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Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming
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Original Research Paper
Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming Q4
Milhan Moomen a,*, Mahdi Rezapour a, Mustaffa N. Raja a, Khaled Ksaibati b a b
Department of Civil & Architectural Engineering, University of Wyoming, Laramie, WY, 82071, USA Wyoming Technology Transfer Center, University of Wyoming, Laramie, WY, 82071, USA
highlights The geometry of mountainous terrain increases crash risk. This study identified geometric factors impacting downgrade crashes. Separate prediction models were estimated to determine the impacts of mountain pass geometry on crash severity and frequency. Downgrade length, number of lanes, shoulder width, and horizontal curve length were identified as important geometric factors impacting downgrade crashes. Q1
Important measures were suggested to reduce the incidence and severity of crashes on mountain passes.
article info
abstract
Article history:
Road deaths, injuries and property damage places a huge burden on the economy of most
Received 21 November 2018
nations. Wyoming has one of the highest truck-related fatality rates among the states in
Received in revised form
the US. The high crash rates observed in the state is as a result of many factors mainly
22 April 2019
related to the challenging mountainous terrain in the state, which places extra burden on
Accepted 28 April 2019
truck drivers in terms of requiring higher levels of alertness and driving skills. The difficult
Available online xxx
geometry of roads characteristic of mountainous terrain in terms of steep grade lengths adds extra risks of fatalities or injuries occurring as a result of a crash. These risks are more
Keywords:
pronounced for truck-related crashes due to the weight and sizes of trucks. As part of the
Traffic safety
measures to reduce the incidence of truck-related crashes on mountainous areas, the
Downgrade
Wyoming Department of Transportation (WYDOT) initiated a study to investigate causes of
Crash frequency
truck crashes on downgrade areas of Wyoming. Several studies have investigated the
Truck safety
contributory factors to severe injury crashes but the focus has mostly been on level sec-
Geometric factor
tions. This study analyzed the contributory geometric factors of truck crashes on downgrades by calibrating three crash prediction negative binomial models. These models took into account the injury severity of the crashes. The results indicate that downgrade length, shoulder width, horizontal curve length, number of lanes, number of access points and truck traffic on the highway all impact truck-related crashes and injury frequencies on
* Corresponding author. Tel.: þ1 765 237 8230. E-mail addresses: [email protected] (M. Moomen), [email protected] (M. Rezapour), [email protected] (M.N. Raja), khaled@ uwyo.edu (K. Ksaibati). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2019.04.002 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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downgrades. The results of this study will be helpful to future downgrade road design policy aimed at reducing downgrade truck related crashes. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
About 1.2 million people die worldwide every year in road crashes; an average of 3300 deaths a day. The World Health Organization (WHO) indicates that road crashes result in 20e50 million injuries and disabilities (WHO, 2015). According to the Center for Diseases Control and Prevention (CDC), road fatalities in the United States is among the top leading causes of death (CDC, 2014). In 2015, a total of 22,441 drivers and passengers died in motor vehicle crashes in the US, with crashes resulting in more than 2.5 million drivers and passengers being treated in emergency departments (CDC, 2015). According to the Federal Motor Carrier Safety Administration (FMCSA) (2017), there were 3598 fatal crashes involving at least one large truck, and there were 667 large truck occupant deaths (both drivers and passengers). Wyoming has one of the highest highway fatality rates in the nation and truck related crash rates in the United States (Weber and Murray, 2014). In 2014, the state ranked first in terms of large truck crash rate. This high truck crash and fatality rate is attributed to a myriad of key factors, among which are the challenging driving conditions in mountainous terrain that characterize the state, and adverse weather conditions common to such locations. WYDOT has undertaken several safety improvement projects to mitigate the problem of truck crashes on mountain passes. These have included reconstruction of sections, installation of downgrade warning signs, installation of cable catch-net systems among others. However, the incidence of truck-related crashes is still prevalent. An analysis of crash rates on mountain passes in the state shows that truck crash
rates have generally been increasing over the past decade though total crash rates have been decreasing or remained stable. Fig. 1 shows the truck crash rates trends for US 14, one of the hazardous mountain passes in the states, which has been increasing consistently. Downgrade truck crash rates are shown along with crash rates on upgrades. It can be seen that the downgrade rates increased over the reporting period while upgrade truck crash rates decreased slightly. To address the precarious situation of truck drivers, it is important to study the causal factors relating to downgrade truck crashes and their severity on mountainous roads. There undeniably have been several studies that have incorporated geometric variables that resulted in safety improvements with regards to geometric design, e.g., Karlaftis and Golias (2002), Venkataraman et al. (2014). However, such studies have mainly focused on level sections and mostly did not consider the exclusive effects downgrades have on crashes. This study was undertaken to identify underlying factors contributing to truck crash frequency and severity by analyzing only downgrade crashes. This study will help to alleviate the frequency and severity of truck crashes by providing an insight into roadway characteristics and provide recommendations that may contribute to a safer environment for drivers who have to traverse the state. Traffic crashes occur due to a host of different contributory factors such as driver (94%), vehicle (5%), and environment (1%) (Singh, 2015). Previous studies have also indicated that roadway geometric characteristics impact drivers’ perception about environmental conditions and consequently impact their driving behavior (Janssen et al., 2006; Milton and Mannering, 1998). It is therefore
Fig. 1 e Truck crash rate trend (US 14). Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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imperative to account for the impact of geometric variables on crash frequency and severity. Different methodological approaches to understand the relationships between crashes and crash factors abound in the literature. The predominant methods are the Poisson and negative binomial models which have been commonly adopted to predict crash frequencies. The Poisson regression model is admittedly superior to the linear regression model. The use of linear regression modeling in crash data analysis has been limited because of the many issues associated with this method when applied to crash data (Jovanis and Chang, 1986). However, the Poisson model restricts the mean to be equal to the variance; a phenomenon which is hardly observed in crash data. In most crash data, the variance of crash frequency exceeds the mean and in such cases, the data is said to be overdispersed (Milton and Mannering, 1998). It has also been argued that the use of the Poisson model may underestimate the variances of the estimated coefficients (Lord and Mannering, 2010). Miaou and Lum in an attempt to restrict the effects of overdispersion in their predictive model relaxed the Poisson constraint of the mean being equal to the variance by using the Wedderburn's over dispersion parameter (Miaou and Lum, 1993). The results showed that the use of the Poisson model with over dispersed data leads to erroneous inferences in terms of the probability of crashes because the model may over- or under-estimate the likelihood of occurrence. The negative binomial model which is an extension of the Poisson model has been suggested as an alternative to the Poisson model because of its ability to handle overdispersed data and other statistical issues related to crash data. This is probably the most frequently used model in crash frequency modeling (Lord and Mannering, 2010). Miaou evaluated the performance of Poisson, negative binomial, and zero-inflated Poisson regression models by investigating the relationship between truck crashes and geometric characteristics of road sections (Miaou, 1994). The study found that grade, AADT, percent trucks, horizontal curvature, and yearly dummy variables, which account for year-to-year changes in the overall truck accident involvement, all have a significant effect on truck crashes. The study concluded that using the maximum-likelihood procedure, all three models have consistent parameter estimates. The study however concluded that the negative binomial model performs better in estimating the frequency of road sections with zero truck crash involvement. Shankar and Mannering used Poisson and negative binomial distributions to study the effects of roadway geometry and environmental factors on rural accident frequency in the state of Washington (Shankar and Mannering, 1995). The authors modeled frequencies of specific types of crashes (overturns, fixed objects, parked vehicles, fixed objects, and same direction crashes). They argued that separate regressions of specific crash types provide valuable information. Another research carried out by Milton and Mannering developed crash prediction models using data from principal arterials in Washington State (Milton and Mannering, 1998). The negative binomial model was used to assess the effects
