Maximum attainable discrimination and the utilization of radiologic examinations

Discriminant Analysis and other related statistical techniques are frequently used to sort patients into those most likely and those least likely to benefit from a certain intervention. Considerable data analysis and computation are often required to arrive at the best-fitting mathematical model which translates discriminating variables or indicants into probability predictions regarding the presence or absence of disease or the likelihood of a favourable outcome. Attempts to judge how well discriminant analysis performs or to determine why it does not perform better are hampered by not knowing what is the greatest degree of discrimination theoretically possible in a data set. In this paper we describe a method of calculating the maximum discrimination attainable in a data set and show how it can be used (1) to decide whether further model building is worthwhile, and (2) if so, to judge the discriminatory performance of any such models. We apply this tool to two previously published studies of radiologic utilization; the results provide reassurance that, at least on the basis of the presenting indicants, the patients were being adequately selected for the studies in question.