Determining sensitivity of mammography from screening data, cancer incidence, and receiver-operating characteristic curve parameters

Objectives. A mathematical model is presented that allows the computation of the sensitivity and specificity of breast screening based on receiver-operating characteristic (ROC) curve shape, the positive predictive value (PPV) of screening mammography, and the cancer incidence, f. Methods. The normal and cancer populations are modeled as normal distributions with independent means and standard deviations. The distributions are scaled such that the area of the normal population is equal to 1 - f and that of the cancer population is f. The PPV for screening mammography is used to deters mine the operating point on the HOC curve. Knowing this leads directly to the computation of sensitivity and specificity. The derivation is general and is applicable to both symmetrical and asymmetrical ROC curves. Results. For symmetric ROC curves and typical values for the PPV of mammography (about 8%) and cancer incidence (f = 0,003), an A(z) value of 0.95 was required to achieve 63% sensitivity and an A(z) value of 0.98 led to 86% sensitivity. Conclusion. A model was developed that should allow researchers to deduce sensitivity and specificity for screening mammography based on ROC curve measurements and using realistic values of PPV and f. This model allows A(z) values to be related to the probability of breast cancer detection.