From the social sciences to machine learning, it has been well documented that metrics to be optimized are not always aligned with social welfare. In healthcare, Dranove et al. [12] showed that publishing surgery mortality metrics actually harmed the welfare of sicker patients by increasing provider selection behavior. Using a principal-agent model, we directly study the incentive misalignments that arise from such average treated outcome metrics, and show that the incentives driving treatment decisions would align with maximizing total patient welfare if the metrics (i) accounted for counterfactual untreated outcomes and (ii) considered total welfare instead of average welfare among treated patients. Operationalizing this, we show how counterfactual metrics can be modified to satisfy desirable properties when used for ranking. Extending to realistic settings when the providers observe more about patients than the regulatory agencies do, we bound the decay in performance by the degree of information asymmetry between the principal and the agent. In doing so, our model connects principal-agent information asymmetry with unobserved heterogeneity in causal inference.

该研究通过一个主体代理模型研究了治疗指标存在的激励错位问题并表明，如果治疗指标考虑了未治疗结果，同时综合考虑整体病人福利而非仅治疗病人的平均福利，就能最大化病人福利；此外，当治疗者观察到的病人信息比监管机构更多时，该模型连接了主体代理信息不对称和因果推断中未观测到的异质性。

操作化反事实度量：激励、排名和信息不对称