Analysis of injury severity of drivers involved in single- and two-vehicle crashes on highways in Ontario

Accident Analysis and Prevention 71 (2014) 286–295

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Analysis of injury severity of drivers involved in single- and two-vehicle crashes on highways in Ontario Chris Lee ∗ , Xuancheng Li Department of Civil and Environmental Engineering, University of Windsor, ON, N9B 3P4, Canada

a r t i c l e

i n f o

Article history: Received 1 February 2014 Received in revised form 4 June 2014 Accepted 6 June 2014 Keywords: Crash Injury severity Car Truck Ordered logit model Heteroscedasticity

a b s t r a c t This study analyzes driver’s injury severity in single- and two-vehicle crashes and compares the effects of explanatory variables among various types of crashes. The study identified factors affecting injury severity and their effects on severity levels using 5-year crash records for provincial highways in Ontario, Canada. Considering heteroscedasticity in the effects of explanatory variables on injury severity, the heteroscedastic ordered logit (HOL) models were developed for single- and two-vehicle crashes separately. The results of the models show that there exists heteroscedasticity for young drivers (≤30), safety equipment and ejection in the single-vehicle crash model, and female drivers, safety equipment and head-on collision in the two-vehicle crash models. The results also show that young car drivers have opposite effects between single-car and car–car crashes, and sideswipe crashes have opposite effects between car–car and truck–truck crashes. The study demonstrates that separate HOL models for single-vehicle and different types of two-vehicle crashes can identify differential effects of factors on driver’s injury severity. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Traffic crashes cause significant losses to society such as life and property losses, medical cost and traffic congestion, etc. In 2010, the numbers of motor vehicle fatalities and serious injuries in Canada were 2227 and 11,226, respectively (Transport Canada, 2012). In the same year, there were 579 fatalities and 2558 serious injuries in Ontario (Ministry of Transportation of Ontario, 2012). In particular, the cost of fatal traffic crashes is enormous. For example, although fatal collisions are less than 1% of reportable collisions in Ontario in 2004, they account for 64% of total social costs or $11 billion (Ministry of Transportation of Ontario, 2007). In addition, collisions involving trucks usually result in more severe injuries. According to Transport Canada (2010), there was an annual average of 8,985 heavy truck casualty collisions in 2010. These collisions represent 7% of all collisions, 18% of fatal collisions and 15% ($3 billion) of the social costs (Transport Canada, 2010). Given this difference in injury severity between light and heavy vehicles, the type of vehicles should be considered as a factor in modeling of injury severity.

∗ Corresponding author. Tel.: +1 519 2533000; fax: +1 519 9713686. E-mail address: [email protected] (C. Lee). http://dx.doi.org/10.1016/j.aap.2014.06.008 0001-4575/© 2014 Elsevier Ltd. All rights reserved.

Furthermore, the effects of vehicle type on injury severity are likely to be different between single-vehicle and multi-vehicle crashes. This is because the impacts of collision with fixed objects on vehicles in single-vehicle crashes are different from the impacts of collision with other vehicles (mostly moving objects) in multivehicle crashes. Due to this difference, injury severity has been analyzed for single-vehicle crashes and multi-vehicle crashes separately (Wang and Kockelman, 2005; Savolainen and Mannering, 2007; Chen and Chen, 2011). However, there were some limitations in the past studies. For two-vehicle crashes, most studies only considered the effects of one vehicle on driver’s injury severity or the highest injury severity of two drivers. However, it is expected that driver’s injury severity is not only affected by characteristics of his/her own vehicle, but also characteristics of a partner vehicle. This is because size and weight may differ between the two vehicles and this difference has differential impacts of collision on each vehicle. Also, there is a lack of study on the comparison of injury severity between single-vehicle crashes and different types of two-vehicle crashes to identify differential effects of the same explanatory variables. Thus, the objectives of this study are to identify the factors that significantly influence on the injury severity of drivers involved in single- and two-vehicle crashes, and to investigate effects of these factors on injury severity using statistical models. This paper is organized as follows: The second section reviews the past studies

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on injury severity and identifies their limitations. The third section describes the data used in this study. The fourth section explains the methods. The fifth section discusses the results of the analysis. The last section draws conclusions based on the findings and makes recommendations.

