Many analyses of longitudinal cohorts require incorporating sampling weights to account for unequal sampling probabilities of participants, as well as the use of multiple imputation (MI) for dealing with missing data. However, there is no guidance on how MI and sampling weights should be implemented together. We simulated a target population based on the Australian Bureau of Statistics Estimated Resident Population and drew 1000 random samples dependent on three design variables to mimic the Longitudinal Study of Australian Children. The target analysis was the weighted prevalence of overweight/obesity over childhood. We evaluated the performance of several MI approaches available in Stata, based on multivariate normal imputation (MVNI), fully conditional specification (FCS) and twofold FCS: a weighted imputation model, imputing missing data separately for each quintile sampling weight grouping, including the design stratum indicator in the imputation model, and using sampling weights as a covariate in the imputation model. Approaches based on available cases and inverse probability weighting (IPW), with time-varying weights, were also compared. We observed severe issues of convergence with FCS and twofold FCS. All MVNI-based approaches performed similarly, producing minimal bias and nominal coverage, except for when imputation was conducted separately for each quintile sampling weight group. IPW performed equally as well as MVNI-based approaches in terms of bias, however, was less precise. In similar longitudinal studies, we recommend using MVNI with the design stratum as a covariate in the imputation model. If this is unknown, including the sampling weight as a covariate is an appropriate alternative.

中文翻译：

---

使用抽样权重处理纵向研究中缺失值的多重插补方法：Stata 中实施的方法的比较

许多纵向队列分析需要结合抽样权重来解释参与者的不等抽样概率，以及使用多重插补 (MI) 来处理缺失数据。但是，没有关于 MI 和抽样权重应如何一起实施的指南。我们根据澳大利亚统计局估计的居民人口模拟了一个目标人口，并根据三个设计变量抽取了 1000 个随机样本，以模拟澳大利亚儿童的纵向研究。目标分析是儿童超重/肥胖的加权患病率。我们基于多元正态插补 (MVNI)、完全条件规范 (FCS) 和双重 FCS：加权插补模型，评估了 Stata 中可用的几种 MI 方法的性能，为每个五分位数抽样权重分组分别插补缺失数据，包括插补模型中的设计层指标，并在插补模型中使用采样权重作为协变量。还比较了基于可用案例和具有时变权重的逆概率加权 (IPW) 的方法。我们观察到 FCS 和双重 FCS 收敛的严重问题。所有基于 MVNI 的方法都表现相似，产生最小偏差和名义覆盖率，除非对每个五分位数采样权重组单独进行插补。IPW 在偏差方面的表现与基于 MVNI 的方法一样好，但是精度较低。在类似的纵向研究中，我们建议使用 MVNI 和设计层作为插补模型中的协变量。如果这是未知的，