Modelling the cumulative risk of a false-positive screening test

The goal of a screening test is to reduce morbidity and mortality through the early detection of disease; but the benefits of screening must be weighed against potential harms, such as false-positive (FP) results, which may lead to increased healthcare costs, patient anxiety, and other adverse outcomes associated with diagnostic follow-up procedures. Accurate estimation of the cumulative risk of an FP test after multiple screening rounds is important for program evaluation and goal setting, as well as informing individuals undergoing screening what they should expect from testing over time. Estimation of the cumulative FP risk is complicated by the existence of censoring and possible dependence of the censoring time on the event history. Current statistical methods for estimating the cumulative FP risk from censored data follow two distinct approaches, either conditioning on the number of screening tests observed or marginalizing over this random variable. We review these current methods, identify their limitations and possibly unrealistic assumptions, and propose simple extensions to address some of these limitations. We discuss areas where additional extensions may be useful. We illustrate methods for estimating the cumulative FP recall risk of screening mammography and investigate the appropriateness of modelling assumptions using 13 years of data collected by the Breast Cancer Surveillance Consortium (BCSC). In the BCSC data we found evidence of violations of modelling assumptions of both classes of statistical methods. The estimated risk of an FP recall after 10 screening mammograms varied between 58% and 77% depending on the approach used, with an estimate of 63% based on what we feel are the most reasonable modelling assumptions.