Reassessing Accuracy Rates from Median Decision Procedures
Andrea Capotorti and Frank Lad
View Report [PDF - 220 KB]
Abstract
We re–examine the procedure of median decision making in the context of radiological determination of asbestosis by three B–readers. Our assessment addresses the specificity, sensitivity and predictive values from this procedure compared to merely an individual radiologist’s diagnosis. Conditional exchangeability of the radiologists’ classifications is recognised as more appropriate than independence which is often presumed. The framework of de Finetti’s fundamental theorem of probability makes the analysis tractable when it is formulated in terms of a linear programming problem, yielding coherent bounds on probabilities of interest even when a complete distribution is not specified. Further natural assertions motivate a partial ordering of conditional probabilities. In this context the computation of bounds develops into a quadratic programming problem. Using sensible assertions, the median decision procedure is found to be relatively weaker than has been thought based on the presumption of independence of radiologists’ assessments. However that presumption is also shown to overstate the predictive qualities of individual diagnoses. We re–evaluate substantive claims about the use of median X–ray decisions as an indicator of cancer, based on the appropriate computations.
Back to Research Reports
