Background Numerous studies have found associations when change scores are regressed onto initial impairments in people with stroke (slopes ≈ 0.7). However, there are important statistical considerations that limit the conclusions we can draw about recovery from these studies. Objective To provide an accessible checklist of conceptual and analytical issues on longitudinal measures of stroke recovery. Proportional recovery is an illustrative example, but these considerations apply broadly to studies of change over time. Methods Using a pooled data set of n = 373 Fugl-Meyer Assessment upper extremity scores, we ran simulations to illustrate 3 considerations: (1) how change scores can be problematic in this context; (2) how “nil” and nonzero null-hypothesis significance tests can be used; and (3) how scale boundaries can create the illusion of proportionality, whereas other analytical procedures (eg, post hoc classifications) can augment this problem. Results Our simulations highlight several limitations of common methods for analyzing recovery. We find that uniform recovery leads to similar group-level statistics (regression slopes) and individual-level classifications (into fitters and nonfitters) that have been claimed as evidence for the proportional recovery rule. New analyses, however, also speak to the complexities in variance about the regression slope. Conclusions Our results highlight that one cannot identify whether proportional recovery is true or not based on commonly used methods. We illustrate how these techniques, measurement tools, and post hoc classifications (eg, nonfitters) can create spurious results. Going forward, the field needs to carefully consider the influence of these factors on how we measure, analyze, and conceptualize recovery.

中文翻译：

---

得出关于恢复的结论的统计考虑

背景 许多研究发现，将变化评分回归到卒中患者的初始损伤（斜率 ≈ 0.7）时存在关联。然而，有一些重要的统计考虑限制了我们从这些研究中得出的关于恢复的结论。目的 提供关于中风恢复纵向测量的概念和分析问题的可访问清单。比例恢复是一个说明性的例子，但这些考虑广泛适用于随时间变化的研究。方法 使用 n = 373 Fugl-Meyer Assessment 上肢评分的汇总数据集，我们进行了模拟以说明 3 个考虑因素：(1) 在这种情况下，变化评分如何成为问题；(2) 如何使用“nil”和非零零假设显着性检验；(3) 尺度边界如何产生比例错觉，而其他分析程序（例如，事后分类）可以增加这个问题。结果 我们的模拟突出了分析回收率的常用方法的几个局限性。我们发现统一恢复导致类似的组级统计数据（回归斜率）和个人级别分类（分为拟合者和非拟合者），这些分类已被称为比例恢复规则的证据。然而，新的分析也说明了回归斜率方差的复杂性。结论 我们的结果强调，不能根据常用方法确定比例回收是否正确。我们说明了这些技术、测量工具和事后分类（例如，非拟合者）如何产生虚假结果。