Department of Pediatrics, Faculty of Medicine Dentistry and Health Sciences, The University of Melbourne, Melbourne, Victoria, Australia.
Clinical Epidemiology and Biostatistics Unit, Murdoch Children's Research Institute, Melbourne, Victoria, Australia.
Stat Med. 2022 Sep 30;41(22):4385-4402. doi: 10.1002/sim.9515. Epub 2022 Jul 27.
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.
在医学研究中，常见的是在高层次单位内聚类的个体进行重复测量产生的三级数据。当个体随时间改变聚类时，就会出现交叉分类数据结构，从而增加了复杂性。在这些研究中，缺失值通常通过多重插补（MI）来处理。如果在分析中对三级交叉分类结构进行建模，则也需要在插补模型中进行调整，以确保结果有效。虽然在 MI 中可以使用各种方法来处理不完整的三级数据，但在交叉分类数据设置中，这些方法的性能仍不清楚。我们在一系列场景下进行了模拟，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，该模型通过简单的加法随机效应来模拟随时间变化的聚类成员。模拟研究基于学生纵向队列中聚类的学校的案例研究。我们评估了通过为每个个体取第一个或最常见的聚类来忽略随时间变化的聚类成员的方法；在联合建模（JM）和完全条件规范（FCS）框架内的单级和两级 MI 方法的实用扩展，使用虚拟指标（DI）和/或将重复测量值插补为宽格式以考虑交叉分类结构；以及专门为交叉分类数据开发的三级 FCS MI 方法。结果表明，在偏差和精度方面，FCS 实现表现良好，而 JM 方法表现不佳。在这两种框架下，在存在稀疏数据的情况下，应谨慎使用使用 DI 扩展的方法。
