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.

翻译：本文探究了固定效应模型在分析纵向整群试验（如阶梯楔形设计、基线平行设计及交叉设计）中的模型稳健性，涵盖随机试验（CRTs）和准实验（CQTs）设计。我们澄清了生物统计学中一个长期存在的误解，证明传统上被认为仅针对有限样本条件估计量的固定效应模型，可通过M估计框架有效估计超总体边际估计量。我们全面证明，在治疗效应结构正确设定的线性与对数链接固定效应模型中，即使其他模型成分被任意错误设定，仍能对纵向CRTs中非参数定义的治疗效应估计量生成一致且渐近正态的估计量。研究发现常数治疗效应估计量通常可估计重叠人群的时期平均治疗效应（P-ATO）；因此，某些CRT设计甚至无需正确设定治疗效应结构即可实现模型稳健性。我们进一步刻画了在纵向CQTs中，固定效应模型通过调整聚类层面及个体层面的时不变混杂因素以保持一致性的条件。综合模拟研究与案例重分析证据，我们确立固定效应模型可作为纵向CT分析中混合效应模型的稳健且更优替代方案。