Purpose: We introduce the concepts of non-additive measures, Shapley values, and interaction indices, as means to provide a theoretical framework for informed medical decision-making, and to provide better decision support for patients, leading to better informed decision making.
Method: Additive methods for decision-making (e.g. probabilities, weighted sums) are not well suited to represent dependencies in multi-criteria decision-making, and often lead to paradoxes, such as loss of transitivity. A decision-making framework can be built around the concept of non-additive measure, which provides a general tool to evaluate multi-dimensional preferences, even when the data is imprecise. A measure is called non-additive if it respects the same boundary conditions as a probability, and if it is increasing with respect to set inclusion. It is used to construct an aggregate value for multidimensional preferences, and thus to order preferences. The concepts of Shapley value, stemming from game theory, and of interaction indices offer natural metrics to evaluate the importance of a criterion or attribute, as well as interaction between pairs, or more, of criteria. These values can be either provided by medical experts, or extracted from quantitative or qualitative data (e.g. patients’ surveys.) We build a robust and reliable tool that can be used to facilitate a patient’s decision, and to help us understand which criteria are key in the decision process, as well as which criteria can be ignored. Subsequently, we formalize how the set of criteria considered can be pruned, in order for the decision process to be more tractable for the patient.
Result: We show that non-additive approaches offer an optimal approach to multi-criteria decision-making that encompasses many other utility-based approaches, and explain why they are optimal. We also demonstrate how Shapley values and interaction indices are effective metrics to prune the set of criteria to consider, and thus simplify the patient’s decision process.
Conclusion: We have introduced the concepts of non-additive measures, Shapley values, and interaction indices that provide a solid theoretical foundation for informed medical decision-making. The next step is to develop an algorithm to extract non-additive measures from patients’ surveys, in order to provide a theoretically grounded decision support system.
See more of: The 34th Annual Meeting of the Society for Medical Decision Making