Random effects regression imputation has been recommended for multiple imputation (MI) in cluster randomized trials (CRTs) because it is congenial to analyses that use random effects regression. This method relies heavily on model assumptions and may not be robust to misspecification of the imputation model. MI by predictive mean matching (PMM) is a semiparametric alternative, but current software for multilevel data relies on imputation models that ignore clustering or use fixed effects for clusters. When used directly for imputation, these two models result in underestimation (ignoring clustering) or overestimation (fixed effects for clusters) of variance estimates. We develop MI procedures based on PMM that leverage these opposing estimated biases in the variance estimates in one of three ways: weighting the distance metric (PMM-dist), weighting the average of the final imputed values from two PMM procedures (PMM-avg), or performing a weighted draw from the final imputed values from the two PMM procedures (PMM-draw). We use Monte-Carlo simulations to evaluate our newly proposed methods relative to established MI procedures, focusing on estimation of treatment group means and their variances after MI. The proposed PMM procedures reduce the bias in the MI variance estimator relative to established methods when the imputation model is correctly specified, and are generally more robust to model misspecification than even the random effects imputation methods. The PMM-draw procedure in particular is a promising method for multiply imputing missing data from CRTs that can be readily implemented in existing statistical software.

中文翻译：

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在聚类随机试验中通过预测均值匹配进行多重插补。

在群集随机试验（CRT）中，建议对多重插补（MI）进行随机效应回归插补，因为使用随机效应回归分析是有益的。此方法在很大程度上依赖于模型假设，并且可能对插补模型的错误指定不可靠。通过预测均值匹配（PMM）的MI是一种半参数替代方案，但是当前用于多级数据的软件依赖于忽略聚类或对聚类使用固定效应的插补模型。当直接用于估算时，这两个模型会导致方差估计的低估（忽略聚类）或高估（聚类的固定效应）。我们基于PMM开发了MI程序，该程序以三种方式之一利用方差估计中的这些相反估计偏差：加权距离度量（PMM-dist），对来自两个PMM程序的最终估算值的平均值进行加权（PMM-avg），或者根据来自两个PMM程序的最终估算值进行加权抽取（PMM-draw）。我们使用蒙特卡洛模拟来评估我们相对于已建立的MI程序的新提议方法，重点是估计MI后的治疗组均值及其方差。当正确指定插补模型时，提出的PMM程序相对于已建立的方法减少了MI方差估计器中的偏差，并且与随机效应插补方法相比，通常在模型错误指定方面更强大。特别地，PMM绘制过程是一种有前景的方法，可以从现有的统计软件中轻松实现CRT的缺失数据的倍增估算。