Longitudinal randomized controlled trials (RCTs) have been commonly used in psychological studies to evaluate the effectiveness of treatment or intervention strategies. Outcomes in longitudinal RCTs may follow either straight-line or curvilinear change trajectories over time, and missing data are almost inevitable in such trials. The current study aims to investigate (a) whether the estimate of average treatment effect (ATE) would be biased if a straight-line growth (SLG) model is fit to longitudinal RCT data with quadratic growth and missing completely at random (MCAR) or missing at random (MAR) data, and (b) whether adding a quadratic term to an SLG model would improve the ATE estimation and inference. Four models were compared via a simulation study, including the SLG model, the quadratic growth model with arm-invariant and fixed quadratic effect (QG-AIF), the quadratic growth model with arm-specific and fixed quadratic effects (QG-ASF), and the quadratic growth model with arm-specific and random quadratic effects (QG-ASR). Results suggest that fitting an SLG model to quadratic growth data often yielded severe biases in ATE estimates, even if data were MCAR or MAR. Given four or more waves of longitudinal data, the QG-ASR model outperformed the other methods; for three-wave data, the QG-ASR model was not applicable and the QG-ASF model performed well. Applications of different models are also illustrated using an empirical data example. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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二次项在估计数据缺失的纵向随机对照试验的平均治疗效果中的作用。


纵向随机对照试验 （RCT） 常用于心理学研究，以评估治疗或干预策略的有效性。纵向 RCT 的结局可能随着时间的推移遵循直线或曲线变化轨迹，在此类试验中，数据缺失几乎是不可避免的。本研究旨在调查 （a） 如果直线生长 （SLG） 模型适合具有二次生长和完全随机缺失 （MCAR） 或随机缺失 （MAR） 数据的纵向 RCT 数据，平均治疗效果 （ATE） 的估计是否会有偏差，以及 （b） 向 SLG 模型添加二次项是否会改善 ATE 估计和推理。通过仿真研究比较了四种模型，包括 SLG 模型、具有手臂不变和固定二次效应的二次生长模型 （QG-AIF）、具有手臂特异性和固定二次效应的二次生长模型 （QG-ASF） 和具有手臂特异性和随机二次效应的二次生长模型 （QG-ASR）。结果表明，即使数据是 MCAR 或 MAR，将 SLG 模型拟合到二次生长数据通常也会在 ATE 估计中产生严重的偏差。给定四波或更多波纵向数据，QG-ASR 模型优于其他方法;对于三波数据，QG-ASR 模型不适用，QG-ASF 模型表现良好。还使用经验数据示例说明了不同模型的应用。（PsycInfo 数据库记录 （c） 2024 APA，保留所有权利）。