Three-class ROC analysis - A sequential decision model developed for the diagnostic task rest-stress myocardial perfusion SPECT imaging

Previously we have developed a decision model for three-class ROC analysis where classification is made three simultaneously, i.e., with a single decision. In this paper, an alternative sequential decision model was developed for the specific three-class diagnostic procedure of rest-stress myocardial perfusion SPECT (MPS) imaging. This sequential decision model was developed based on the fact that sometimes this diagnostic task is performed using a two-step process. First, the stress (^99mTc) image is read to determine whether a patient is normal or abnormal based on the presence of a defect in the stress image. If a defect is found, the rest (²⁰¹Tl) image is then read to determine whether this is a reversible defect or a fixed defect based on the presence of defect on the rest image. In fact, in some MPS protocols where sequential stress/rest imaging is performed, the rest imaging is not performed if there is no defect in the stress image. Therefore, the three-class task is decomposed to a sequence of two two-class tasks. For this task we determined, by maximizing the expected utility of both steps of the decision process, that log likelihood ratios were the optimal decision variables and provide the optimal ROC surface under the assumption that incorrect decisions have equal utilities under the same hypothesis. The properties of the sequential decision model were then studied. We found that the sequential decision model shares most of the features of a 2-class ROC curve. While this model was developed in the context of rest-stress MPS, it may have applications to other two-step diagnostic tasks.