Evaluating Supplemental Samples in Longitudinal Research: Replacement and Refreshment Approaches

Despite the wide application of longitudinal studies, they are often plagued by missing data and attrition. The majority of methodological approaches focus on participant retention or modern missing data analysis procedures. This paper, however, takes a new approach by examining how researchers may <i>supplement</i> the sample with additional participants. First, <i>refreshment</i> samples use the same selection criteria as the initial study. Second, <i>replacement</i> samples identify auxiliary variables that may help explain patterns of missingness and select new participants based on those characteristics. A simulation study compares these two strategies for a linear growth model with five measurement occasions. Overall, the results suggest that <i>refreshment</i> samples lead to less relative bias, greater relative efficiency, and more acceptable coverage rates than <i>replacement</i> samples or not supplementing the missing participants in any way. Refreshment samples also have high statistical power. The comparative strengths of the refreshment approach are further illustrated through a real data example. These findings have implications for assessing change over time when researching at-risk samples with high levels of permanent attrition.

尽管纵向研究（longitudinal studies）应用范围广泛，但这类研究常受困于数据缺失与失访（attrition）问题。现有主流方法论研究多聚焦于提升被试留存率，或是采用现代化的缺失数据分析流程。然而本研究提出了一种全新的研究路径，探讨研究者如何通过招募额外被试**补充**原有样本。其一，**更新样本（refreshment samples）**采用与初始研究完全一致的筛选标准；其二，**替换样本（replacement samples）**则先识别可用于解释缺失模式的辅助变量，并基于这些特征招募新被试。本研究针对包含5次测量时点的线性增长模型，通过模拟实验对比了这两种策略的效果。整体结果显示，相较于**替换样本**或是完全不补充缺失被试的方案，**更新样本**能带来更低的相对偏差、更高的相对效率，以及更符合统计学要求的覆盖率。此外，**更新样本**还具备较高的统计效力。一项真实数据分析案例进一步验证了**更新样本**策略的相对优势。本研究结果对于针对存在高持续性失访风险的群体开展追踪研究、评估其随时间的变化趋势具有重要的实践启示。