This paper presents a general framework for assessing imaging systems and image-analysis methods on the basis of therapeutic rather than diagnostic efficacy. By analogy to receiver operating characteristic (ROC) curves, it introduces the Therapy Operating Characteristic or TOC curve, which is a plot of the probability of tumor control vs. the probability of normal-tissue complications as the overall level of a radiotherapy treatment beam is varied. The proposed figure of merit is the area under the TOC, denoted AUTOC. If the treatment planning algorithm is held constant, AUTOC is a metric for the imaging and image-analysis components, and in particular for segmentation algorithms that are used to delineate tumors and normal tissues. On the other hand, for a given set of segmented images, AUTOC can also be used as a metric for the treatment plan itself. A general mathematical theory of TOC and AUTOC is presented and then specialized to segmentation problems. Practical approaches to implementation of the theory in both simulation and clinical studies are presented. The method is illustrated with a a brief study of segmentation methods for prostate cancer.