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.

翻译：从社会科学到机器学习，已有充分文献表明，待优化的指标并不总是与社会福祉相一致。在医疗领域，德雷诺夫等人[12]指出，公布手术死亡率指标实际上通过增加医疗服务提供者的筛选行为损害了病情较重患者的福祉。利用委托-代理模型，我们直接研究了此类平均治疗结果指标所引发的激励错位问题，并证明如果指标（i）考虑了反事实的未治疗结果，且（ii）关注总体福祉而非已治疗患者的平均福祉，那么驱动治疗决策的激励将与患者总体福祉最大化保持一致。在操作化层面，我们展示了如何对反事实指标进行修正，使其在用于排名时满足理想性质。将研究扩展到更现实的场景中（即医疗服务提供者比监管机构掌握更多患者信息时），我们通过委托人与代理人之间的信息不对称程度来界定绩效衰减的边界。通过这一方式，我们的模型将委托-代理信息不对称与因果推断中的未观测异质性联系了起来。