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of geometric variables on crash frequency. Traffic and several geometric variables were included in the various models developed. The authors suggested that the negative binomial regression tool is a powerful predictive tool which should be used in future studies. Poch and Mannering estimated negative binomial models of crash frequencies at intersection approaches from 63 intersections in Bellevue, Washington. To better identify the most significant traffic and geometric elements that determine crash frequencies at intersections, separate models were developed for total, rear end, angle and approach-turn crashes (Pock and Mannering, 1996). Dong et al. conducted a study to identify the impacts of different roadway geometric design features on truck-related crash frequency. The factors were investigated across different collision vehicle types. The results indicated that traffic, truck percentage, segment length, and posted speed limit are some of the factors that influence truck crashes, regardless of collision type (Dong et al., 2016). Guevara et al. modeled fatality and injury crash outcomes using a simultaneous negative binomial crash model. The writers argued that the three crash categories were unrelated and shared observable characteristics in the error term, such as omitted variables, measurement errors, and random errors. However, it was found that estimation problems prohibit the simultaneous estimation of injury and property damage only (PDO) crashes. Therefore, fatal and injury were modeled together with a separate model developed for PDO (Guevara et al., 1997). Another justification for developing a separate model for PDO crashes was that highway agencies are more interested in crashes with severe injuries. Other studies have considered methodological approaches such as logistic regression (Chen et al., 2016), multinomial regression (Agbelie, 2016; Zeng et al., 2017), non-linear models (Mustakim and Fujita, 2011; Zegeer et al., 1978), and empirical Bayesian methods (Hauer et al., 2002). Agbelie investigated contributory factors to crash frequency and injury severity using random-parameters negative binomial and multinomial models (Agbelie, 2016). The study found that an increase in the number of combination trucks is associated with a decrease in crash frequency. However, the presence of combination trucks increased the crash severity once a crash occurred. Also vertical grades greater than 5%, rolling terrain, lane width, increase in urbanization were found to increase the probability of crash injury severity while the presence of stop signs, and wider median widths had the reverse effects. Fitzsimmons et al. evaluated large truck crashes at horizontal curves on two-lane rural highways on Kansas using odds ratio analysis. They found that significant differences exist among single- and multiple-vehicle, and truck-involved crashes (Fitzsimmons et al., 2013). The literature review highlighted the importance of contributory factors to different crash types. It also justified separating different crash injury levels. Although much research incorporated roadway geometric designs in their analyses, the authors found no study that used only downgrade crash data to identify the contributory factors of downgrade truck crashes. Therefore, this study was set forth
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
to identify contributory factors of influence to downgrade truck crashes in Wyoming.
2.
Method
Poisson regression model is the most widely used model for count data (SAS Institute, 1985). This model is based on the assumption that the response is Poisson distributed. This distribution models the probability of discrete events (truck crashes for this study), according to the Poisson process as follow. P Yi ¼ yi jxi ¼
y em mi i
yi !
yi ¼ 0; 1; 2; …
(1)
where Y is the number of crashes, and m is the mean number of crashes. If the number of crashes is assumed to be Poisson distributed, the relation can be defined as follow (Hadi et al., 1995). PðY ¼ Yi Þ ¼
emðxi ;bÞ ½mi ðXi ; bÞyi Yi !
(2)
where Yi is the number of observed crashes, b is a vector that denotes a set of parameters to be estimated, mi ðXi ; bÞ is the mean of the number of crashes on road section, Xi is a vector that represents the value of regression variables for highway section i. Eq. (2) is based on Poisson distribution, which assumes the variance to be equal to the mean. When overdispersion is present, using Poisson regression would result in the variance of the parameters to be inconsistently estimated (Hadi et al., 1995). The negative binomial distribution can be written as follow. G yi þ a1 f yi jxi ¼ yi Gða1 Þ
a1 a1 þ mi
a1
mi a1 þ mi
(3)
Under Eq. (2), the negative binomial distribution is derived as a gamma mixture of Poisson random variable with conditional mean of E and variance of Var. E yi jxi ¼ mi
(4)
1 Var yi jxi ¼ mi 1 þ mi ¼ mi ð1 þ ami Þ > mi q
(5)
When overdispersion is present, the conditional variance exceeds the conditional means (Eq. (5)). Negative binomial can be used to address this overdispersion (SAS Institute, 1985). The negative binomial model can be written as follow (Guevara et al., 1997). l ¼ exp bX0i þ ei
(6)
where exp (ei ) is a gamma-distributed error term, l is the dependent variable, while X0 is the different geometry and traffic explanatory variables. A p-value smaller than or equal to 0.05 was used as a criteria to maintain variables in the models. The Akaike information criteria (AIC) was used to indicate the best fit model. The AIC is defined as AIC ¼ 2lnðmaximum likelihoodÞ þ 2k where k is the number of estimated parameters.
(7)
The model includes the maximum likelihood value in each subset model output. The smaller the AIC, the smaller the maximum likelihood, which indicate a better model. To examine the implications of the significant variables, elasticities could be computed to determine the marginal effects of the variables. Elasticities measure the effect of a variable on the expected frequency and are taken as the effect of a 1% change in the variable on the expected frequency (Washington et al., 2011). Elasticity is computed as 00
EIxj ¼
vl0 Xj 00 l0 vXj
(8)
where EI is elasticity of the jth independent variable with respect to crash frequency, X}j is magnitude of the variable under consideration, l0i is expected crash frequency estimated from regression model. An elasticity value greater than 1 corresponds in a proportional manner to changes in the response variable. Elasticity values less than 1 indicate an inelastic variable. The research objective of assessing the geometric factors relating to downgrade truck crash injury severity and frequency on mountain pass roads in Wyoming was achieved by the following methodology. In the early stages of the study, data was collected for the horizontal and vertical geometric features on all rural two-lane highways in Wyoming from the WYDOT database. The vertical geometric dataset was examined to determine the locations that require special attention by road users as defined within the Manual on Uniform Traffic Control Devices (MUTCD). Thereafter, crash data and geometric features were extracted for each of the identified section and collected in a database. Three models were then developed with the various geometric characteristics of the roadways and traffic information as the explanatory variables. The explanatory variables were related to the severity of crashes including PDO crashes, fatal/injury crashes, and total truck crashes. Significant predictors identified from the models for various severity levels were assessed to quantify the causal factors and variables that influence the risk of truck crash severity on mountainous downgrades. Recommendations for reducing the crash frequency on mountainous downgrades are presented based on the results of the study.
3.