2. Literature review In order to analyze the effects of various factors on injury severity and predict different levels of injury severity based on the factors, researchers have applied various statistical models including a multinomial logit (MNL) model, a nested logit (NL) model, an ordered logit (OL) or ordered probit (OP) model, a heteroskedastic ordered logit (HOL) model, a generalized ordered logit (GOL) model, a mixed logit (MXL) model, a Bayesian ordered probit model, and a bivariate ordered probit model. The past studies identified the factors affecting injury severity using the above models. The factors are categorized into the following five groups: (1) driver characteristics; (2) vehicle characteristics; (3) road geometric characteristics; (4) environmental characteristics and (5) impact speed. First, driver characteristics include driver demographic factors such as age and gender. Zhang et al. (2000) reported that older drivers are more likely to be killed or seriously injured in traffic crashes than middle-age drivers. Harb et al. (2009) observed that drivers younger than 35 years old are more likely to have evasive actions that will prevent severe injury. In general, females are more likely to face fatal injury than males (Srinivasan, 2002; Kockelman and Kweon, 2002). Some researchers found influence of driver conditions on injury severity. Nassiri and Edrissi (2006) found that driver fatigue increases the likelihood of more severe injuries in truck crashes for two-lane rural highways in Iran using OL model. Similarly, Zhu and Srinivasan (2011) reported that driver fatigue, illness, distraction and unfamiliarity with vehicle significantly increase injury severity. Moreover, Zajac and Ivan (2003) found that drinking and driving can significantly increase the risk of fatal crashes. Use of restraint devices is also associated with injury severity. Bedard et al. (2002) found that seatbelts or helmets significantly reduce injury severity. On the other hand, Srinivasan (2002) found that injury severity in a crash in which an air bag was deployed was higher than a crash in which an air bag was not deployed. This is because air bag is usually deployed at high impact speed where drivers are more likely to be severely injured. Vehicle rollover generally increases injury severity. Khattak et al. (2003) found that rollover leads to more severe injuries in single-truck crashes. Srinivasan (2002) claimed that tripped rollover will result in nearly eight time higher chance of fatal injury for moped riders, compared to non-rollover. Some studies investigated influence of vehicle characteristics on injury severity. Harb et al. (2009) found that truck drivers are more likely to perform evasive actions to avoid crashes compared to passenger car drivers. In addition, since crash injury severity increases with the mass and speed of vehicles (Sobhani et al., 2011) and collision force (Wang and Qin, 2014), collisions with trucks increase injury severity than collisions with passenger cars (Duncan et al., 1998). Xie et al. (2009) found that drivers in SUV and van are less likely to be severely injured than passenger car drivers since larger vehicles can better protect the drivers. On the other hand, Yu and Abdel-Aty (2014) found that the drivers in passenger cars are more likely to be severe injured than the drivers in the other vehicle types. Model year of vehicles is another important factor associated with injury severity as it indirectly reflects vehicle technology. Khorashadi et al. (2005) developed MNL models using a four-year crash data in California and found that 1981 or older model years

