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：在一项分组观察研究中,对群体进行处理,对群体内的所有单位都进行处理;我们开发了一种新方法,对分组观察研究进行统计调整,使用近似平衡加权数,对反向偏差分分数加权数进行概括化,解决了螺旋优化问题,以找到一组加权数,从而直接最大限度地减少共变不平衡的衡量标准,但对于加权数的差异将处以额外的惩罚;我们根据每个案件的平均平方误差设定一个上限界限,并找出将这一上限界限最小化的加权数,将共变平衡数与偏差的界限联系起来,从而将这一程序专门适用于随机的集群效应模型,从而导致一种差异性处罚,将信号对噪音的比例纳入其中,并根据阶级内部相关性对个人的重量和对群体的总重量进行不同的处罚。