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Closed-Form Solution of the Unit Normal Loss Integral in 2 Dimensions, with Application in Value-of-Information
Tae Yoon Lee1, Paul Gustafson2, Mohsen Sadatsafavi1
1Respiratory Evaluation Sciences Program, Collaboration for Outcomes Research and Evaluation, Faculty of Pharmaceutical Sciences, University of British Columbia, Vancouver, BC, Canada.
Highlights:
The unit normal loss integral (UNLI) is widely used in decision analysis and risk modeling, including in the computation of various value-of-information metrics, but its closed-form solution is only applicable to comparisons of 2 strategies.We derive a closed-form solution for 2-dimensional UNLI, extending the applicability of the UNLI to 3-strategy comparisons.Such closed-form computation takes only a fraction of a second and is free from simulation errors that affect the hitherto available methods.In addition to the relevance in 3-strategy model-based and data-driven decision analyses, a particular application is in risk prediction modeling, where the net benefit of a classifier should always be compared with 2 default strategies of treating none and treating all.
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