# Road Crash Analysis and Modeling: A Systematic Review of Methods, Data, and Emerging Technologies
## 6 Applications and Policy Implications
### Safety Performance Functions and Crash Modification Factors  
Safety Performance Functions (SPFs) have become the cornerstone of modern traffic safety analysis since their introduction in the Highway Safety Manual (HSM) [112] by the American Association of State Highway and Transportation Officials (AASHTO). These statistical models, which predict the average crash frequency for a given site type under specific conditions, are now widely used by the Federal Highway Administration (FHWA) and infrastructure analysts across the United States, providing transportation agencies with robust tools for identifying high-risk locations and evaluating safety improvements.  
The foundation for modern SPF implementation was established by [PERSON] [113], who demonstrated the Empirical Bayes (EB) method's effectiveness in addressing two critical challenges: improving precision with limited crash data and mitigating regression-to-mean bias. This methodological breakthrough, combined with the increasing availability of calibrated SPFs and overdispersion parameters, has facilitated the widespread adoption of EB estimation in safety analysis.  
The practical implementation of these methods has been demonstrated in various contexts. [PERSON] and [PERSON] [114] developed an accessible Excel-based approach for evaluating safety improvements in Montana's roadway reconstruction projects. Their work highlighted both the method's utility and its constraints, particularly the requirement for three-year aggregated crash data to ensure reliable SPF modeling.  
[PERSON] and [PERSON] [115] provided crucial validation of the EB methodology, demonstrating its superiority over traditional approaches in before-after safety studies. Their research emphasized the importance of comprehensive data collection and proper analyst training while also identifying potential pitfalls in CMF derivation. They proposed future research directions, including refinements to SPFs and the exploration of Full Bayes (FB) modeling for handling spatial correlations in accident data.  
A significant methodological advancement came from [PERSON] [116], who challenged the conventional assumption of uniform overdispersion parameters. His work showed that shorter road sections were disproportionately affected by this assumption, leading to potentially biased estimates. By proposing length-dependent overdispersion parameters, [PERSON] improved the accuracy of EB estimates across varying road section lengths.  
[PERSON] [117] conducted a comprehensive assessment of the EB method's performance in observational studies, confirming its position as the leading approach for before-after safety analyses. His research demonstrated that EB estimates based on accident prediction models achieved the highest accuracy among available methods, though noting variations in prediction errors across different techniques.  
Recent developments, exemplified by [PERSON] et al. [118], have expanded the application of both EB and FB methods to specific safety interventions. Their analysis of roadside barriers revealed the importance of considering multiple factors in safety assessments, including vehicle characteristics, driver demographics, and environmental conditions. This work demonstrates the evolution of CMFs toward more nuanced, condition-specific applications, reflecting the increasing sophistication of safety analysis methods.  
This progression in methodology, from basic prediction models to sophisticated multi-factor analyses, coupled with FHWA's standardization of SPFs, has established a robust framework for evidence-based safety analysis in transportation infrastructure. Future developments will likely focus on incorporating emerging data sources and refining condition-specific applications while maintaining the fundamental principles that have made these methods successful. Table 2 summarizes the development of SPFs and CMFs.