

This paper develops and justifies model-assisted linear regression estimators for dynamic causal effects in staggered rollout cluster randomized experiments, ensuring valid inference without outcome modeling assumptions.

Contribution

It provides a rigorous, design-based framework establishing consistency, asymptotic normality, and efficiency comparisons for various estimators in SR-CREs.

Findings

Scaled cluster-period totals with covariate adjustment are more efficient.

Variance estimators are asymptotically conservative.

Linear regression estimators are justified as model-assisted methods.

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 L\"{o}wner 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.