Utility as a rationale for choosing observer performance assessment paradigms for detection tasks in medical imaging

Studies of lesion detectability are often carried out to evaluate medical imaging technology. For such studies, several approaches have been proposed to measure observer performance, such as the receiver operating characteristic (ROC), the localization ROC (LROC), the free-response ROC (FROC), the alternative free-response ROC (AFROC), and the exponentially transformed FROC (EFROC) paradigms. Therefore, an experimenter seeking to carry out such a study is confronted with an array of choices. Traditionally, arguments for different approaches have been made on the basis of practical considerations (statistical power, etc.) or the gross level of analysis (case-level or lesion-level). This article contends that a careful consideration of utility should form the rationale for matching the assessment paradigm to the clinical task of interest.

In utility theory, task performance is commonly evaluated with total expected utility, which integrates the various event utilities against the probability of each event. To formalize the relationship between expected utility and the summary curve associated with each assessment paradigm, the concept of a "natural" utility structure is proposed. A natural utility structure is defined for a summary curve when the variables associated with the summary curve axes are sufficient for computing total expected utility, assuming that the disease prevalence is known.

Natural utility structures for ROC, LROC, FROC, AFROC, and EFROC curves are introduced, clarifying how the utilities of correct and incorrect decisions are aggregated by summary curves. Further, conditions are given under which general utility structures for localization-based methodologies reduce to case-based assessment.

Overall, the findings reveal how summary curves correspond to natural utility structures of diagnostic tasks, suggesting utility as a motivating principle for choosing an assessment paradigm.