Safety Performance Functions for Mountain Two-lane Rural Roads in Ecuador

Segment selection

Initially, 25 two-lane roads were selected, with lengths ranging from 7,4 to 40 miles, as indicated in Table II. The AADT values, calculated or measured in 2017, have been included in this table. It is worth noting that the AADT estimation process was primarily carried out by students participating in the Road Projects course at Universidad Técnica Particular de Loja, along with the OSEVI-UTPL traffic counter ¹⁸.

Table II: Selected two-lane rural roads in this study

Source: Master’s students of the Road Projects course at Universidad Técnica Particular de Loja and the OSEVI-UTPL traffic counter ¹⁸

The features of every road listed in Table II were analyzed. These roads have a width between 11 and 12 ft, which is similar to the base condition. Additionally, these roads have a shoulder width between 2 and 4 ft, which is less than the base condition. However, it is important to note that these roads were constructed using older standards, where the shoulder width was narrower. The entire shoulder is paved, in accordance with national guidelines and base conditions. The roadside hazard rating (RHR) ranged between 3 and 7, as these are mountain roads. It is common for Ecuadorian mountain roads to have this level of risk, and it can be challenging to find RHR values equal to 3, which is the base condition. The driveway density was less than 5 driveways per mile, which is also common in mountain roads. Despite these differences, the remaining road features were consistent with the base conditions. Even though it may not be possible to meet all base conditions, efforts were made to align with the majority of them.

Crash data

Crash data were sourced from the National Transport Agency of Ecuador’s website ¹⁹. For each segment listed in Table II, three types of data were collected: total crashes (T), fatal and injury crashes (FI), and property damage only (PDO). It is important to note that these data were not directly available on the website and had to be estimated based on the causes of the accidents. The HSM recommends certain guidelines for data collection. It suggests a minimum sample size of 30-50 sites, with the entire group of calibration sites representing at least 100 crashes per year. It may take one to three years to accumulate a sufficient number of crash events to meet these crash frequency criteria ¹.

The road segments were associated with the closest crash record. Subsequently, the database was organized into two time periods: 2017-2019 and 2020-2021. This non-probability sampling division allowed calibrating predictive models via the crash data from the earlier period (2017-2019) and validating them using the more recent data (2020-2021). Initially, an analysis was conducted on individual segments, where 50 sites were randomly selected from those available. Between 2017 and 2019, 1.042 sites had no accidents, while 197 did. In total, 246 crashes were recorded during this period. Due to the low number of records and the high number of sites with no accidents, the random selection did not yield 100 crashes, despite a three-year analysis period. Consequently, we decided to use all 25 road sections as if they were individual segments, as shown in Table III.

Table III: Number of crashes in every road for the period of time analyzed (based on ANT data)

The data from 2019-2021 were then used for model calibration. It is worth noting that, if more than three years of data were available, they could be useful for assessing potential time trends in anual calibration factor estimates ¹⁷.

Table III shows that the highest number of observed accidents took place on road No. 4, which also has the highest AADT. Surprisingly, the longest road ¹⁴ does not have the highest number of accidents, possibly due to its low AADT value. This pattern is consistent with previously estimated SPFs. Interestingly, several roads had no recorded accidents in the analyzed period, while others had no records in the first period but did in the second. It is worth noting that the total crashes (T) value is approximately double that of fatal and injury crashes (FI) or property damage only (PDO). However, this is coincidental, as this pattern does not hold when analyzing each site separately. These variations and trends suggest that the selected sites may be representative since they encompass various situations encountered in engineering practice.

Calibration of the models

The calibration methodology employed in this study aims to refine the SPFs for two-lane rural highways in mountainous environments in Ecuador. Calibration is a crucial step in developing accurate predictive models for road safety, ensuring that the models align with local conditions and offer enhanced predictive accuracy. The specific methods and approaches for calibrating SPFs can vary, but they generally follow a systematic process. Here are the methods and considerations used in this calibration:

• Data collection. The calibration process relied on crash data from the National Transport Agency of Ecuador, covering the period from 2017 to 2019. This dataset included information from 25 distinct road sections, allowing for a comprehensive analysis.

• Data preprocessing. Before calibration, the crash data underwent preprocessing, which involved categorizing crashes by severity (fatal, injury, property damage only), cleaning the data to remove duplicates or errors, and geocoding crash locations.

• Selection of predictive variables. SPFs are typically developed as regression models that relate crash frequency to various roadway and traffic characteristics. The key variables used in the calibration process include AADT and segment length. In instances where no crashes were recorded, an exponent value of zero was assumed.

• Cluster analysis. Subsequently, a cluster analysis was performed to categorize data points based on AADT ranges. This analysis helped to identify groups of data points with similar characteristics, aiding in the calibration process. The clustering approach allowed for a more tailored calibration process based on traffic volume.

• Model formulation. A negative binomial or Poisson regression model was selected for formulating the model, whose form determines the relationship between crash frequency and the selected predictive variables.

• Exponent estimation. The model was then fitted to the data, including the estimation of model parameters and the exponent for each predictive variable. The exponent values indicate how each variable affects crash frequency. An average of all exponents was calculated for each type of accident and for all accidents combined.

