Fixed-Effects Models for Causal Inference in Longitudinal Cluster Randomized and Quasi-Experimental Trials

TL;DR

This paper demonstrates that fixed-effects models are robust and effective for causal inference in various longitudinal cluster trials, even under model misspecification, challenging traditional views in biostatistics.

Contribution

It clarifies that fixed-effects models can target super-population estimands and remain consistent under misspecification, broadening their applicability in longitudinal cluster trials.

Findings

Fixed-effects models can target super-population estimands via M-estimation.

Correctly specified fixed-effects models yield consistent estimators in longitudinal CRTs.

Some designs do not require correct treatment effect specification for robustness.

Abstract

This article investigates the model-robustness of fixed-effects models for analyzing a broad class of longitudinal cluster trials (CTs) such as stepped-wedge, parallel-with-baseline and crossover designs, encompassing both randomized (CRTs) and quasi-experimental (CQTs) designs. We clarify a longstanding misconception in biostatistics, demonstrating that fixed-effects models, traditionally perceived as targeting only finite-sample conditional estimands, can effectively target super-population marginal estimands through an M-estimation framework. We comprehensively prove that linear and log-link fixed-effects models with correctly specified treatment effect structures can broadly yield consistent and asymptotically normal estimators for nonparametrically defined treatment effect estimands in longitudinal CRTs, even under arbitrary misspecification of other model components. We identify that the constant treatment effect estimator generally targets the period-average treatment effect for the overlap population (P-ATO); accordingly, some CRT designs don't even require correct specification of the treatment effect structure for model-robustness. We further characterize conditions where fixed-effects models can maintain consistency by adjusting for both cluster-level and individual-level time-invariant confounding in longitudinal CQTs. Altogether, supported by simulation and a case study re-analysis, we establish fixed-effects models as a robust and potentially preferable alternative to mixed-effects models for longitudinal CT analysis.