In a clustered observational study, a treatment is assigned to groups and all units within the group are exposed to the treatment. We develop a new method for statistical adjustment in clustered observational studies using approximate balancing weights, a generalization of inverse propensity score weights that solve a convex optimization problem to find a set of weights that directly minimize a measure of covariate imbalance, subject to an additional penalty on the variance of the weights. We tailor the approximate balancing weights optimization problem to both adjustment sets by deriving an upper bound on the mean square error for each case and finding weights that minimize this upper bound, linking the level of covariate balance to a bound on the bias. We implement the procedure by specializing the bound to a random cluster-level effects model, leading to a variance penalty that incorporates the signal signal-to-noise ratio and penalizes the weight on individuals and the total weight on groups differently according to the the intra-class correlation.

翻译：在聚类观察性研究中，处理分配至群体，且群体内的所有单元均暴露于处理。我们提出了一种基于近似平衡权重的新统计调整方法，该方法是对逆倾向得分权重的推广，通过求解凸优化问题得到一组权重，直接最小化协变量不平衡性的度量，并附加对权重方差的惩罚。我们针对两种调整集定制了近似平衡权重的优化问题，通过推导每种情况下均方误差的上界，并寻找最小化该上界的权重，将协变量平衡水平与偏差上界联系起来。通过将该上界特化至随机聚类水平效应模型来实现程序，从而得到一种包含信噪比且根据组内相关系数对个体权重和群体总权重进行差异化惩罚的方差惩罚项。