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of cars are more likely to cause severe or fatal injury. Similarly, Kim et al. (2012) found that newer vehicles can reduce injury severity in single-vehicle crashes using MXL models. This is mainly due to the advance in vehicle and safety design for newer vehicle models. The effect of road geometry on injury severity has also been examined. Chung (2013) found that fatality is associated with narrower median islands and the fixed object in the median islands increases injury severity. Moreover, Zhu and Srinivasan (2011) found that crashes on roadways with more number of lanes would result in less severe injury. Some environmental factors such as lighting and road surface conditions are also found to be closely related to injury severity. Khorashadi et al. (2005) claimed that crashes in the morning (5:31–8:00) are less likely to result in severe or fatal injury in both urban and rural areas. Rana et al. (2010) found that driver injury severity was lower when crashes occurred on icy road surface than dry or wet road surface. Zhu and Srinivasan (2011) found that crashes in dark but lighted conditions lead to most severe injury, but the injury is less severe on wet road surface. In fact, impact speed has the most dominant effect on injury severity. Krafft et al. (2009) reported that 10% speed reduction before impact can reduce fatal injury of car crashes by 30%. Similarly, Watanabe et al. (2012) and Seyer et al. (2000) also showed that the risk of injury increases with impact speed. However, actual impact speeds are not readily available in most crash reports. Thus, the other variables such as the posted speed limits have been used as proxy variables for impact speed. For instance, Stigson et al. (2011) found that fatal crashes occurred more frequently on the roads with higher speed limit. This is because vehicle speeds increase with speed limits. Martin et al. (2003) found that car weight is associated with the risk of injury since it reflects the speed capability. This indicates that vehicle weight can also be used as a proxy variable for impact speed in modeling of injury severity. Moskal et al. (2007) reported that the risk of injury is higher for motorcycle riders than moped riders due to difference in impact speed between the two wheelers. Thus, vehicle types indirectly reflect the effect of impact speed. To identify unique characteristics of single-vehicle crashes, some studies focused on single-vehicle crashes only. The studies commonly found that injury severity in single-vehicle crashes is associated with driver’s error or abnormal behavior such as distraction, alcohol/drug use, non-seat-belt use and speeding (Kim et al., 2012; Schneider et al., 2009; Xie et al., 2012; Anowar et al., 2012; Peng and Boyle, 2012; Jiang et al., 2013a). On the other hand, some studies focused on two-vehicle crashes only. For instance, Duncan et al. (1998) investigated injury severity of truck-passenger car rear-end crashes using OP model. Zhu and Srinivasan (2011) analyzed injury severity of different collision types of car–truck crashes and found that injury severity was higher for head-on and sideswipe crashes. However, these studies did not report injury severity of the other types of two-vehicle crashes (e.g. car–car and truck–truck crashes). Recently, Abay et al. (2013) considered characteristics of both vehicles involved in twovehicle crashes to estimate injury severity. The study found that lighter vehicle’s driver is more likely to be severely injured than heavier vehicle’s driver. However, it did not examine the difference in injury severity among different types of two-vehicle crashes. Qin et al. (2013) compared injury severity between car–truck and truck–truck crashes but could not find a significant difference in spite of differential impacts of collisions. Jiang et al. (2013b) found that light-truck-involved crashes produced less severe injury than car–car crashes but could not find a significant difference in injury severity between car–car crashes and heavy-truck-involved crashes. Torrão et al. (2014) reported that the engine size of the partner vehicle affects serious injury and fatality in the vehicle. However, the study only considered characteristics of two

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vehicles (e.g. age, weight, speed), but not characteristics of occupants in the vehicles. Some studies found differences in injury severity between single-vehicle and two-vehicle/multi-vehicle crashes. For example, Wang and Kockelman (2005) found opposite effects of several variables such as curb weight, lighting condition, and grade on driver injury severity between single-vehicle and two-vehicle crashes using HOL models. Savolainen and Mannering (2007) found that helmet use is more likely to lower motorcyclist’s fatality for right-angle multi-vehicle crashes, but not fatality of single-vehicle crashes using NL models. Chen and Chen (2011) found that the effects of old drivers and truck cargo defect on injury severity were opposite between the single-vehicle and multi-vehicle truckinvolved crashes using MXL models. Weiss et al. (2014) reported that injury severity of young drivers (15–24) in larger vehicles is higher in single-vehicle crashes but lower in two-vehicle crashes compared to young drivers in smaller vehicles using MXL models. However, these studies focused on a specific two-vehicle crashes (e.g. crashes involving motorcycles or trucks only) or did not clearly show the types of both vehicles involved in each two-vehicle crash. Based on this literature review, it was found that no study has been conducted to comprehensively evaluate injury severity for two-vehicle crashes considering driver characteristics and different types of vehicles involved in crashes, and compare it with injury severity of single-vehicle crashes. Thus, there is a need for more extensive study on characteristics of injury severity of singlevehicle crashes and different types of two-vehicle crashes. 3. Description of data The data used in this study are a five-year (2004–2008) crash record for provincial highways in Ontario provided by the Ministry of Transportation of Ontario (MTO). The data consist of crash data, traffic volume data and road geometry data for roadway segments. The crash data include the information on time of crash, drivers/passengers and types of vehicles involved in crashes, weather/surface conditions at the time of crash, and collision types. Five levels of injury severity are shown as follows (MTO, 2012): - Fatal injury: Person was killed immediately or within 30 days of the motor vehicle collision. - Major injury: Person was admitted to hospital. - Minor injury: Person went to hospital and was treated in the emergency room but was not admitted. - Minimal injury: Person did not go to hospital when leaving the scene of the collision, Includes minor abrasions, bruises and complaints of pain. - No injury: No person was injured. The location of each crash was identified as a roadway segment designated in LHRS (Linear Highway Referencing System) number. MTO’s LHRS data include road geometric characteristics and average traffic volume of each roadway segment. Table 1 summarizes the list of variables included in the data. The values in each variable were categorized based on similarity and the distribution of original data such that there are sufficient samples in each category. This study analyzed single-vehicle and two-vehicle crashes involving at least one injury (driver or passenger). However, there were cases of non-injury drivers in single-vehicle crashes where passengers were injured, but not drivers. Also, there were cases of non-injury drivers in two-vehicle crashes where passengers or the drivers of the partner vehicles were injured. A total of 13,880 singlevehicle crashes and 15,556 two-vehicle crashes have occurred during the five-year period. Due to low frequency of fatality (1.3% of total single- and two-vehicle crashes), fatal and major injuries

