Abstract
The fundamental information theory functions of entropy, relative entropy, and mutual information are directly applicable to clinical diagnostic testing. This is a consequence of the fact that an individual’s disease state and diagnostic test result are random variables. In this paper, we review the application of information theory to the quantification of diagnostic uncertainty, diagnostic information, and diagnostic test performance. An advantage of information theory functions over more established test performance measures is that they can be used when multiple disease states are under consideration as well as when the diagnostic test can yield multiple or continuous results. Since more than one diagnostic test is often required to help determine a patient’s disease state, we also discuss the application of the theory to situations in which more than one diagnostic test is used. The total diagnostic information provided by two or more tests can be partitioned into meaningful components.
Highlights
Information theory was developed during the first half of the twentieth century to quantify aspects of communication
Subsequent papers helped to clarify the ability of information theory to quantify diagnostic uncertainty, diagnostic information, and diagnostic test performance, e.g., [4,5,6,7,8,9]
In Appendix A, we show that the modified relative entropy satisfies the triangle inequality but still fails to meet the criteria for a distance metric
Summary
Information theory was developed during the first half of the twentieth century to quantify aspects of communication. The pioneering work of Ralph Hartley and, subsequently, Claude Shannon was primarily motivated by problems associated with electronic communication systems [1,2]. Subsequent papers helped to clarify the ability of information theory to quantify diagnostic uncertainty, diagnostic information, and diagnostic test performance, e.g., [4,5,6,7,8,9]. Applications of information theory can be highly technical, fundamental concepts of information theory are not difficult to understand. They are profound in the sense that they apply to situations in which “communication” is broadly defined
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