Extending Peaks-Over-Threshold Methods to Public Health: Modified Threshold Selection and Scenario-Based Risk Estimation

Rare but extreme events in public health, such as sudden dengue outbreaks or surges in urgent cancer referrals, pose disproportionate threats to healthcare systems by overwhelming diagnostic capacity, straining resources, and elevating mortality risks. Traditional statistical approaches, which emphasize average behavior, often fail to capture these high-impact tail risks. This study advances the application of Extreme Value Theory (EVT) in public health by extending the peaks-over-threshold (POT) framework to short, structured medical time series. We introduce a modified AD-L threshold selection procedure, tailored for small-sample health datasets, which enhances robustness and objectivity compared to conventional graphical diagnostics. Using monthly dengue prevalence data from Bangladesh (2008–2023) and urgent cancer referrals from Wales (2005–2020), we demonstrate a systematic workflow that integrates stationarity testing, STL decomposition, transformation through differencing, and scenario-based tail modeling. Our results show that the modified AD-L method yields stable thresholds and consistent generalized Pareto distribution fits across both datasets, including when analyses are restricted to positive increments—capturing the public health priority of sudden increases rather than declines. Return level estimates quantify the scale of extreme month-to-month surges, offering forward-looking insights into outbreak severity and system demand. Methodologically, this study bridges a gap by adapting POT methods for medical data, while practically, it equips decision-makers with interpretable metrics of extreme health shocks. Limitations include reliance on differencing for non-stationarity and the scope of monthly data, but the framework remains generalizable to other health outcomes. By emphasizing both statistical rigor and actionable interpretation, this research positions EVT as a vital tool for anticipating and managing rare but consequential public health extremes.