Non-Homogeneous Markov Chain for Estimating the Cumulative Risk of Multiple False Positive Screening Tests

Screening tests are widely recommended for the early detection of disease among asymptomatic individuals. While detecting disease at an earlier stage has the potential to improve outcomes, screening also has negative consequences, including false positive results which may lead to anxiety, unnecessary diagnostic procedures and increased healthcare costs. In addition, multiple false positive results could discourage participating at subsequent screening rounds. Screening guidelines typically recommend repeated screening over a period of many years, but little prior research has investigated how often individuals receive multiple false positive test results. Estimating the cumulative risk of multiple false positive results over the course of multiple rounds of screening is challenging due to the presence of censoring and competing risks, which may depend on false positive risk, screening round and number of prior false positive results. To address the general challenge of estimating the cumulative risk of multiple false positive test results, we propose a non-homogeneous multi-state model to describe the screening process including competing events. We developed alternative approaches for estimating the cumulative risk of multiple false positive results using this multi-state model based on existing estimators for cumulative risk of a single false positive. We compared the performance of the newly proposed models through simulation studies and illustrate model performance using data on screening mammography from the Breast Cancer Surveillance Consortium. Across most simulation scenarios, the multi-state extension of a censoring bias model demonstrated lower bias compared to other approaches. In the context of screening mammography, we found that the cumulative risk of multiple false positive results is high. For instance, based on the censoring bias model, for a high risk individual, the cumulative probability of at least two false positive mammography results after 10 rounds of annual screening is 40.4