The Average Treatment Effect on the Treated (ATT) is a common causal parameter defined as the average effect of a binary treatment among the subset of the population receiving treatment. We propose a novel family of parameters, Generalized ATTs (GATTs), that generalize the concept of the ATT to longitudinal data structures, multi-valued or continuous treatments, and conditioning on arbitrary treatment subsets. We provide a formal causal identification result that expresses the GATT in terms of sequential regressions, and derive the efficient influence function of the parameter, which defines its semi-parametric efficiency bound. Efficient semi-parametric inference of the GATT requires estimating the ratios of functions of conditional probabilities (or densities); we propose directly estimating these ratios via empirical loss minimization, drawing on the theory of Riesz representers. Simulations suggest that estimation of the density ratios using Riesz representation have better stability in finite samples. Lastly, we illustrate the use of our methods to evaluate the effect of chronic pain management strategies on the development of opioid use disorder among Medicare patients with chronic pain.

翻译：处理组平均效应（ATT）是一个常见的因果参数，定义为在接收处理的总体子集中，二元处理的平均效应。我们提出了一族新颖的参数——广义ATT（GATT），将ATT的概念推广至纵向数据结构、多值或连续处理，以及对任意处理子集的条件化。我们提供了一个形式化的因果识别结果，通过序列回归表达GATT，并推导了该参数的有效影响函数，从而定义了其半参数效率界。GATT的高效半参数推断需要估计条件概率（或密度）函数之比的函数；我们借鉴Riesz表示子理论，提出通过经验损失最小化直接估计这些比率。模拟实验表明，使用Riesz表示估计密度比在有限样本中具有更好的稳定性。最后，我们通过评估慢性疼痛管理策略对医疗保险慢性疼痛患者阿片类药物使用障碍发展的影响，展示了我们方法的应用。