Rescue at risk: a new metric to evaluate emergency medical service covering solutions

Abstract Expected coverage is a key performance indicator to assess Emergency Medical Service (EMS) systems. Frequently, a response time threshold (RTT) is stipulated, within which a specified percentage of emergency calls needs to be met. Although defined exogenously, the RTT has a decisive influence on model outcomes. When statutory coverage goals cannot be achieved, however, coverage metrics alone obscure essential aspects of system performance, such as how far response times exceed the RTT or how quickly different solutions deliver coverage. This underscores the need for evaluation metrics that assess not only whether coverage goals are met but also the time required to achieve them. To address this, we propose a novel evaluation metric, Rescue at Risk (RaR), which quantifies the time required to achieve a specific coverage goal. Analogously to the Value at Risk in financial management, RaR serves as a general measure of the risk of failing to arrive at emergencies on time. Complementing this, we introduce the Relative Critical Coverage Time Deviation (RCD), which measures the vulnerability of emergencies when the predefined RTT cannot be met. Response time distributions form the basis of both measures, generated by a simulation-based framework. Applying the proposed evaluation framework to a real-world case study, we employ a well-known probabilistic EMS covering location model with differing RTTs and capacities as input. The results demonstrate that RaR and RCD provide EMS decision-makers with an interpretable tool for quantifying the consequences of different real-world or optimized site and ambulance configurations, taking stochastic environmental influences into account.