## 2 Materials and Methods
### Data Preparation  
#### 2.2.1 Data Source  
This study integrates the crash data of the Crash Reporting Sampling System (CRSS, 2019 and 2020) and the Fatal Accident Analysis Reporting System (FARS, 2016-2020) as part of the NHTSA program of the U.S. Department of Transportation to better validate and analyze the risk factors in a data-driven method [41]. A total of 275,380 separate crash records are covered. The CRSS and FARS databases provide adequate information related to crashes, which is essential for in-depth investigations. Given that the detailed information in both databases is extracted from police records, the authenticity of the dataset is guaranteed.  
Specifically, CRSS collects approximately 55,000 representative crash records from a total sample of 6 million crashes each year, ranging from property loss to fatal injuries. Meanwhile, FARS is a census of all fatal crashes in the US. A crash will be coded in FARS if at least one person involved dies within 30 consecutive days of the crash. Considering the difference for the property of severity cases, the fusion of these two databases could result in a balanced dataset. In both databases, crash information related to the driver and passenger, crash characteristics, vehicle, environmental factors, and injury severity is coded in three aspects, namely levels of accident, vehicle, and person, with approximately 120 explanatory variables. The key features, such as relative motion relationships and collision deformation classification (CDC), prior to the crash can be obtained.  
Considering that the PCIs rely on detailed motion information, the evaluation was performed based on the vehicle level in this study. The following criteria were used to filter the crash data from the FARS and CRSS databases:  
1. Vehicles that cannot provide external structural protection, such as motorcycles and non-motorized vehicles, were excluded. In addition, only vehicles within 15 years of registration were extracted. This is because the structures of the vehicle body frames determine the passive protection.
2. Cases with vacant data were excluded because vehicle motion, passenger information, road, and environmental conditions may significantly affect the outcome of crashes.
3. Crashes involving rollovers, roadside run-off, and secondary accidents were excluded. These patterns are associated with completely different deformation patterns, making it difficult to measure the degree of severity with general parameters.
4. Only the events in which the use of belt and airbags by occupants is reported were considered. The influence of these factors should be ruled out because seat belts and airbags have been shown to significantly enhance the passive safety performance.
5. Three impact configurations were extracted, namely head-on, rear-end, and side-impact crashes.  
In addition, this study encoded the levels of injury severity as a categorical variable using three levels, namely minor level (SEV1, property damage only), moderate level (SEV2, non-disabling injuries), and major level (SEV3, disabling and fatal injuries), to measure the risk of injury under different conditions.  
The imbalanced data for the different severity levels represent a prevailing issue for studies involving FARS or CRSS datasets, causing the prediction results to be lopsided toward the majority category [42]. To tackle this issue, a combination of the two datasetswas utilized, leveraging the larger volume of data in the CRSS database and the inclusion of fatal accidents in the FARS database. The timeframe of 2019-2020 was chosen for CRSS data, while the timeframe of 2016-2020 was chosen for FARS data. This approach aimed to achieve a balanced distribution of severity levels, resulting in controlled proportions of 43.1% for SEV1, 27.9% for SEV2, and 29.0% for SEV3. By adopting this approach, the issue of over-sampling or under-sampling involved could be effectively addressed.