How Accurate Should a Medical Test be to Meet Cost-Effectiveness

Precision medical test is the cornerstone of personalized medicine and targeted therapies, play a crucial role in tailoring treatment plans to individual patients and optimizing medical resource utilization. This paper establishes a quantitative model to systematically analyze the relationship between the accuracy of a precision medical test and its cost-effectiveness. It is proven that the accuracy of a precision medical test must exceed two lower bounds to be considered cost-effective. The first lower bound requires that the test accuracy exceed the lower limit of matching requirements to match each patient's most appropriate individualized intervention plan, thereby achieving the local optimal decision-making. The second lower bound requires that the test accuracy must exceed the overall lower limit of medical testing for maximizing the net monetary benefit of the entire group of patients, that is, to achieve the global optimum. The special case of sensitivity and specificity on binary test results gives a more intuitive proof of the theorems. In addition, the theorems also provide an economic explanation for the underdiagnosis of rare diseases and the challenge of implementing precision medicine in small groups of patients. Numerical simulations support these findings.