Data preparation
The first step in the data preparation involved the identification of hazardous downgrade sections. The MUTCD specifies grade and length combinations that are deemed unsafe to trucks in terms of braking ability and crash risks. The combination of downgrade length and grade requiring extra attention are (Federal Highway Administration, 2012). A five percent (5%) grade that is more than 3000 ft. (914.4 m) in length. A six percent (6%) grade that is more than 2000 ft. (609.6 m) in length. A seven percent (7%) grade that is more than 1000 ft. (304.8 m) in length.
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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An eight percent (8%) grade that is more than 750 ft. (228.6 m) in length. A nine percent (9%) grade that is more than 500 ft. (152.4 m) in length. Geometric data was obtained from WYDOT for mountain passes in Wyoming. Mileposts (MP) and elevations from the vertical alignment data were used to compute grades for each route. The gradient between two mileposts was computed as Gradient ¼
Elevationi Elevationði1Þ 100 MPi MPði1Þ
(9)
Graphical plots were then generated for each route to help identify grades that met the criteria set out in the MUTCD. Fig. 2 shows a typical plot of the grades on a Wyoming highway, Main Line (ML) 36. A compound grade was then computed sections identified. A total of 157 sections were identified as downgrades important to this study. Crash data was extracted from the Critical Analysis Reporting Environment (CARE) package from 2005 to 2015. Crashes that occurred one mile beyond the end of the downgrade were included with crashes within the downgrade section as recommended by the Grade Severity Rating System (GSRS) Users’ Manual. This was done to account for runaway truck crashes attributable to the downgrade that occurred beyond it (Bowman, 1989). The CARE package generated crash reports that enabled extractions and analysis of crashes for the identified locations. Geometric data obtained from WYDOT was merged with the crash database.
4.
Exploratory data analysis
The study area consists of 192 miles of downgrades made mainly of two-way lanes. Data were aggregated based on the criterion discussed by MUTCD. The data included different characteristics related to various geometric variables and traffic. The data set contains over 20 columns of traffic and geometry variables such as horizontal curve length, average of crest curve and number of sag curve. A complete list of
5
variables along with their descriptive analysis is presented in Tables 1 and 2. Table 2 shows the descriptive statistics for the major, noncontinuous variables used in the study. As can be seen from Table 2, PDO crashes constituted a large portion, 62 percent of all downgrade truck crashes, while fatal/injury crashes consisted of 38 percent. This difference indicates that on average a truck crash on a downgrade would likely result in an injury/fatality about 40 percent of the time. This underscores a severe risk undertaken by truck drivers who traverse mountain passes. Non-continuous variables such as number of lanes, presence of passing lane and presence of warning signs were also quantified and presented below.
5.
Estimation results
The negative binomial models were estimated for total, PDO, and fatal/injury crash frequencies. The dispersion parameters for all the three crash frequency models are statistically significant and point to the inherent over dispersed nature of the crash data. The following sections present the result of the maximum likelihood estimation of the different types of crash frequency, and severity outcomes.
5.1.
Fatal/injury crash frequency model
There were a low number of observations for fatal crashes. This necessitated the combination of fatal crashes with injury crashes for the estimation of the model. The results for the negative binomial model specification for fatal and injury crash frequency are shown in Table 3. The analysis shows that an increase in the length of the downgrade section leads to a higher number of fatal/injury crashes. This is consistent with other studies (Ahmed et al., 2011; Bowman, 1989; Myers et al., 1981). An increase in the number of lanes was found to be associated with a decrease in the frequency of fatal/injury crashes on downgrades. Some studies found that increasing the number of lanes reduces the frequency of severe injury crashes (Fitzpatrick et al., 2005),
Fig. 2 e Grade profile plot for route ML 36 (US 16). Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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Table 1 e Summary statistics of key variables (continuous variables). Variable Length (mile) Grade (%) Average horizontal curve radius (ft.) Average horizontal curve length (ft.) Horizontal curve length (ft.) No. of horizontal curves Average sag curve length (vertical curve) (ft.) Average crest curve length (vertical) (ft.) No. of sag curves No. of crest curves Lane width (ft.) No. of access points Shoulder width (ft.) Average AADT Average ADTT No. of Lanes
Mean
Std. Dev.
Minimum
Maximum
1.220 6.510 2148.760 946.92 1353.360 8.430 762.670 974.280 2.590 2.610 11.940 0.850 3.620 1203.240 101.290 2.220
1.098 1.337 2303.507 1432.94 172.924 9.251 503.616 662.829 2.496 2.301 1.007 1.307 2.366 1787.311 106.557 0.496
0.150 5.000 0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.000 8.000 0.000 0.000 119.000 9.000 0.000
5.730 9.610 17,178.000 16,445.00 11,459.000 47.000 3000.000 3800.000 15.000 16.000 18.000 6.000 12.000 11,183.000 645.000 4.000
5.2.
Table 2 e Summary statistics of major variables (categorical variables). Category
Variable
Frequency
Percentage (%)
Response
PDO Fatality/injury Total crashes Yes No Yes No
166 102 267 38 119 56 101
62 38 100 24 76 64 36
Passing lane presence Warning sign presence
while others found the opposite to be true (Kononov et al., 2008). The safety in increasing the number of lanes may be attributed to the extra opportunities for vehicles to take evasive action to lessen the severity of the crash. An examination of the computed elasticities show that no variable was elastic (had an absolute value greater than one). However, length and average daily truck traffic (ADTT) had elasticities above 0.5. Specifically, a 1% increase in the length of the downgrade leads to a 0.665% increase in the number of severe downgrade truck crashes. A 1% increase in the number of lanes causes a 0.224% decrease in the number of severe downgrade truck crashes. Finally, a 1% increase in truck traffic is associated with a 0.665% increase in severe truck crashes on downgrades.
