Limit Regret in Binary Treatment Choice with Misspecified Plug-In Predictors and Decision Thresholds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917256489861120 |
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| author | Dominitz, Jeff Manski, Charles F. |
| author_facet | Dominitz, Jeff Manski, Charles F. |
| contents | We study the population limit maximum regret (MR) of plug-in prediction when the decision problem is to choose between two treatments for the members of a population with observed covariates x. In this setting, the optimal treatment for persons with covariate value x is B if the conditional probability P(y = 1|x) of a binary outcome y exceeds an x-specific known threshold and is A otherwise. This structure is common in medical decision making and also arises in non-medical contexts such as criminal justice. Plug-in prediction uses data to estimate P(y|x) and acts as if the estimate is accurate. We are concerned that the model used to estimate P(y|x) may be misspecified, with true conditional probabilities being outside the model space. In practice, plug-in prediction has been performed with a wide variety of prediction models that commonly are misspecified. Further, applications often use a conventional x-invariant threshold, whereas optimal treatment choice uses x-specific thresholds. The main contribution of this paper is to shed new light on limit MR when plug-in prediction is performed with misspecified models. We use a combination of algebraic and computational analysis to study limit MR, demonstrating how it depends on the limit estimate and on the thresholds used to choose treatments. We recommend that a planner who wants to use plug-in prediction to achieve satisfactory MR should jointly choose a predictive model, estimation method, and x-specific thresholds to accomplish this objective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit Regret in Binary Treatment Choice with Misspecified Plug-In Predictors and Decision Thresholds Dominitz, Jeff Manski, Charles F. Econometrics We study the population limit maximum regret (MR) of plug-in prediction when the decision problem is to choose between two treatments for the members of a population with observed covariates x. In this setting, the optimal treatment for persons with covariate value x is B if the conditional probability P(y = 1|x) of a binary outcome y exceeds an x-specific known threshold and is A otherwise. This structure is common in medical decision making and also arises in non-medical contexts such as criminal justice. Plug-in prediction uses data to estimate P(y|x) and acts as if the estimate is accurate. We are concerned that the model used to estimate P(y|x) may be misspecified, with true conditional probabilities being outside the model space. In practice, plug-in prediction has been performed with a wide variety of prediction models that commonly are misspecified. Further, applications often use a conventional x-invariant threshold, whereas optimal treatment choice uses x-specific thresholds. The main contribution of this paper is to shed new light on limit MR when plug-in prediction is performed with misspecified models. We use a combination of algebraic and computational analysis to study limit MR, demonstrating how it depends on the limit estimate and on the thresholds used to choose treatments. We recommend that a planner who wants to use plug-in prediction to achieve satisfactory MR should jointly choose a predictive model, estimation method, and x-specific thresholds to accomplish this objective. |
| title | Limit Regret in Binary Treatment Choice with Misspecified Plug-In Predictors and Decision Thresholds |
| topic | Econometrics |
| url | https://arxiv.org/abs/2512.19824 |