Statistical decision making with a dual detector probe.

Abstract

Conventional imaging techniques for cancer detection have difficulty finding small, deep tumors. Single-detector radiation probes have been developed to search for deep lesions in a patient who has been given a tumor-seeking radiopharmaceutical. These probes perform poorly, however, when the background activity in the patient varies greatly from site to site. We have developed a surgical dual-detector probe that solves the problem of background activity variation, by simultaneously monitoring counts from a region of interest and counts from adjacent normal tissue. A comparison of counts from the detectors can reveal the class of tissue, tumor or normal, in the region of interest. In this dissertation we apply methods from statistical decision theory and derive a suitable comparison of counts to help us decide whether a tumor is present in the region of interest. We use the Hotelling trace criterion with a few assumptions to find a linear discriminant function, which can be reduced to a normalized subtraction of the counts for large background count-rate variations. If area under the ROC curve is our figure of merit, the likelihood ratio is the optimum discriminant. We model likelihood functions of the data given the "tumor" and "no-tumor" hypotheses, and calculate the likelihood ratio. Using a spatial response map of the dual probe, a computer torso phantom, and estimates of activity distribution, we simulate a surgical staging procedure to test the dual probe and the discriminant functions. Results of the simulations show that the dual probe effectively solves the problem of background activity variations when used with any of the discriminant functions derived in this dissertation.