PDO crash frequency model
For the PDO crash frequency model, length, horizontal curve length, number of access points, shoulder width, and ADTT were found to be significant (Table 4). The analysis shows that an increase in length, shoulder width and ADTT lead to an increase in PDO crash frequency while horizontal curve length and number of access points are associated with a decrease in PDO crash frequency. Horizontal curves with long lengths were found to decrease the occurrence of PDO crashes. Theoretically, motorists are less likely to be involved in crashes on long horizontal curves due to improved sight distances. An increase in number of access points decreases the occurrence of PDO truck crashes on downgrades. This can be attributed to access points interrupting truck movements due to entering and exiting vehicles that may result in a decrease truck crashes. The association of increasing shoulder width and higher crash frequencies was unexpected. However a review of the literature indicates that wider shoulders appear to result in faster operating speeds (TRB, 2011). The Highway Capacity Manual (HCM) predicts a 1.3e1.7 mile increase in speeds for every 1 ft increase in shoulder width on two-lane highways (TRB, 2010). The association of shoulder width with increasing speed therefore seems to be the reason why the
Table 3 e Negative binomial model estimation of fatal/injury crash frequency model. Variable description Constant Length (mile) Number of lanes Average daily truck traffic (ADTT) Negative binomial dispersion parameter Number of observations Log-likelihood at zero LL (0) Log-likelihood at convergence LL(b) AIC
Estimated parameter
Standard error
t-statistic
p-value
Elasticity
0.5938 0.5115 0.7072 0.0066 0.7679 157 152.2997 144.7260 1.9098
0.7294 0.1233 0.3461 0.0012 0.3590 -
0.814 4.147 2.043 5.184 2.139 -
0.4156 0.0000 0.0410 0.0000 0.0325 -
0.6243 0.2238 0.6651 -
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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Q2
Table 4 e Negative binomial model estimation of PDO crash frequency model. Variable description Constant Length (mile) Horizontal curve length (ft.) Number of access points Shoulder width (ft.) ADTT Negative binomial dispersion parameter Number of observations Log-likelihood at zero LL (0) Log-likelihood at convergence LL(b) AIC
Estimated parameter
Standard error
t-statistic
p-value
Elasticity
1.2178 0.3626 1.654 104 0.2716 0.0887 0.0055 0.6626 157 203.7729 190.751 2.523
0.2893 0.09625 6.598 104 0.1111 0.0462 0.0012 0.2211 -
4.210 3.767 2.506 2.442 1.923 4.473 2.996 -
0.0000 0.0002 0.0122 0.0146 0.0454 0.0000 0.0027 -
0.4426 0.2238 0.2300 0.3211 0.5616 -
Table 5 e Negative binomial model estimation of truck crash frequency model. Variable description Constant Grade length (mile) Horizontal curve length (ft.) Number of access points Shoulder width (ft.) Average daily truck traffic (ADTT) Negative binomial dispersion parameter Number of observations Log-likelihood at zero LL (0) Log-likelihood at convergence LL(b) AIC
Estimated parameter
Standard error
t-statistic
p-value
Elasticity
1.0040 0.4437 1.664 104 0.2460 0.1174 0.0054 0.7765 157 265.1639 235.7594 3.0924
0.2578 0.0967 7.318 104 0.1066 0.0499 0.0013 0.2045 -
3.893 4.586 2.273 2.307 2.350 4.172 3.741 -
0.0001 0.0000 0.0230 0.0211 0.0188 0.0000 0.0002 -
0.542 0.225 0.208 0.425 0.548 -
parameter estimate for shoulder width is positive for this analysis. The elasticity for PDO truck crashes on downgrades shows none of the significant variables is elastic. The analysis indicates that a 1% increase in length, shoulder width and ADTT is associated with 0.442%, 0.321% and 0.562% increase in PDO truck crash frequency on downgrades, respectively. Elasticity for horizontal curve length and number of access points suggests a 1% increase in those variables will result in 0.224% and 0.220% decrease in PDO crash frequency.
5.3.
Truck crash frequency model
The truck crash frequency model was estimated based on the combined injury severity models. The analysis shows that length, horizontal curve length, number of access points, shoulder width and ADTT were statistically significant (Table 5). The results show that length, shoulder width, and ADTT all increase the frequency of truckrelated crashes on downgrades while horizontal curve length and shoulder width decrease crash frequency. The reasons for the effect of these variables on truck crash frequency on downgrades were discussed in the previous sections. The truck crash frequency model was found to be similar to the PDO model. This may be related to the high number of PDO crashes (62%), which dominate the crash data. However, the parameter estimates for the truck crash model were higher for most variables meaning they had higher effects on downgrade truck crashes. The elasticity values showed a similar trend.
Also, the log-likelihood estimates and AIC values show the truck crash model has a better fit to the crash data compared to the PDO crash frequency model.
6.
Conclusions and recommendations
Identification of the contributory factors to downgrade crash frequency is needed to address the high truck crash rate in the state of Wyoming. As no study has been conducted on the evaluation of contributory geometric variables, specifically on downgrades, this study will benefit policy makers and designers to adopt strategies and policies that counter the incidence of truck-related crashes on downgrades. In addition to including only downgrade truck-related crashes, crashes were also analyzed based on their crash severity. This is important as one of the main objectives of WYDOT, highlighted in the Wyoming strategic safety plan, is to reduce the number of severe crashes. The results showed that some variables such as length of downgrade segment, shoulder width and ADTT, have positive coefficients, indicating that these factors are associated with an increase in crash frequency on downgrades and mountain passes. However other factors were found to decrease truck crash severity including length of horizontal curve and number of access points. Based on the results of the analysis, countermeasures can be recommended to different organizations in charge of traffic safety on Wyoming highways, and also drivers to have safer downgrade roads in the state.
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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The study indicated that grade length, shoulder width and ADTT are major factors impacting truck-related crashes and injury frequency on downgrades. These factors may indicate inappropriate driving behaviors on downgrades. It is therefore imperative to install warning signs cautioning truck drivers on the presence of hazardous downgrades and the need to adopt cautious behaviors such as reducing speed and heeding signs. Longer horizontal curve lengths were found to decrease both truck and injury frequencies. Wherever possible on mountain passes, highway designers are encouraged to make the curve lengths long and flat for safe operation of trucks. However, drivers must be cautioned on such sections to discourage speeding. Installation of cable catch-net systems and truck escape ramps should be undertaken at feasible locations on extremely hazardous downgrades. This will decrease severe crashes on the mountain passes in the state. Future studies should explore the interaction of critical vehicle maneuvers and driver actions with geometric variables prior to crashes. As data from sources such as naturalistic driving studies and black boxes become available, these vehicle-geometry and vehicle-driver interaction research is becoming possible.
Declaration of Competing Interest The authors do not have any conflict of interest with other entities or researchers.
Acknowledgments Q3
The Wyoming Department of Transportation (WYDOT) and the Wyoming Technology Transfer (WYT2/LTAP) Center at the University of Wyoming provided extensive resources to assist in the compilation of the data sets used. The authors would like to acknowledge that this work is part of project #RS08216 funded by WYDOT.
references
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Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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Mahdi Rezapour, PhD, has a few years of working experience as an engineer and project manager. In August 2015, he received his master of science in civil engineering with an emphasis on pavement engineering from the University of North Dakota. He then moved to Wyoming to pursue his PhD in civil engineering with an emphasis on traffic safety at the University of Wyoming. His current research is focused on truck safety and he is currently working for Wyoming Technology Transfer Centre.
Milhan Moomen, PhD candidate, got his BSc. degree from the Kwame Nkrumah University of Science and Technology in Ghana. He then worked for Ghana Highway Authority as a Contracts Engineer. He subsequently received an MSc. from Purdue University in 2016 where he researched on bridge infrastructure management. Currently, he is pursuing a PhD in civil engineering and his research is focused on traffic safety.
Khaled Ksaibati, PhD, P.E., obtained his BS degree from Wayne State University and his MS and PhD degrees from Purdue University. Dr. Ksaibati worked for the Indiana Department of Transportation for a couple of years prior to coming to the University of Wyoming in 1990. He was promoted to an associate professor in 1997 and full professor in 2002. Dr. Ksaibati has been the director of the Wyoming Technology Transfer Center since 2003.
Mustaffa N. Raja, MSc, received his BS degree in petroleum engineering from the University of Wyoming. He received a masters degree in transportation engineering from the University of Wyoming. He currently works as a civil engineer in Wyoming.
