We consider the problem of learning how to optimally allocate treatments whose cost is uncertain and can vary with pre-treatment covariates. This setting may arise in medicine if we need to prioritize access to a scarce resource that different patients would use for different amounts of time, or in marketing if we want to target discounts whose cost to the company depends on how much the discounts are used. Here, we show that the optimal treatment allocation rule under budget constraints is a thresholding rule based on priority scores, and we propose a number of practical methods for learning these priority scores using data from a randomized trial. Our formal results leverage a statistical connection between our problem and that of learning heterogeneous treatment effects under endogeneity using an instrumental variable. We find our method to perform well in a number of empirical evaluations.
翻译:我们考虑了如何以最佳方式分配成本不确定且与预处理共变情况不同的治疗方法的问题。如果我们需要优先获取不同病人在不同时间使用的宝贵资源,或者如果我们想要针对公司成本取决于使用折扣多少的折扣目标,那么在药品方面可能会出现这种环境。在这里,我们表明预算限制下的最佳治疗分配规则是基于优先分数的门槛规则,我们提出若干切实可行的方法,利用随机试验的数据来学习这些优先分数。我们的正式结果使我们的问题和在使用工具变量的内源性下学习不同治疗效应的问题有统计联系。我们发现,我们的方法是在若干经验评估中很好地发挥作用。