The existing literature on crash prediction models primarily attributes crashes to inadequate driving performance with the demands of the road environment. Factors such as traffic flow, geometric attributes, road signs, and vehicle characteristics have been identified as contributing to this mismatch [15,16,17,18,19,20]. Moreover, SPFs have been developed to estimate crash rates within a specific timeframe or exposure [5,21,22,23,24,25,26]. These SPFs utilize statistical models that analyze risk indicators, including absolute numbers, frequency, and crash rates, as defined by Equation (1).

where λ is the expected crash number, N is the exposure, and p is the crash rate. The introduction of the HSM has provided a systematic approach to assessing crashes by employing analytical techniques and tools that quantify the impacts of road network planning, design, operation, and maintenance decisions. In research-based studies, the HSM has played a significant role in evaluating crashes.

The SPFs included in the HSM were developed using negative binomial (NB) regression models. These models were constructed using a generalized linear modeling (GLM) procedure, as outlined by Srinivasan et al. [27]. The SPFs consider both the infrastructure and operational characteristics.

Equation (2) illustrates how the predicted number of crashes (N_predicted) is determined using the SPF [28]. The SPF equation is specific to each facility, considering its base conditions, and adjusted by a calibration factor (C_x) and multiple crash modification factors (CMFs). Each CMF accounts for the operational and geometric characteristics (y) of the facility (x).

To determine C_x, Equation (3) provides the necessary calculation. The observed crashes are summed up across all sites and divided by the predicted crashes across all sites. The resulting C_x value is rounded to two decimal places and applied to the predictive model.

Calculating the corresponding C_x value for each facility type and year is advisable to customize the model. By substituting default values with locally derived values, the reliability of the predictive model can be improved. To apply this methodology, the HSM recommends a minimum desirable sample of 30 to 50 sites, representing at least 100 crashes annually [28]. Following the initial calibration, the HSM suggests utilizing the Empirical Bayes (EB) method to enhance the reliability of results and account for the regression-to-the-mean effect.

However, the model has limitations, particularly regarding its failure to consider speed limits. A study by Shirazinejad et al. [29] demonstrated that increasing the speed limit from 70 mph to 75 mph led to a significant 27% increase in total crashes and a notable 35% increase in fatal and injury crashes. Additionally, the HSM methodology fails to account for factors such as road infrastructure damage and unreasonable road design, all of which have been identified as impacting traffic safety [30].

Numerous studies have investigated the transferability and calibration of the HSM predictive model in different countries and regions. Over the past decade, researchers have explored the performance and parameters of the HSM model to assess its applicability and effectiveness in various contexts. The following studies shed light on the transferability and calibration challenges and the practical solutions and results in different countries.

Sun et al. conducted a statewide calibration of the HSM model for rural divided multilane highways in the US [31]. Their findings indicated that the HSM model reasonably predicted crashes in Missouri, with a calibration factor (C_x) of 0.98. In a study on rural two-lane roads in Arizona, Srinivasan et al. identified limitations in applying the HSM predictive models [32]. They emphasized the importance of gathering a larger sample and exploring the estimation of calibration functions to fit local data better. The overall calibration factor in this study was 1.079, indicating the success of the HSM model for US cases. D’Agostino examined the calibration factor for Italian motorways and found that the HSM model underestimated observed crash counts, with a C_x of 1.26 [33]. La Torre et al. concluded that a jurisdiction-specific base model derived from the HSM’s SPF provided a solid and reliable tool for crash prediction on the Italian freeway network [34].

In Brazilian studies, Rodrigues-Silva applied the HSM predictive model to two-lane highways in São Paulo State and found a calibration factor of 3.73 [35]. Barbosa et al. developed SPFs for intersections in Belo Horizonte, Brazil, with a calculated C_x of 2.06 [36]. Another study in Fortaleza city found a calibration factor of 0.65, highlighting the challenges in developing a nationwide SPF. Waihrich & Andrade investigated the calibration of the HSM model for multilane highways in the states of Minas Gerais and Goiás, Brazil. The resulting C_x values were 2.37 and 1.58 for each region, respectively, indicating a lack of transferability of the original HSM model in these scenarios [37]. Rodrigues-Silva compared the transferability between the HSM method and a local SPF for two-lane highways in different regions of Brazil. The calculated calibration factors were 3.67, 3.77, and 2.60 for São Paulo, Minas Gerais, and Paraná, respectively. This study highlighted the need for more parameters and knowledge in models for different facility types [38].

