Maximum likelihood analysis of free-response receiver operating characteristic (FROC) data

Receiver operating characteristic (ROC) methodology is widely used in evaluating medical imaging modalities. While appropriate in some cases, it has several drawbacks when the detection task, e.g., nodule detection, involves localizing the abnormality. Free-response receiver operating characteristic (FROC) methodology offers a more natural framework to describe observer performance in such studies and has other advantages. Due to the lack of a statistical analysis procedure comparable to the maximum likelihood procedure (ROCFIT program) available for ROC studies, the FROC method has not gained widespread acceptance. This work presents and solves a two parameter model for the statistical analysis of FROC data. The model assumes that the probability density of the signal stimuli is normally distributed, as is the probability density for producing one or more false positives per image. A program (FROCFIT) is described for estimating the parameters and their uncertainties from experimental data. An index of performance is proposed to quantify observer performance in FROC experiments. Application of this methodology to several FROC data sets produced good to excellent fits.