Potential Impact of Updated Bayesian Deduction in Medicine: Application to Colonoscopy Prioritization

<b>Background/Objectives:</b> This study presents and explores the potential of Updated Bayesian Deduction (UBD) using colorectal cancer (CRC) detection and prioritisation as a case example. 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 <i>symptomatic</i> 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 faecal immunochemical test (FIT), often yield uncertain results, contributing to inefficiencies in resource allocation. <b>Methods:</b> We propose a deductive approach that integrates evidence from multiple sequential and independent FITs to dynamically update the posterior probability of CRC. A case study is analysed with this Updated Bayesian Deduction over a four-round FIT protocol to assess how this could improve risk stratification compared to standard symptoms-based screening. <b>Results:</b> Our mathematical model shows that over 85% of colonoscopies for symptomatic patients were not urgent. We then demonstrate that, if 4-FIT UBD were used to screen Chile's Metropolitan Region population, only 96 out of 100,000 people would require an urgent colonoscopy to detect the 19.6 out of 100,000 individuals with CRC in this region. Many countries cannot afford a colonoscopy-based population screening, such as what is performed in Germany. Performing 4x FITs + a very small number of colonoscopies would be much more affordable and would get more countries to adopt general CRC screening. <b>Conclusions:</b> In countries with limited colonoscopy availability, such as Chile, where symptomatic patients can wait over a year for treatment in public hospitals, implementing a UBD-based strategy could drastically reduce costs and optimise the use of resources. This would improve access to colonoscopies for critical cases and ultimately enhance five-year survival rates. These findings highlight UBD as a promising approach for evidence-based precision medicine in CRC screening and prioritisation that is both explainable and adaptable.