Date of Award


Document Type

Campus Access Dissertation



First Advisor

Don Edwards

Second Advisor

Xiaoyan Lin


In the context of a subjective binary medical decision based on a diagnostic test we propose and study a nonlinear hierarchical model. The model includes a latent propensity-to-disease effect for each item (e.g. patient mammogram, MRI, radiograph, ultra sound, etc) and two effects for each rater, called bias and diagnostic skill. For a fixed rater, using a general decision-theoretic framework including costs for false negatives and false positives, we show that there is an optimal value for the rater bias parameter and that when this value is chosen optimally the total expected cost is a decreasing function of diagnostic skill. Assuming complete judging of m items by n judges, as well as the availability of a gold standard outcome for each patient, we discuss and compare model fitting by both constrained likelihood and Gibbs sampling. Estimation and inference on rater-specific sensitivity and specificity are also discussed. These methods are illustrated using a mammography example (Beam et al, Arch. Intern. Med.,2003) where 148 patient mammograms are each assessed by 110 qualified clinicians.