Joint analysis of intervals and injury severities involving the same driver: A novel multivariate joint survival model approach

Survival analysis has emerged as a powerful tool for predicting traffic accident recurrence, yet traditional univariate approaches fail to account for the interdependence between recurrent events (e.g., minor and no-injury accidents) and terminal events (e.g., severe injury or fatal accidents) experienced by the same driver. This study proposes a novel multivariate joint survival model to simultaneously analyze the temporal correlations between accidents of varying injury severities involving the same driver. Utilizing a dataset of 800 drivers from a southwestern Chinese city (2016–2020), we classify accidents into three severity categories: severe injury (SI), minor injury (MI), and no injury (NI). The recurrent events (MI and NI) and terminal event (SI) are jointly modeled using a frailty-based framework to quantify their interdependencies. Key findings include: (1) Most drivers have an initial period of increasing crash risk, ranging from 0 to 270 days, where the likelihood of a crash increases the longer drivers go without having a crash. (2) The developed multivariate joint survival model overcomes the limitations of traditional univariate survival models, where significant variables may be overlooked and parameter estimates tend to be underestimated. (3) Positive correlations exist between recurrent and terminal events involving the same driver, with stronger associations for MI-SI (0.904, p = 0.0000) than NI-SI (0.589, p = 0.0000). (4) Driver and vehicle related characteristics are identified as risk factors for both types of recurrent events, as well as the terminal event. For example, novice drivers (with less than 3 years of driving experience) exhibit 230.7 % and 293.3 % higher risks of NI and SI accidents, respectively. Elderly drivers (aged 60 and above) face elevated risks across all severities, with rates ranging from 11.6 % to 23.6 %. While road and environmental characteristics only significantly affect both types of recurrent events. For example, complex road geometries (e.g., curved slopes) reduce MI risks by 33.2 %, while low visibility (50–100 m) increases NI risks by 45.2 %. These findings provide valuable insights for traffic safety modeling and analysis by examining the correlations among different accidents involving the same driver, and offer critical support for decision-making in risk warning and the proactive prevention of accidents with varying injury severities.