Studies conducted in Egypt by Elagamy et al. and in California, Maine, and Washington by Matarage & Dissanayake found that the HSM model overpredicted crash occurrences on multilane rural roads [39,40]. These studies emphasized the importance of considering local conditions and conducting calibration to improve the accuracy of predictions. Dadvar et al. proposed a method to adjust the HSM crash prediction model to provide a better fit for local data, as misallocating resources due to incorrect calibration factors can be problematic [41]. Al-Ahmadi et al. studied multilane rural highway segments in Saudi Arabia [42]. They found C_x values ranging from 0.63 to 0.78, emphasizing the need for in-depth local calibration and assessment of SPF quality. Researchers agree that the transferability of a model is dependent on the similarity of site characteristics to base conditions, and models must be built by associating regions with similar characteristics. The effectiveness of the local calibration factor as a method for transferring SPFs is widely discussed, considering socio-economic characteristics, traffic safety data distributions, and traffic flow influences on the transferability process. Kronprasert et al. compared different regression models for prediction accuracy, and the calibrated HSM SPF was the most effective model in predicting crashes on horizontal curve segments, underscoring its usefulness [43]. In a comprehensive overview, Heydari S. et al. [44] addressed road safety in low-income countries (LICs). They stressed the importance of accurate and complete road crash data for effective road safety interventions. They acknowledged that traditional sources such as police records suffer from varying levels of under-reporting, especially in LICs. They also emphasized the need to improve the quality and accuracy of road crash data through techniques like combining police and hospital records.

Countries like Brazil, with comprehensive databases integrating crash counts, traffic volume, and infrastructure data, must evaluate the performance of crash prediction models to shape investment planning strategies effectively. Conducting local calibration exercises considering regional peculiarities is crucial to enhance the transferability and precision of the HSM model across diverse countries and regions. These efforts aim to optimize the reliability of crash predictions, facilitating sustainable and informed interventions in transportation systems.

Assessing the accuracy of crash prediction models is essential in enhancing road safety measures. One approach to improve model performance is incorporating a local calibration factor (C_x) that considers the specific conditions of the target region. However, it is equally important to evaluate the model’s goodness of fit (GOF) and examine how well it aligns with observed data. In this regard, two widely used measures of forecast accuracy, the mean absolute percentage error (MAPE) and the mean absolute deviance (MAD), are commonly employed for comparative analysis.

Moreover, in recent research, the root mean square error (RMSE) has emerged as another evaluation metric for prediction accuracy in studies conducted by Li et al., Yao et al., and Yehia et al. [46,47,48]. However, it should be noted that the effectiveness of CURE plots in assessing model performance may be limited in studies with smaller sample sizes, as highlighted by Dadvar et al. [41].

The COVID-19 pandemic has brought about significant changes in traffic patterns and increased interest in investigating its impact on traffic safety globally. During the period of lockdowns and restrictions, there was a noticeable reduction in traffic flow in many affected countries [49]. However, studies have revealed a concerning increase in the severity of crashes during this period [50].

Research suggests that implementing nonpharmaceutical interventions (NPIs) and the higher percentage of people staying at home have had mixed effects on traffic safety. On the one hand, these measures have been associated with potential improvements in pedestrian and cyclist safety but have also increased crash risk for motor vehicle drivers [51]. Surprisingly, the average number of cyclists killed or injured per crash has tripled compared to previous years [52].

It is important to note that simply reducing traffic volume during the pandemic does not necessarily lead to improved traffic safety. This can be attributed to the homeostasis effect, wherein drivers compensate for reduced traffic by engaging in risky driving behaviors such as speeding and failure to signal [47]. Furthermore, crashes resulting in severe injuries are more likely to occur on highways due to, i.a., increased speeding, reduced law enforcement, lack of seat belt usage, and alcohol and drug abuse [49]. Therefore, effective law enforcement mechanisms should focus on preventing these behaviors [53].

Another significant pandemic effect was the shortened trip lengths and decreased travel frequency as people engaged in more online activities as an alternative to physical travel [50]. These changes in transportation characteristics and reduced traffic intensity on the roads, driven by the rise of e-commerce, have had implications for traffic patterns.

The sudden disruptions in traffic behavior caused by the pandemic offer a valuable opportunity to broaden the understanding of risk factors and the application of SPFs. As such, the calibrated HSM SPF for 2020 is compared to the crash data count in 2020 to assess its capability in evaluating the impacts of COVID-19 on the studied highways. This analysis can provide valuable insights into the effects of the pandemic on road safety and inform future strategies and interventions.