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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Original Research Paper
Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming Q4
Milhan Moomen a,*, Mahdi Rezapour a, Mustaffa N. Raja a, Khaled Ksaibati b a b
Department of Civil & Architectural Engineering, University of Wyoming, Laramie, WY, 82071, USA Wyoming Technology Transfer Center, University of Wyoming, Laramie, WY, 82071, USA
highlights The geometry of mountainous terrain increases crash risk. This study identified geometric factors impacting downgrade crashes. Separate prediction models were estimated to determine the impacts of mountain pass geometry on crash severity and frequency. Downgrade length, number of lanes, shoulder width, and horizontal curve length were identified as important geometric factors impacting downgrade crashes. Q1
Important measures were suggested to reduce the incidence and severity of crashes on mountain passes.
article info
abstract
Article history:
Road deaths, injuries and property damage places a huge burden on the economy of most
Received 21 November 2018
nations. Wyoming has one of the highest truck-related fatality rates among the states in
Received in revised form
the US. The high crash rates observed in the state is as a result of many factors mainly
22 April 2019
related to the challenging mountainous terrain in the state, which places extra burden on
Accepted 28 April 2019
truck drivers in terms of requiring higher levels of alertness and driving skills. The difficult
Available online xxx
geometry of roads characteristic of mountainous terrain in terms of steep grade lengths adds extra risks of fatalities or injuries occurring as a result of a crash. These risks are more
Keywords:
pronounced for truck-related crashes due to the weight and sizes of trucks. As part of the
Traffic safety
measures to reduce the incidence of truck-related crashes on mountainous areas, the
Downgrade
Wyoming Department of Transportation (WYDOT) initiated a study to investigate causes of
Crash frequency
truck crashes on downgrade areas of Wyoming. Several studies have investigated the
Truck safety
contributory factors to severe injury crashes but the focus has mostly been on level sec-
Geometric factor
tions. This study analyzed the contributory geometric factors of truck crashes on downgrades by calibrating three crash prediction negative binomial models. These models took into account the injury severity of the crashes. The results indicate that downgrade length, shoulder width, horizontal curve length, number of lanes, number of access points and truck traffic on the highway all impact truck-related crashes and injury frequencies on
* Corresponding author. Tel.: þ1 765 237 8230. E-mail addresses: [email protected] (M. Moomen), [email protected] (M. Rezapour), [email protected] (M.N. Raja), khaled@ uwyo.edu (K. Ksaibati). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2019.04.002 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
downgrades. The results of this study will be helpful to future downgrade road design policy aimed at reducing downgrade truck related crashes. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
About 1.2 million people die worldwide every year in road crashes; an average of 3300 deaths a day. The World Health Organization (WHO) indicates that road crashes result in 20e50 million injuries and disabilities (WHO, 2015). According to the Center for Diseases Control and Prevention (CDC), road fatalities in the United States is among the top leading causes of death (CDC, 2014). In 2015, a total of 22,441 drivers and passengers died in motor vehicle crashes in the US, with crashes resulting in more than 2.5 million drivers and passengers being treated in emergency departments (CDC, 2015). According to the Federal Motor Carrier Safety Administration (FMCSA) (2017), there were 3598 fatal crashes involving at least one large truck, and there were 667 large truck occupant deaths (both drivers and passengers). Wyoming has one of the highest highway fatality rates in the nation and truck related crash rates in the United States (Weber and Murray, 2014). In 2014, the state ranked first in terms of large truck crash rate. This high truck crash and fatality rate is attributed to a myriad of key factors, among which are the challenging driving conditions in mountainous terrain that characterize the state, and adverse weather conditions common to such locations. WYDOT has undertaken several safety improvement projects to mitigate the problem of truck crashes on mountain passes. These have included reconstruction of sections, installation of downgrade warning signs, installation of cable catch-net systems among others. However, the incidence of truck-related crashes is still prevalent. An analysis of crash rates on mountain passes in the state shows that truck crash
rates have generally been increasing over the past decade though total crash rates have been decreasing or remained stable. Fig. 1 shows the truck crash rates trends for US 14, one of the hazardous mountain passes in the states, which has been increasing consistently. Downgrade truck crash rates are shown along with crash rates on upgrades. It can be seen that the downgrade rates increased over the reporting period while upgrade truck crash rates decreased slightly. To address the precarious situation of truck drivers, it is important to study the causal factors relating to downgrade truck crashes and their severity on mountainous roads. There undeniably have been several studies that have incorporated geometric variables that resulted in safety improvements with regards to geometric design, e.g., Karlaftis and Golias (2002), Venkataraman et al. (2014). However, such studies have mainly focused on level sections and mostly did not consider the exclusive effects downgrades have on crashes. This study was undertaken to identify underlying factors contributing to truck crash frequency and severity by analyzing only downgrade crashes. This study will help to alleviate the frequency and severity of truck crashes by providing an insight into roadway characteristics and provide recommendations that may contribute to a safer environment for drivers who have to traverse the state. Traffic crashes occur due to a host of different contributory factors such as driver (94%), vehicle (5%), and environment (1%) (Singh, 2015). Previous studies have also indicated that roadway geometric characteristics impact drivers’ perception about environmental conditions and consequently impact their driving behavior (Janssen et al., 2006; Milton and Mannering, 1998). It is therefore
Fig. 1 e Truck crash rate trend (US 14). Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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imperative to account for the impact of geometric variables on crash frequency and severity. Different methodological approaches to understand the relationships between crashes and crash factors abound in the literature. The predominant methods are the Poisson and negative binomial models which have been commonly adopted to predict crash frequencies. The Poisson regression model is admittedly superior to the linear regression model. The use of linear regression modeling in crash data analysis has been limited because of the many issues associated with this method when applied to crash data (Jovanis and Chang, 1986). However, the Poisson model restricts the mean to be equal to the variance; a phenomenon which is hardly observed in crash data. In most crash data, the variance of crash frequency exceeds the mean and in such cases, the data is said to be overdispersed (Milton and Mannering, 1998). It has also been argued that the use of the Poisson model may underestimate the variances of the estimated coefficients (Lord and Mannering, 2010). Miaou and Lum in an attempt to restrict the effects of overdispersion in their predictive model relaxed the Poisson constraint of the mean being equal to the variance by using the Wedderburn's over dispersion parameter (Miaou and Lum, 1993). The results showed that the use of the Poisson model with over dispersed data leads to erroneous inferences in terms of the probability of crashes because the model may over- or under-estimate the likelihood of occurrence. The negative binomial model which is an extension of the Poisson model has been suggested as an alternative to the Poisson model because of its ability to handle overdispersed data and other statistical issues related to crash data. This is probably the most frequently used model in crash frequency modeling (Lord and Mannering, 2010). Miaou evaluated the performance of Poisson, negative binomial, and zero-inflated Poisson regression models by investigating the relationship between truck crashes and geometric characteristics of road sections (Miaou, 1994). The study found that grade, AADT, percent trucks, horizontal curvature, and yearly dummy variables, which account for year-to-year changes in the overall truck accident involvement, all have a significant effect on truck crashes. The study concluded that using the maximum-likelihood procedure, all three models have consistent parameter estimates. The study however concluded that the negative binomial model performs better in estimating the frequency of road sections with zero truck crash involvement. Shankar and Mannering used Poisson and negative binomial distributions to study the effects of roadway geometry and environmental factors on rural accident frequency in the state of Washington (Shankar and Mannering, 1995). The authors modeled frequencies of specific types of crashes (overturns, fixed objects, parked vehicles, fixed objects, and same direction crashes). They argued that separate regressions of specific crash types provide valuable information. Another research carried out by Milton and Mannering developed crash prediction models using data from principal arterials in Washington State (Milton and Mannering, 1998). The negative binomial model was used to assess the effects
