## 3 Results
### Analysis of Partial Dependency  
Figures 4-6 qualitatively analyze the association between injury severity and risk factors. To further quantify the influence of the PCIs on crash risk, Figure 7 shows the partial dependence of \(\Delta\)V, CMI, and EES derived from the LCE-CF model, reflecting the injury severity probability for the specific feature value. The increase in these three indicators results in more severe outcomes, and the distribution will stabilize after a certain value. We  
Figure 6: Ranking of SHAP values of the different crash types. labeled the 40 th and 70 th percentiles of each variable with a dashed line in Figure 7, which is close to the proportion of each severity category in the overall dataset (43.1% vs. 27.9% vs. 29.0% for SEV1-SEV3). The partial dependence of each injury level almost peaks within the expected interval, which indicates that the delineated critical intervals correspond to high probability area. In addition, these critical values also converge on the inflection points of distribution curves. \(\Delta\)V, as the key factor identified, directly affects the probability of injury severity: when \(\Delta\)V is greater than 17.6 km/h, the dependence curves of SEV2 and SEV3 sharply increase; when \(\Delta\)V equals 25.8 km/h, the probability of SEV2 reaches its maximum, close to 37.6%; and when \(\Delta\)V is greater than 53.1 km/h, the probability of minor injury tends to 0%-4.5%, and the probability of a severe injury is greater than 70%, indicating a rather serious IR. This actual probability distribution is similar to the fitted S-curve in a previous study [50] and further provides more details about the moderate level (SEV2). Larger EES and CMI also elevated the likelihood of serious injury, but their sensitivity is lower than \(\Delta\)V.  
Figure 7: Partial dependence plot of \(\Delta\)V, CMI, and EES. CI is the confidence interval of individual expectation distribution. To verify the effect of impact position on casualty risk, Figure 8 shows the partial dependence of \(\Delta\)V for the different impact positions. The trend of the IR for these four impacts can be ranked in a descending order as near, front, far, and back sides. When a vehicle is exposed to a backside impact, the potential IR is lower than otherwise because more than 80% of backside impacts result in only minor or moderate severity. By contrast, near-side impact tends to the highest casualty risk probability. When \(\Delta\)V is greater than 50 km/h, the probability of a near-side crash resulting in a serious accident is higher than 80%, while the corresponding probability of a back side impact is only 12.4%. In addition, the partial dependence distribution of the front side and near side impacts is similar to the overall probability in Figure 8.  
The partial dependence at each severity level has been integrated to further quantify the impact of the proposed PCIs. According to the threshold setting guidelines from the United States CDC expert panel [4], the critical thresholds T1 and T2 of \(\Delta\)V, CMI, and EES for three severity levels are summarized in Table 5. The criteria for threshold delineation are represented by the dashed lines labeled as T1 and T2 in Figure 8. These lines serve as a reference for the 60% acceptance rate of dependence distribution for the different severity probabilities. Values below T1 or above T2 imply that the probability of SEVI or SEV3 will surpass the other cases. Higher thresholds for T1 and T2 correspond to increased safety margins for the corresponding impact type. This means that in the case of a far-side impact (T2 with \(\Delta\)V = 70.04 km/h) or a back-side impact (T1 with \(\Delta\)V = 35.83 km/h), the risk of severe injury to occupants is significantly reduced. For these two types, the vehicle body provides additional buffer space, allowing the structure and safety systems to better absorb and distribute the impact energy. As a result, the force exerted on the occupants is mitigated, reducing the potential for severe injuries.