Evaluating Tests in Medical Diagnosis: Combining Machine Learning with Game-Theoretical Concepts

Abstract

In medical diagnosis, information about the health state of a patient can often be obtained through different tests, which may perhaps be combined into an overall decision rule. Practically, this leads to several important questions. For example, which test or which subset of tests should be selected, taking into account the effectiveness of individual tests, synergies and redundancies between them, as well as their cost. How to produce an optimal decision rule on the basis of the data given, which typically consists of test results for patients with or without confirmed health condition. To address questions of this kind, we develop an approach that combines (semi-supervised) machine learning methodology with concepts from (cooperative) game theory. Roughly speaking, while the former is responsible for optimally combining single tests into decision rules, the latter is used to judge the influence and importance of individual tests as well as the interaction between them. Our approach is motivated and illustrated by a concrete case study in veterinary medicine, namely the diagnosis of a disease in cats called feline infectious peritonitis.

Usefulness of acute phase proteins in differentiating between feline infectious peritonitis and other diseases in cats with body cavity effusions

“…32,33 To overcome the problem of not having post-mortem examination performed for all cats in this study, a sophisticated statistical method combining the results of multiple tests was used to classify cats as having or not having FIP with high confidence. 24 The assays used for the measurement of APPs were not specifically evaluated for the measurement of these analytes in the effusion. However, according to the manufacturer's instructions, the AGP assay used in this study can be used to determine AGP concentration in feline serum or other specimens.…”

“…18 The remaining cats, for which no immunohistochemistry was available, either because cats were discharged from the clinic or owners declined post-mortem examination, were classified as either FIP-positive or FIP-negative by means of a sophisticated statistical method. 24 This method combines semi-supervised machine-learning methodology with concepts from cooperative game theory using the results of several diagnostic tests in individuals where the true health condition is unknown. 24 The method takes into account diagnostic accuracy and clinical relevance of individual tests and their combinations to establish the final diagnosis.…”

Redundancy-aware unsupervised ranking based on game theory: Ranking pathways in collections of gene sets

“…The CGT framework led to developments in various contexts and applications in the computer science community. In particular, Shapley values have been extended to supervised, semisupervised and unsupervised feature selection [5][6][7], networks and security [8] and explainable machine learning [4]. A recent article by Rozemberczki et al [3] summarizes most of the applications in machine learning literature.…”

“…CGT led to applications in computer science in various contexts and applications; In particular, Shapley values have been extended to feature selection [2,7,18], networks and security [24], explainable machine learning [13] and bioinformatics [23]. A recent paper by Rozemberczki et al exact computation, on the other hand, requires 2 𝑁 evaluations of a value function where 𝑁 is the number of players; on the other hand, the introduction of microarray games [15] reduces the computational challenges of exact Shapley values' computation to polynomial time under the assumption that the game can be written using only binary relationships.…”

Unsupervised Features Ranking via Coalitional Game Theory for Categorical Data

“…In 2007 game theory found application in supervised feature selection [6,15] where the value function was defined as the accuracy or the generalization error of the trained model; to the best of our knowledge, the approaches proposed in the recent years are limited to labeled data. A recent paper [17] underlined how Shapley values spread through machine learning; in particular, they appear in several techniques to increase the overall interpretability of black-box models [13,21] and new insights on Shapley values and their applications continue appearing in the literature [4].…”