3
of geometric variables on crash frequency. Traffic and several geometric variables were included in the various models developed. The authors suggested that the negative binomial regression tool is a powerful predictive tool which should be used in future studies. Poch and Mannering estimated negative binomial models of crash frequencies at intersection approaches from 63 intersections in Bellevue, Washington. To better identify the most significant traffic and geometric elements that determine crash frequencies at intersections, separate models were developed for total, rear end, angle and approach-turn crashes (Pock and Mannering, 1996). Dong et al. conducted a study to identify the impacts of different roadway geometric design features on truck-related crash frequency. The factors were investigated across different collision vehicle types. The results indicated that traffic, truck percentage, segment length, and posted speed limit are some of the factors that influence truck crashes, regardless of collision type (Dong et al., 2016). Guevara et al. modeled fatality and injury crash outcomes using a simultaneous negative binomial crash model. The writers argued that the three crash categories were unrelated and shared observable characteristics in the error term, such as omitted variables, measurement errors, and random errors. However, it was found that estimation problems prohibit the simultaneous estimation of injury and property damage only (PDO) crashes. Therefore, fatal and injury were modeled together with a separate model developed for PDO (Guevara et al., 1997). Another justification for developing a separate model for PDO crashes was that highway agencies are more interested in crashes with severe injuries. Other studies have considered methodological approaches such as logistic regression (Chen et al., 2016), multinomial regression (Agbelie, 2016; Zeng et al., 2017), non-linear models (Mustakim and Fujita, 2011; Zegeer et al., 1978), and empirical Bayesian methods (Hauer et al., 2002). Agbelie investigated contributory factors to crash frequency and injury severity using random-parameters negative binomial and multinomial models (Agbelie, 2016). The study found that an increase in the number of combination trucks is associated with a decrease in crash frequency. However, the presence of combination trucks increased the crash severity once a crash occurred. Also vertical grades greater than 5%, rolling terrain, lane width, increase in urbanization were found to increase the probability of crash injury severity while the presence of stop signs, and wider median widths had the reverse effects. Fitzsimmons et al. evaluated large truck crashes at horizontal curves on two-lane rural highways on Kansas using odds ratio analysis. They found that significant differences exist among single- and multiple-vehicle, and truck-involved crashes (Fitzsimmons et al., 2013). The literature review highlighted the importance of contributory factors to different crash types. It also justified separating different crash injury levels. Although much research incorporated roadway geometric designs in their analyses, the authors found no study that used only downgrade crash data to identify the contributory factors of downgrade truck crashes. Therefore, this study was set forth
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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to identify contributory factors of influence to downgrade truck crashes in Wyoming.
2.
Method
Poisson regression model is the most widely used model for count data (SAS Institute, 1985). This model is based on the assumption that the response is Poisson distributed. This distribution models the probability of discrete events (truck crashes for this study), according to the Poisson process as follow. P Yi ¼ yi jxi ¼
y em mi i
yi !
yi ¼ 0; 1; 2; …
(1)
where Y is the number of crashes, and m is the mean number of crashes. If the number of crashes is assumed to be Poisson distributed, the relation can be defined as follow (Hadi et al., 1995). PðY ¼ Yi Þ ¼
emðxi ;bÞ ½mi ðXi ; bÞyi Yi !
(2)
where Yi is the number of observed crashes, b is a vector that denotes a set of parameters to be estimated, mi ðXi ; bÞ is the mean of the number of crashes on road section, Xi is a vector that represents the value of regression variables for highway section i. Eq. (2) is based on Poisson distribution, which assumes the variance to be equal to the mean. When overdispersion is present, using Poisson regression would result in the variance of the parameters to be inconsistently estimated (Hadi et al., 1995). The negative binomial distribution can be written as follow. G yi þ a1 f yi jxi ¼ yi Gða1 Þ
a1 a1 þ mi
a1
mi a1 þ mi
(3)
Under Eq. (2), the negative binomial distribution is derived as a gamma mixture of Poisson random variable with conditional mean of E and variance of Var. E yi jxi ¼ mi
(4)
1 Var yi jxi ¼ mi 1 þ mi ¼ mi ð1 þ ami Þ > mi q
(5)
When overdispersion is present, the conditional variance exceeds the conditional means (Eq. (5)). Negative binomial can be used to address this overdispersion (SAS Institute, 1985). The negative binomial model can be written as follow (Guevara et al., 1997). l ¼ exp bX0i þ ei
(6)
where exp (ei ) is a gamma-distributed error term, l is the dependent variable, while X0 is the different geometry and traffic explanatory variables. A p-value smaller than or equal to 0.05 was used as a criteria to maintain variables in the models. The Akaike information criteria (AIC) was used to indicate the best fit model. The AIC is defined as AIC ¼ 2lnðmaximum likelihoodÞ þ 2k where k is the number of estimated parameters.
(7)
The model includes the maximum likelihood value in each subset model output. The smaller the AIC, the smaller the maximum likelihood, which indicate a better model. To examine the implications of the significant variables, elasticities could be computed to determine the marginal effects of the variables. Elasticities measure the effect of a variable on the expected frequency and are taken as the effect of a 1% change in the variable on the expected frequency (Washington et al., 2011). Elasticity is computed as 00
EIxj ¼
vl0 Xj 00 l0 vXj
(8)
where EI is elasticity of the jth independent variable with respect to crash frequency, X}j is magnitude of the variable under consideration, l0i is expected crash frequency estimated from regression model. An elasticity value greater than 1 corresponds in a proportional manner to changes in the response variable. Elasticity values less than 1 indicate an inelastic variable. The research objective of assessing the geometric factors relating to downgrade truck crash injury severity and frequency on mountain pass roads in Wyoming was achieved by the following methodology. In the early stages of the study, data was collected for the horizontal and vertical geometric features on all rural two-lane highways in Wyoming from the WYDOT database. The vertical geometric dataset was examined to determine the locations that require special attention by road users as defined within the Manual on Uniform Traffic Control Devices (MUTCD). Thereafter, crash data and geometric features were extracted for each of the identified section and collected in a database. Three models were then developed with the various geometric characteristics of the roadways and traffic information as the explanatory variables. The explanatory variables were related to the severity of crashes including PDO crashes, fatal/injury crashes, and total truck crashes. Significant predictors identified from the models for various severity levels were assessed to quantify the causal factors and variables that influence the risk of truck crash severity on mountainous downgrades. Recommendations for reducing the crash frequency on mountainous downgrades are presented based on the results of the study.
3.