were combined into one category of injury severity. Therefore, four injury severity levels were considered in the analysis. In this study, only driver record was selected in each crash because the impact of collision varies with person’s positions in the vehicle. For instance, when a head-on collision occurs, occupants (driver or passenger) in the front seats are more likely to be severely injured than those in the rear seats. By selecting driver records only, the effect of person’s position in the vehicle will be eliminated. The vehicles involved in crashes are classified into the following four categories: passenger car, light truck, heavy truck and others. Light truck includes passenger van, buses, school vehicle, fire vehicle and pickup truck. Heavy truck includes tractor-trailer, tow trucks, and farm tractor. A majority of heavy trucks (70%) are tractor-trailers. Others include motorbike and motorcycle. A majority of other vehicle type (99%) are motorcycles. However, principle variables explaining injury severity were missing in the study data–for instance, actual impact speed, crashworthiness of the car (stiffness, mass and geometry), more detailed classification of restraint systems including load limiters, pre tensioners, and anti-submarining systems, car structure, and type of obstacle. In general, higher impact speed, lower vehicle structural strength, less protection from restraint systems, and more rigid obstacle increase the levels of driver’s injury severity. Due to the absence of these explanatory variables in the data, the study could not account for their main effects and interaction effects with the other variables on driver’s injury severity. The variables in Table 1 can be grouped into direct and indirect variables based on their nature and association with injury severity. Driver characteristics and collision types are considered as direct variables as driver’s physical conditions and the impact of collision on driver’s body are critical factors for injury severity. The other variables are considered as indirect variables because they implicitly reflect the driving environments at the time of crashes. These variables can also capture the effects of the above mentioned missing variables as proxy variables. For instance, higher number of lanes and speed limit of roadway segments reflect that drivers are more likely to travel at higher speeds and they hit the roadside objects with higher impacts if they lose their control. These conditions will result in more severe injury. Thus, number of lanes and speed limit indirectly capture the effect of actual speed of vehicles. Each two-vehicle crash has unique geometric, weather and traffic characteristics, which are common to both drivers involved in the crash. Thus, if both driver records are used, these characteristics will be duplicated in the data. To avoid this duplication, the driver record for only one of two vehicles was randomly selected. Since driver’s citation record was not provided, the driver at fault was unknown. Injury severity is expected to be different among passenger car (C), light truck (L) and heavy truck (H) drivers involved in the same crash due to difference in weights of vehicles and impact of collisions on vehicle bodies. Thus, the driver record was separated into nine data sets as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9)

Car drivers involved in C–C crashes (C–C). Car drivers involved in C–H crashes (C–H(C)). Heavy truck drivers involved in C–H crashes (C–H(H)). Heavy truck drivers involved in H–H crashes (H–H). Car drivers involved in C–L crashes (C–L(C)). Light truck drivers involved in C–L crashes (C–L(L)). Light truck drivers involved in L–L crashes (L–L). Light truck drivers involved in L–H crashes (L–H(L)). Heavy truck drivers involved in L–H crashes (L–H(H)).

