Screening mammography is a widely used method for breast cancer detection. For each mammogram we propose a performance model based on order of outcomes. That is, we envision an initial assessment, a follow up assessment if the initial one is positive and, eventually, a determination of whether cancer was present or not. A model can be built at each stage reflecting effects due to patient characteristics, to the facility where mammogram was performed and to the radiologist reading the mammogram. Since assessment is not perfectly associated with outcome, familiar rates of agreement and disagreement are of interest. These rates can be investigated at various levels of risk factors of interest. The approach is illustrated with screening mammography data from the Group Health Cooperative in Seattle, WA. A Bayesian framework is adopted for inference and an analysis of the data set is presented.