Data preparation
The first step in the data preparation involved the identification of hazardous downgrade sections. The MUTCD specifies grade and length combinations that are deemed unsafe to trucks in terms of braking ability and crash risks. The combination of downgrade length and grade requiring extra attention are (Federal Highway Administration, 2012). A five percent (5%) grade that is more than 3000 ft. (914.4 m) in length. A six percent (6%) grade that is more than 2000 ft. (609.6 m) in length. A seven percent (7%) grade that is more than 1000 ft. (304.8 m) in length.
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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An eight percent (8%) grade that is more than 750 ft. (228.6 m) in length. A nine percent (9%) grade that is more than 500 ft. (152.4 m) in length. Geometric data was obtained from WYDOT for mountain passes in Wyoming. Mileposts (MP) and elevations from the vertical alignment data were used to compute grades for each route. The gradient between two mileposts was computed as Gradient ¼
Elevationi Elevationði1Þ 100 MPi MPði1Þ
(9)
Graphical plots were then generated for each route to help identify grades that met the criteria set out in the MUTCD. Fig. 2 shows a typical plot of the grades on a Wyoming highway, Main Line (ML) 36. A compound grade was then computed sections identified. A total of 157 sections were identified as downgrades important to this study. Crash data was extracted from the Critical Analysis Reporting Environment (CARE) package from 2005 to 2015. Crashes that occurred one mile beyond the end of the downgrade were included with crashes within the downgrade section as recommended by the Grade Severity Rating System (GSRS) Users’ Manual. This was done to account for runaway truck crashes attributable to the downgrade that occurred beyond it (Bowman, 1989). The CARE package generated crash reports that enabled extractions and analysis of crashes for the identified locations. Geometric data obtained from WYDOT was merged with the crash database.
4.
Exploratory data analysis
The study area consists of 192 miles of downgrades made mainly of two-way lanes. Data were aggregated based on the criterion discussed by MUTCD. The data included different characteristics related to various geometric variables and traffic. The data set contains over 20 columns of traffic and geometry variables such as horizontal curve length, average of crest curve and number of sag curve. A complete list of
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variables along with their descriptive analysis is presented in Tables 1 and 2. Table 2 shows the descriptive statistics for the major, noncontinuous variables used in the study. As can be seen from Table 2, PDO crashes constituted a large portion, 62 percent of all downgrade truck crashes, while fatal/injury crashes consisted of 38 percent. This difference indicates that on average a truck crash on a downgrade would likely result in an injury/fatality about 40 percent of the time. This underscores a severe risk undertaken by truck drivers who traverse mountain passes. Non-continuous variables such as number of lanes, presence of passing lane and presence of warning signs were also quantified and presented below.
5.
Estimation results
The negative binomial models were estimated for total, PDO, and fatal/injury crash frequencies. The dispersion parameters for all the three crash frequency models are statistically significant and point to the inherent over dispersed nature of the crash data. The following sections present the result of the maximum likelihood estimation of the different types of crash frequency, and severity outcomes.
5.1.
Fatal/injury crash frequency model
There were a low number of observations for fatal crashes. This necessitated the combination of fatal crashes with injury crashes for the estimation of the model. The results for the negative binomial model specification for fatal and injury crash frequency are shown in Table 3. The analysis shows that an increase in the length of the downgrade section leads to a higher number of fatal/injury crashes. This is consistent with other studies (Ahmed et al., 2011; Bowman, 1989; Myers et al., 1981). An increase in the number of lanes was found to be associated with a decrease in the frequency of fatal/injury crashes on downgrades. Some studies found that increasing the number of lanes reduces the frequency of severe injury crashes (Fitzpatrick et al., 2005),
Fig. 2 e Grade profile plot for route ML 36 (US 16). Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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Table 1 e Summary statistics of key variables (continuous variables). Variable Length (mile) Grade (%) Average horizontal curve radius (ft.) Average horizontal curve length (ft.) Horizontal curve length (ft.) No. of horizontal curves Average sag curve length (vertical curve) (ft.) Average crest curve length (vertical) (ft.) No. of sag curves No. of crest curves Lane width (ft.) No. of access points Shoulder width (ft.) Average AADT Average ADTT No. of Lanes
Mean
Std. Dev.
Minimum
Maximum
1.220 6.510 2148.760 946.92 1353.360 8.430 762.670 974.280 2.590 2.610 11.940 0.850 3.620 1203.240 101.290 2.220
1.098 1.337 2303.507 1432.94 172.924 9.251 503.616 662.829 2.496 2.301 1.007 1.307 2.366 1787.311 106.557 0.496
0.150 5.000 0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.000 8.000 0.000 0.000 119.000 9.000 0.000
5.730 9.610 17,178.000 16,445.00 11,459.000 47.000 3000.000 3800.000 15.000 16.000 18.000 6.000 12.000 11,183.000 645.000 4.000
5.2.
Table 2 e Summary statistics of major variables (categorical variables). Category
Variable
Frequency
Percentage (%)
Response
PDO Fatality/injury Total crashes Yes No Yes No
166 102 267 38 119 56 101
62 38 100 24 76 64 36
Passing lane presence Warning sign presence
while others found the opposite to be true (Kononov et al., 2008). The safety in increasing the number of lanes may be attributed to the extra opportunities for vehicles to take evasive action to lessen the severity of the crash. An examination of the computed elasticities show that no variable was elastic (had an absolute value greater than one). However, length and average daily truck traffic (ADTT) had elasticities above 0.5. Specifically, a 1% increase in the length of the downgrade leads to a 0.665% increase in the number of severe downgrade truck crashes. A 1% increase in the number of lanes causes a 0.224% decrease in the number of severe downgrade truck crashes. Finally, a 1% increase in truck traffic is associated with a 0.665% increase in severe truck crashes on downgrades.
