On probabilities of missed target and false alarm іn medical decision-making systems

Abstract

Binary classifiers are widely used in solving a number of applied problems, in particular, problems of medical diagnostics. The effectiveness of such systems is characterized by target miss errors and false alarms. Since the probability of a false alarm error usually increases with a decrease in the probability of an allowance error, and vice versa, the tuning of systems implies a certain compromise between the indicated errors. To build a diagnostic algorithm under a priori uncertainty, the Neyman–Pearson strategy is often used, which involves minimizing the probability of a target miss error with a given constraint on the probability of a false alarm error. To study the question of the formal choice of an acceptable constraint, conditions for the usefulness of a diagnostic algorithm are formulated. On the basis of these conditions, the admissible limits of the probabilities of target miss errors and false alarms are determined. The boundary values of the prevalence of diseases are determined, at which a diagnostic algorithm with known operational characteristics remains useful in terms of reducing average losses. Examples are given to illustrate the practical value of the obtained conditions. The features of the decision-making algorithm based on medical symptoms are considered. It has been shown that if, according to medical statistics, a certain symptom is typical for most sick patients and uncharacteristic for most healthy people, but this does not mean high reliability of diagnostic decisions based on the analysis of this symptom in a particular person. Using the example of the analysis of the symptom «Characteristic skin rashes», it was demonstrated that even if the probability of the absence of a symptom in healthy people is 0,99, the probability of a false alarm may be lower than 0,01. This is explained by the fact that in order to make an substantiated decision for a particular patient, it is necessary to make sure that the indicated symptom is absent during a certain observation interval.