Three-level data arising from repeated measures on individuals clustered within higher-level units are common in medical research. A complexity arises when individuals change clusters over time, resulting in a cross-classified data structure. Missing values in these studies are commonly handled via multiple imputation (MI). If the three-level, cross-classified structure is modeled in the analysis, it also needs to be accommodated in the imputation model to ensure valid results. While incomplete three-level data can be handled using various approaches within MI, the performance of these in the cross-classified data setting remains unclear. We conducted simulations under a range of scenarios to compare these approaches in the context of an acute-effects cross-classified random effects substantive model, which models the time-varying cluster membership via simple additive random effects. The simulation study was based on a case study in a longitudinal cohort of students clustered within schools. We evaluated methods that ignore the time-varying cluster memberships by taking the first or most common cluster for each individual; pragmatic extensions of single- and two-level MI approaches within the joint modeling (JM) and the fully conditional specification (FCS) frameworks, using dummy indicators (DI) and/or imputing repeated measures in wide format to account for the cross-classified structure; and a three-level FCS MI approach developed specifically for cross-classified data. Results indicated that the FCS implementations performed well in terms of bias and precision while JM approaches performed poorly. Under both frameworks approaches using the DI extension should be used with caution in the presence of sparse data.

中文翻译：

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处理具有时变集群成员的不完整三级数据的多重插补方法

对聚集在更高级别单位内的个体的重复测量产生的三级数据在医学研究中很常见。当个人随着时间的推移改变集群时，就会出现复杂性，从而产生交叉分类的数据结构。这些研究中的缺失值通常通过多重插补 (MI) 处理。如果在分析中对三级交叉分类结构进行建模，则还需要在插补模型中进行调整以确保结果有效。虽然可以使用 MI 中的各种方法处理不完整的三级数据，但这些在交叉分类数据设置中的性能仍不清楚。我们在一系列情景下进行了模拟，以在急性效应交叉分类随机效应实质性模型的背景下比较这些方法，它通过简单的加性随机效应对随时间变化的集群成员资格进行建模。模拟研究基于对聚集在学校内的纵向学生群体的案例研究。我们通过为每个个体获取第一个或最常见的集群来评估忽略随时间变化的集群成员资格的方法；在联合建模 (JM) 和完全条件规范 (FCS) 框架内对单级和两级 MI 方法进行实用扩展，使用虚拟指标 (DI) 和/或以宽格式输入重复测量以解释交叉分类结构体; 以及专门为交叉分类数据开发的三级 FCS MI 方法。结果表明，FCS 实现在偏差和精度方面表现良好，而 JM 方法表现不佳。