PDO crash frequency model
For the PDO crash frequency model, length, horizontal curve length, number of access points, shoulder width, and ADTT were found to be significant (Table 4). The analysis shows that an increase in length, shoulder width and ADTT lead to an increase in PDO crash frequency while horizontal curve length and number of access points are associated with a decrease in PDO crash frequency. Horizontal curves with long lengths were found to decrease the occurrence of PDO crashes. Theoretically, motorists are less likely to be involved in crashes on long horizontal curves due to improved sight distances. An increase in number of access points decreases the occurrence of PDO truck crashes on downgrades. This can be attributed to access points interrupting truck movements due to entering and exiting vehicles that may result in a decrease truck crashes. The association of increasing shoulder width and higher crash frequencies was unexpected. However a review of the literature indicates that wider shoulders appear to result in faster operating speeds (TRB, 2011). The Highway Capacity Manual (HCM) predicts a 1.3e1.7 mile increase in speeds for every 1 ft increase in shoulder width on two-lane highways (TRB, 2010). The association of shoulder width with increasing speed therefore seems to be the reason why the
Table 3 e Negative binomial model estimation of fatal/injury crash frequency model. Variable description Constant Length (mile) Number of lanes Average daily truck traffic (ADTT) Negative binomial dispersion parameter Number of observations Log-likelihood at zero LL (0) Log-likelihood at convergence LL(b) AIC
Estimated parameter
Standard error
t-statistic
p-value
Elasticity
0.5938 0.5115 0.7072 0.0066 0.7679 157 152.2997 144.7260 1.9098
0.7294 0.1233 0.3461 0.0012 0.3590 -
0.814 4.147 2.043 5.184 2.139 -
0.4156 0.0000 0.0410 0.0000 0.0325 -
0.6243 0.2238 0.6651 -
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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Q2
Table 4 e Negative binomial model estimation of PDO crash frequency model. Variable description Constant Length (mile) Horizontal curve length (ft.) Number of access points Shoulder width (ft.) ADTT Negative binomial dispersion parameter Number of observations Log-likelihood at zero LL (0) Log-likelihood at convergence LL(b) AIC
Estimated parameter
Standard error
t-statistic
p-value
Elasticity
1.2178 0.3626 1.654 104 0.2716 0.0887 0.0055 0.6626 157 203.7729 190.751 2.523
0.2893 0.09625 6.598 104 0.1111 0.0462 0.0012 0.2211 -
4.210 3.767 2.506 2.442 1.923 4.473 2.996 -
0.0000 0.0002 0.0122 0.0146 0.0454 0.0000 0.0027 -
0.4426 0.2238 0.2300 0.3211 0.5616 -
Table 5 e Negative binomial model estimation of truck crash frequency model. Variable description Constant Grade length (mile) Horizontal curve length (ft.) Number of access points Shoulder width (ft.) Average daily truck traffic (ADTT) Negative binomial dispersion parameter Number of observations Log-likelihood at zero LL (0) Log-likelihood at convergence LL(b) AIC
Estimated parameter
Standard error
t-statistic
p-value
Elasticity
1.0040 0.4437 1.664 104 0.2460 0.1174 0.0054 0.7765 157 265.1639 235.7594 3.0924
0.2578 0.0967 7.318 104 0.1066 0.0499 0.0013 0.2045 -
3.893 4.586 2.273 2.307 2.350 4.172 3.741 -
0.0001 0.0000 0.0230 0.0211 0.0188 0.0000 0.0002 -
0.542 0.225 0.208 0.425 0.548 -
parameter estimate for shoulder width is positive for this analysis. The elasticity for PDO truck crashes on downgrades shows none of the significant variables is elastic. The analysis indicates that a 1% increase in length, shoulder width and ADTT is associated with 0.442%, 0.321% and 0.562% increase in PDO truck crash frequency on downgrades, respectively. Elasticity for horizontal curve length and number of access points suggests a 1% increase in those variables will result in 0.224% and 0.220% decrease in PDO crash frequency.
5.3.
Truck crash frequency model
The truck crash frequency model was estimated based on the combined injury severity models. The analysis shows that length, horizontal curve length, number of access points, shoulder width and ADTT were statistically significant (Table 5). The results show that length, shoulder width, and ADTT all increase the frequency of truckrelated crashes on downgrades while horizontal curve length and shoulder width decrease crash frequency. The reasons for the effect of these variables on truck crash frequency on downgrades were discussed in the previous sections. The truck crash frequency model was found to be similar to the PDO model. This may be related to the high number of PDO crashes (62%), which dominate the crash data. However, the parameter estimates for the truck crash model were higher for most variables meaning they had higher effects on downgrade truck crashes. The elasticity values showed a similar trend.
Also, the log-likelihood estimates and AIC values show the truck crash model has a better fit to the crash data compared to the PDO crash frequency model.
6.
Conclusions and recommendations
Identification of the contributory factors to downgrade crash frequency is needed to address the high truck crash rate in the state of Wyoming. As no study has been conducted on the evaluation of contributory geometric variables, specifically on downgrades, this study will benefit policy makers and designers to adopt strategies and policies that counter the incidence of truck-related crashes on downgrades. In addition to including only downgrade truck-related crashes, crashes were also analyzed based on their crash severity. This is important as one of the main objectives of WYDOT, highlighted in the Wyoming strategic safety plan, is to reduce the number of severe crashes. The results showed that some variables such as length of downgrade segment, shoulder width and ADTT, have positive coefficients, indicating that these factors are associated with an increase in crash frequency on downgrades and mountain passes. However other factors were found to decrease truck crash severity including length of horizontal curve and number of access points. Based on the results of the analysis, countermeasures can be recommended to different organizations in charge of traffic safety on Wyoming highways, and also drivers to have safer downgrade roads in the state.
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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The study indicated that grade length, shoulder width and ADTT are major factors impacting truck-related crashes and injury frequency on downgrades. These factors may indicate inappropriate driving behaviors on downgrades. It is therefore imperative to install warning signs cautioning truck drivers on the presence of hazardous downgrades and the need to adopt cautious behaviors such as reducing speed and heeding signs. Longer horizontal curve lengths were found to decrease both truck and injury frequencies. Wherever possible on mountain passes, highway designers are encouraged to make the curve lengths long and flat for safe operation of trucks. However, drivers must be cautioned on such sections to discourage speeding. Installation of cable catch-net systems and truck escape ramps should be undertaken at feasible locations on extremely hazardous downgrades. This will decrease severe crashes on the mountain passes in the state. Future studies should explore the interaction of critical vehicle maneuvers and driver actions with geometric variables prior to crashes. As data from sources such as naturalistic driving studies and black boxes become available, these vehicle-geometry and vehicle-driver interaction research is becoming possible.
Declaration of Competing Interest The authors do not have any conflict of interest with other entities or researchers.
Acknowledgments Q3
The Wyoming Department of Transportation (WYDOT) and the Wyoming Technology Transfer (WYT2/LTAP) Center at the University of Wyoming provided extensive resources to assist in the compilation of the data sets used. The authors would like to acknowledge that this work is part of project #RS08216 funded by WYDOT.
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Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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Mahdi Rezapour, PhD, has a few years of working experience as an engineer and project manager. In August 2015, he received his master of science in civil engineering with an emphasis on pavement engineering from the University of North Dakota. He then moved to Wyoming to pursue his PhD in civil engineering with an emphasis on traffic safety at the University of Wyoming. His current research is focused on truck safety and he is currently working for Wyoming Technology Transfer Centre.
Milhan Moomen, PhD candidate, got his BSc. degree from the Kwame Nkrumah University of Science and Technology in Ghana. He then worked for Ghana Highway Authority as a Contracts Engineer. He subsequently received an MSc. from Purdue University in 2016 where he researched on bridge infrastructure management. Currently, he is pursuing a PhD in civil engineering and his research is focused on traffic safety.
Khaled Ksaibati, PhD, P.E., obtained his BS degree from Wayne State University and his MS and PhD degrees from Purdue University. Dr. Ksaibati worked for the Indiana Department of Transportation for a couple of years prior to coming to the University of Wyoming in 1990. He was promoted to an associate professor in 1997 and full professor in 2002. Dr. Ksaibati has been the director of the Wyoming Technology Transfer Center since 2003.
Mustaffa N. Raja, MSc, received his BS degree in petroleum engineering from the University of Wyoming. He received a masters degree in transportation engineering from the University of Wyoming. He currently works as a civil engineer in Wyoming.
Please cite this article as: Moomen, M et al., Predicting injury severity and crash frequency: Insights into the impacts of geometric variables on downgrade crashes in Wyoming, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.04.002
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