Rg. Swensson et al., A constrained formulation for the receiver operating characteristic (ROC) curve based on probability summation, MED PHYS, 28(8), 2001, pp. 1597-1609
Citations number
36
Categorie Soggetti
Radiology ,Nuclear Medicine & Imaging","Medical Research Diagnosis & Treatment
We propose a principled formulation of the ROC curve that is constrained in
a realistic way by the mechanism of probability summation. The constrained
and conventional ROC formulations were fitted to 150 separate sets of rati
ng data taken from previous observer studies of 250 or 529 chest radio grap
hs. A total of 20 different readers had used either discrete or continuous
rating scales to evaluate those chest cases for likelihood of separate spec
ified abnormalities: interstitial disease, pulmonary nodule, pneumothorax,
alveolar infiltrate, or rib fracture. Both ROC formulations were fitted sep
arately to every set of rating data using maximum-likelihood statistical pr
ocedures that specified each ROC curve by normally distributed latent varia
bles with two scaling parameters, and estimated the area below the ROC curv
e (A(Z)) with its standard error. The conventional and constrained binormal
formulations usually fitted ROC curves that were nearly indistinguishable
in form and in A(Z). But when fitted to asymmetric rating data that contain
ed few false-positive cases, the conventional ROC curves often rose steeply
, then flattened and extrapolated into an unrealistic upward "hook" at the
higher false-positive rates. For those sets of rating data, the constrained
ROC curves (without hooks) estimated larger values for A(Z) with smaller s
tandard errors. The constrained ROC formulation describes observers' rating
s of cases at least as well as the conventional ROC, and always guarantees
a realistic fitted curve for observer performance. Its estimated parameters
are easy to interpret, and may also be used to predict observer accuracy i
n localizing the image abnormalities. (C) 2001 American Association of Phys
icists in Medicine.