Information Asymmetry of Positive and Negative Observations in Medical Diagnostics
摘要
The information asymmetry between positive and negative observations of a binary symptom in medical diagnostics problems is considered. A symptom of a disease is modeled as a spatio-temporal binary field. For independent observations, an analytical expression is derived for the critical number of negative observations equivalent to one positive observation in informativeness. Similar formulas are obtained for homogeneous and inhomogeneous first-order Markov chains. Examples are given showing that the time dependence and direction of state of the disease dynamics, in particular whether the disease persists or the patient recovers, significantly affect the critical number of negative observations. The obtained results provide the mathematical basis for recommendations on the required scope of medical examinations in clinical practice and can be applied to other problems.