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

2026-04-08

AI Summary

This study addresses the sensitivity of causal effect estimation to model misspecification in longitudinal cluster-randomized and quasi-experimental designs. Within an M-estimation framework, it demonstrates that fixed-effects models yield consistent and asymptotically normal estimates of nonparametrically defined treatment effects, provided the treatment effect structure is correctly specified—even when other model components are arbitrarily misspecified. The work establishes, for the first time, that fixed-effects models are valid for estimating superpopulation marginal effects and reveals their robustness to partial misspecification of the treatment effect structure across diverse longitudinal settings. Through theoretical analysis, simulations, and reanalyses of empirical data, the paper further shows that fixed-effects models outperform mixed-effects models in robustness and reliability when time-invariant confounding exists at the cluster or individual level.

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.

Problem

• fixed-effects models
• causal inference
• longitudinal cluster trials
• model robustness
• treatment effect estimands

Innovation

• fixed-effects models
• causal inference
• longitudinal cluster trials
• model robustness
• M-estimation