## 3 Results
### Multivariate COX Proportional Hazard Regression Model Analysis  
The multivariate COX analysis model was employed to quantify the impact of various factors on lane departure risk. Table 4 presents the COX regression result using the no warning condition as the baseline. A \(p\)-value of less than 0.05 indicates a strong overall fit of the model to the data, suggesting that the model's predictions are statistically significant. In survival analysis, when regression coefficient \(\beta\) is positive for a certain covariate, it indicates that the covariate increases the hazard level, and the survival time decreases accordingly [33]. \(\text{Exp}(\beta)\) represents hazard ratio and is used to quantify the relative likelihood of an event occurring at a certain point in one group compare to another [34]. If \(\text{Exp}(\beta)\) is greater than 1, it indicates increased risk associated with the condition, whereas \(\text{Exp}(\beta)\) of less than 1 suggests a protective effect. For cautious drivers, both the early and late warnings increased the risk (\(\beta\)-values are all positive), and the driver's willingness to end the departure was more urgent than with no warning. Under the no-, low-, and medium-level ST conditions, late warning increased the risk significantly compared to the early warning (the \(\beta\)-values for late warning are all larger than those for early warning), probably due to the fact that cautious drivers actively adjusted the state of the vehicle despite being in the distracted state. Thus, the late warning gave full play to the drivers' initiative. Under the high-level ST condition, early warning was more significant in prompting cautious drivers to end the departure compared to the late warning (\(\beta=1.010\) for early warning, \(\beta=0.683\) for late warning). The higher the level of distraction was, the earlier the warning timing should be given to prompt the driver to adjust their driving state. For moderate drivers, similar to cautious drivers, both the early and late warning increased the risk (\(\beta\)-values are all positive), and thereby the urgency to end the departure increased for the driver. Under the no- and low-level ST conditions, the late warning increased the risk more significantly than early warning (the \(\beta\)-values for late warning are all larger than those for early warning), suggesting that the late warning was more effective in shortening lane departure time for moderate drivers at no or low distraction level. Under the medium- and high-level STs, the early warning was more significant role than the late warning (the \(\beta\)-values for early warning are all larger than those for late  
Figure 7: Survivor function of LDD at different levels STs: (**a**) no warning; (**b**) early warning; (**c**) late warning. warning), due to the fact that as the level of the STs increased, alerting moderate drivers of the vehicle departure situation as early as possible could cause the drivers to shift their attention quickly to adjust their driving state or end the departure. When aggressive drivers were in the undistracted state, early warning significantly decreased the risk (\(\beta=-0.910\)), possibly because the warning timing was too early for aggressive drivers and it was more likely to be regarded as a nuisance alert, making the drivers resist and still continue to maintain the lane departure state. Under the low- and medium-level ST conditions, the regression coefficients \(\beta\) of early and late warning are both positive for aggressive drivers, showing that both the two warnings can increased the risk and urge the aggressive drivers to end the departure. According to the hazard ratio \(\text{Exp}(\beta)\), late warning increased the risk more significantly compared to the early warning (the \(\text{Exp}(\beta)\)-values for late warning are all larger than those for early warning).