Optimal Dynamic Treatment Regimes and Partial Welfare Ordering
本文提出一个框架，利用工具变量放松顺序随机化假设，从观测数据中部分学习最优动态治疗方案，并通过线性规划建立反事实福利的偏序关系，识别最优方案的集合。
Dynamic treatment regimes are treatment allocations tailored to heterogeneous individuals (e.g., via previous outcomes and covariates). The optimal dynamic treatment regime is a regime that maximizes counterfactual welfare. We introduce a framework in which we can partially learn the optimal dynamic regime from observational data, relaxing the sequential randomization assumption commonly employed in the literature but instead using (binary) instrumental variables. We propose the notion of sharp partial ordering of counterfactual welfares with respect to dynamic regimes and establish mapping from data to partial ordering via a set of linear programs. We then characterize the identified set of the optimal regime as the set of maximal elements associated with the partial ordering. We relate the notion of partial ordering with a more conventional notion of partial identification using topological sorts. Practically, topological sorts can be served as a policy benchmark for a policymaker. We apply our method to understand returns to schooling and post-school training as a sequence of treatments by combining data from multiple sources. The framework of this article can be used beyond the current context, for example, in establishing rankings of multiple treatments or policies across different counterfactual scenarios. Supplementary materials for this article are available online.