• Calibration. This process involved modifying the exponent values to account for factors specific to the study area. It aimed to ensure that the model accurately predicts crash frequency in the local context. To establish a baseline for calibration, an initial analysis was conducted using data from all the road sections.

Model validation

The calibrated models were put to the test using crash data from 2020-2021. However, due to mobility restrictions resulting from the COVID-19 pandemic, the AADT figures for the sites in Table II needed adjustment. To address this issue, adjustment factors were estimated based on data from the UTPL Road Safety Observatory ¹⁸. Specifically, OSEVI-UTPL recorded the number of vehicles circulating on four two-lane roads in mountainous regions in southern Ecuador. The proportion between the traffic volume in 2017 and that in 2020-2021 was calculated for each road, and the adjustment factors were determined as their average. Consequently, the AADT for 2020 was 0,60 when compared to 2017, and for 2021, it was 0,79 compared to 2017. These factors were applied to adjust the AADT values in Table II.

Subsequently, the calibrated models were employed to predict the number of accidents for 2020-2021. These predicted values were compared with the actual recorded values for the same period, as displayed in Table III. Finally, the errors of the calibrated models were analyzed for further refinement. The prediction errors considered for analysis included the Mean Squared Prediction Error (MSPE), Mean Absolute Deviation (MAD), Mean Prediction Bias (MPB), and Mean Absolute Percentage Error (MAPE).

Model calibration

Table IVpresents the calibration results, beginning with the general model for all traffic, and then the AADT ranges resulting from the cluster analysis, which achieved a 95 % similarity. The histogram in Fig. 1 confirms the ranges obtained in the cluster analysis. However, special attention must be paid to the last range, as there is a lack of AADT values until reaching nearly 15.000 vehicles/day. This stratification of AADT for the calibration of the SPF equations is in line with previous findings (15, 20).

Table IV: Safety performance function proposed by this study

T: total crashes; FI: fatal and injury crashes; PDO: property damage only; N _spf-rs: predicted average crash frequency for base conditions using a statistical regression model (crashes/year); AADT: average annual daily traffic (vehicles per day); L: length of the road segment (miles).

Figure 1: Histogram of AADT

Table IVshows that the exponents for total crashes are lower than those for fatal and injury crashes, while the exponents for the latter are very similar to those for property damage only. Additionally, as the number of vehicles increases, the absolute value of these exponents increases, and this trend applies to all three categories of accidents. Only in the range of up to 1.000 vehicles per day do positive exponents appear, whereas, in the other models, the exponents are negative, as seen in the original equation.

Given these observed trends, using a single model, such as Eqs. (3), (4), and (5), would likely result in higher prediction errors when compared to using Eqs. (6) through (18). In light of this, the general model will not undergo validation in the following section.

Validation of the models

For validation purposes, we utilized the adjusted AADT, segment length, and crash data from 2020-2021. Eqs. (6)-(18) in Table IV were employed to predict the number of crashes for 2020-2021, as summarized in Table V. The selection of specific equations was based on the corresponding AADT values for each road segment. Table V shows that the total number of observed crashes in the period was 140, while the predicted count was 166,00. For fatal and injury crashes (F+I), there were 78 observed crashes, compared to a predicted count of 106,50. Property damage only (PDO) crashes had 62 observed crashes, with a predicted count of 102,15.

Table V: Observed and expected crashes calculated using the equations 6-18 from Table IV

The scatterplot of values from Table V is presented in Fig. 2 . In an ideal scenario, all the points would closely align around a 45° reference line. However, it is essential to remember that SPFs provide ‘long-term average results, not ‘short-term average’ ones ¹⁷. Although there are points where the equations overestimate or underestimate the observed crashes, it is necessary to conduct an error analysis to determine the validity of the equations.

Figure 2: Expected versus observed crash frequency 2020-2021

Table VI presents the prediction errors for the crashes predicted using Eqs. (6)-(18). Regarding the MSPE, lower values are preferable, as they indicate a better fit of the model to the data. In this case, the values could be deemed acceptable, with the highest value being 27,8.

Table VI: Prediction errors of the proposed safety performance function

The MAD provides a measure of the average magnitude of prediction variability, and smaller values are preferred over larger ones. In this case, the maximum value was 3,6, which was deemed acceptable.

The MPB offers insights into whether the equations overpredict or underpredict. A positive value suggests underprediction, while a negative one implies overprediction. As observed in Fig. 2 , the equations are slightly underpredicting, consistent with the calculated positive values of MPB.

Lastly, the MAPE calculates the average error percentage between the observed and predicted values, relative to the former. Lower MAPE values indicate better predictions.

However, in this case, the values are relatively high due to their close relationship with the total recorded crash values.

Despite the higher MAPE values, the rest of the error metrics constitute noteworthy results, suggesting that the models can be regarded as validated.

The presented and validated models represent significant progress in the field of road safety for two-lane roads. Using separate equations for different types of accidents, as demonstrated here, addresses the limitation of a single equation, such as the one proposed by the HSM, which can lead to errors when applied without distinction among accident types. This finding is consistent with previous research ⁹. Furthermore, the utilization of models based on traffic ranges, as shown in this study, has also been recognized in previous studies, and it is confirmed to provide improved results ¹⁷. These advancements contribute to a more nuanced and accurate understanding of road safety, ultimately aiding in the development of more effective safety measures and policies for two-lane roads.