Smooth associations between the emergency medical services response time and the risk of death in road traffic crashes

Background: Understanding the impact of emergency medical services (EMS) response times on the likelihood of death has received repeated attention in the literature. However, the current literature lacks definite and detailed results. This study seeks to contribute by revealing a smoothed conditional association between EMS response times and the odds of fatality, also allowing this association to be heterogeneous with respect to the statuses of other influential variables. Methods: The 2015 Fatality Analysis Reporting System (FARS) national dataset of the United States was adopted as it was large enough to support the sample-size requirement for exhibiting heterogeneous smooth link functions of EMS response times, with higher confidence levels. An additive logistic regression model with smooth interaction terms was introduced. Two ordinary logistic models with different settings for the EMS response time were developed for comparison with the additive logistic model. Results: The overall impact of the EMS response time, as well as age, gender, seating position and manner of collision, on the odds of death, was statistically significant. For the first time, the marginal smooth influential pattern of the EMS response time was found to be non-monotonic, such that, for cases with long EMS response times, it could be negatively associated with the odds of death. Similar phenomena were also found when the EMS response time interacted with several other factors. Conclusion: Two critical values (5.5 minutes and 17 minutes respectively) of the EMS response time were found. The former represents the fastest decline in the chance of survival and the latter is just the “gold time” for operating rescues. Overestimation of the urgency level of certain types of crashes at the very early stages of rescues could be the main reason for observing a negative influential pattern of the EMS response time on the odds of death.