A Decision-Tree-Based Bayesian Approach for Chance-Constrained Health Prevention Budget Rationing

Abstract

Medical test selection is a recurring problem in health prevention and consists of proposing a set of tests to each subject for diagnosis and treatment of pathologies. The problem is characterized by the unknown risk probability distribution across the population and two contradictory objectives: minimizing the number of tests and giving the medical test to all at-risk populations. This article sets this problem in a general framework of chance-constrained medical test rationing with unknown subject distribution over an attribute space and unknown risk probability but with a given sample population. A new approach combining decision-tree and Bayesian inference is proposed to allocate relevant medical tests according to the subjects’ profile. Case studies on screening of hypertension and diabetes are conducted, and the performance of the proposed approach is evaluated. Significant savings on unnecessary tests are achieved with limited numbers of subjects needing but not receiving necessary tests. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Whether a medical test is needed for all subjects in health prevention? Is it possible to reduce unnecessary tests without jeopardizing the goal of screening at-risk populations? This article attempts to answer these questions by proposing a data-driven approach combining decision trees for subject profiling, Bayesian inference for unknown probability distribution estimation, and combinatorial optimization for test allocation. The application of this approach to a real-case study reduces the number of electrocardiogram (ECG) tests by 90% while keeping the number of hypertensive subjects needing but not receiving ECG tests small (five out of 230). A significant cut of unnecessary tests is also achieved in a second case study of diabetes screening. This approach allows decision-makers to better balance the cost-saving and the level of public health objective. Furthermore, the combination with decision trees makes the practical implementation quite straightforward.