Potential Impact of Compound Bayesian Inference in Medicine: Application to Colonoscopy Prioritization

Background/Objectives: Colorectal cancer (CRC) is a leading cause of cancer-related mortality worldwide, and its prognosis strongly depends on early detection and timely treatment. In Chile, colonoscopy waiting lists for symptomatic patients in public hospitals can exceed one year, limiting access to early diagnosis and reducing survival rates. Traditional single-test screening strategies, such as a single fecal immunochemical test (FIT), often yield uncertain results, contributing to inefficiencies in resource allocation. This study explores the potential of Compound Bayesian Inference (CBI) to improve CRC detection and prioritize patients who most urgently require colonoscopy. Methods: We propose a CBI-based approach that integrates evidence from multiple sequential and independent FITs to update the posterior probability of CRC dynamically. A case study was analyzed with this Compound Bayesian Inference over a four-round FIT protocol to assess how this could improve risk stratification compared to standard symptoms-based screening. Results: Our method mathematically shows that over 85% of colonoscopies (resp. 99.9%) were not urgent in symptomatic (resp. asymptomatic) patients, therefore ensuring high-risk patients receive timely diagnostic procedures while allowing for prioritisation and potentially drastically reducing costs, because FIT tests are around 100 times cheaper than colonoscopies. Conclusions: In settings with limited colonoscopy availability, such as Chile, where delays in public hospitals can exceed one year for symptomatic patients, implementing a CBI-based strategy could optimize resource use, potentially drastically reduce costs, improve access for critical cases, and ultimately enhance 5-year survival rates. These findings highlight CBI as a promising, explainable, and adaptable approach for evidence-based precision medicine in CRC screening and priorization.