ABSTRACT
The diagnosis of diabetes, based on measured fasting plasma glucose level, depends on choosing a threshold level for which the probability of failing to detect disease (missed diagnosis), as well as the probability of falsely diagnosing disease (false alarm), are both small. The Bayesian risk provides a tool for aggregating and evaluating the risks of missed diagnosis and false alarm. However, the underlying probability distributions are uncertain, which makes the choice of the decision threshold difficult. We discuss an hypothesis for choosing the threshold that can robustly achieve acceptable risk. Our analysis is based on info-gap decision theory, which is a non-probabilistic methodology for modelling and managing uncertainty. Our hypothesis is that the non-probabilistic method of info-gap robust decision making is able to select decision thresholds according to their probability of success. This hypothesis is motivated by the relationship between info-gap robustness and the probability of success, which has been observed in other disciplines (biology and economics). If true, it provides a valuable clinical tool, enabling the clinician to make reliable diagnostic decisions in the absence of extensive probabilistic information. Specifically, the hypothesis asserts that the physician is able to choose a diagnostic threshold that maximizes the probability of acceptably small Bayesian risk, without requiring accurate knowledge of the underlying probability distributions. The actual value of the Bayesian risk remains uncertain.
