Stochastic thresholds

Abstract

Thresholds have traditionally been represented by a single number; the optimal management of the patient depends on whether his probability of disease is above or below this number. The concept of a threshold as a single number, however, inadequately represents the treatment approach of a group of physicians who do not have all the same threshold or a single physician who is uncertain about the exact value of the threshold. An alternative to a single valued threshold is to consider the threshold as having a probability distribution: for every probability that the patient has the disease there is a probability that the threshold is exceeded. This "stochastic" threshold model contains information about the uncertainty of the threshold estimation. Stochastic thresholds can be useful for testing the sensitivity of a management decision to the patient's probability of disease. They can also be used for comparing the standards of practice of individual physicians or comparing the practice of an individual physician with that of a group.