Test sensitivity in a prospective cancer screening program: A critique of a common proxy measure

Abstract

The true sensitivity of a cancer screening test, defined as the frequency with which the test returns a positive result if the cancer is present, is a key indicator of diagnostic performance. Given the challenges of directly assessing test sensitivity in a prospective screening program, proxy measures for true sensitivity are frequently reported. We call one such proxy empirical sensitivity, as it is given by the observed ratio of screen-detected cancers to the sum of screen-detected and interval cancers. In the setting of the canonical three-state Markov model for progression from preclinical onset to clinical diagnosis, we formulate a mathematical relationship for how empirical sensitivity varies with the screening interval and the mean preclinical sojourn time and identify conditions under which empirical sensitivity exceeds or falls short of true sensitivity. In particular, when the inter-screening interval is short relative to the mean sojourn time, empirical sensitivity tends to exceed true sensitivity, unless true sensitivity is high. The Breast Cancer Surveillance Consortium (BCSC) has reported an estimate of 0.87 for the empirical sensitivity of digital mammography. We show that this corresponds to a true sensitivity of 0.82 under a mean sojourn time of 3.6 years estimated based on breast cancer screening trials. However, the BCSC estimate of empirical sensitivity corresponds to even lower true sensitivity under more contemporary, longer estimates of mean sojourn time. Consistently applied nomenclature that distinguishes empirical sensitivity from true sensitivity is needed to ensure that published estimates of sensitivity from prospective screening studies are properly interpreted.

Random effects models of tumour growth for investigating interval breast cancer

“…Among radiologists, the proportion of interval cancers (of the sum of screen detected and interval cancers) is used as a proxy of the false negative rate and a performance measure of screening 2,3 . For a critique of this proxy and a description of its relationship with “true” test sensitivity, on the basis of multi‐state models see Lange et al 4 The interval cancer proportion is also used to compare different screening modalities or supplemental screening, 5‐8 to compare different screening intervals, 9 to study the incidence of cases in the interval time between consecutive screens, 6,10,11 and to study the importance of mammographic (breast) density 12‐14 and image settings for screening performance 15,16 …”