The proportions of four injury severity levels in total number of crashes were compared among the 9 two-vehicle crash types. It was observed that when different vehicle categories (i.e. different vehicle size and weight) are involved in crashes, the proportions of

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Table 1 Description of variables. Type of variables

Variable

Description

Crash characteristics

Day of week Time of day Collision types

Weekdays, weekend Daytime (6:00–18:00), nighttime (18:00–6:00) Angle, head-on, rear-end, sideswipe, single vehicle, turning

Driver characteristics

Driver action

Proper action Improper action (e.g. speed too fast, following too close) Normal condition Abnormal condition (e.g. alcohol or drug use, fatigue) Young (≤30), middle1 (31–45), middle2 (46–60), old (61 and over) Female, male Fatal and major injury, minor injury, minimal injury, no injury Not used, used Not ejected from vehicle. Ejected from vehicle

Driver condition Driver age Driver sex Injury Safety equipment Ejection Road geometric characteristics

Speed limit Number of lanes Streams

Median type Shoulder type

Median shoulder width Median width Shoulder width Surface width Terrain type Traffic control

Alignment Road character Pavement material

Posted speed limit (km/h) Number of lanes on the road Single stream Divided highway Core/collector system Grass Other Paved Partly paved Gravel Width of the left side shoulder (m) Width of median on the road (m) Width of the right side shoulder (m) Width of drivable surface excluding medians or shoulders (m) Flat terrain, rolling terrain No signal With signal Others Curved road Straight road Divided road Undivided road Asphalt over concrete All other type (e.g. high class bituminous)

Environmental characteristics

Lighting Weather Road surface condition

Good lighting, dark lighting, other lighting conditions Clear weather, Not clear weather Dry surface, wet surface, all other road surface conditions (e.g. icy surface)

Vehicle characteristics

Vehicle type

Vehicle movement Vehicle age

Passenger car Light truck Heavy truck Other (moped and motorcycle) Going ahead, other vehicle movement Vehicle model years minus year of crash

Traffic volume Truck percentage

Annual average daily traffic (AADT) for roadway segment (vehicles/day) Truck percentage in AADT (percentage)

Traffic characteristics

fatal/major crashes were generally higher for the drivers of smaller and lighter vehicles. Also, when two vehicles in the same categories (i.e. similar vehicle size and weight) were involved in crashes, injury severity was higher for collisions between larger and heavier vehicles. 4. Methods In this study, a heteroscedastic ordered logit (HOL) model was developed to identify the factors contributing to driver’s injury severity. The model accounts for ordinal nature of injury severity levels (i.e. higher level indicates more severe injury) and describes injury severity level as a response variable in a function of explanatory variables. The injury severity level is determined by the following latent measure (Aitchison and Silvey, 1957): Ui∗ = ˇXi + εi where Ui∗ = latent and continuous measure of driver i’s injury severity; ˇ = a vector of coefficient for explanatory variables; Xi = a vector

of explanatory variables associated with driver i and crash; and εi = random error term. In the above equation, the random error term reflects unobserved effects of variables not included in the model on injury severity. In this study, the error term was assumed to follow a Gumbel distribution (a logit model) instead of a normal distribution (a probit model) such that the choice probability has a closed form. This assumption makes the estimation of the coefficients easier. In the conventional ordered logit model, the variance in the error term is assumed to be the same for all observations (i.e. crashes and drivers) or homoscedastic. However, this assumption is violated if the unobserved effects of variables (i.e. error terms) on driver’s injury severity are different for different crashes and drivers. On the other hand, the HOL model allows the error term to vary among observations. Thus, the model can better reflect the variance in unobserved effects of a variable on driver’s injury severity across observations or heteroscedasticity. There are other ordered response models that have also been applied to modeling of injury severity – for example, a generalized ordered logit (GOL) model and a mixed ordered logit (MOL) model.

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Table 2 Parameters of HOL model for single-vehicle crashes. Parameter

Estimate

Pr > t

Intercept Speed limit (km/h) Passenger car (1 = passenger car; 0 = otherwise) Light truck (1 = light truck; 0 = otherwise) Heavy truck (1 = heavy truck; 0 = otherwise) Young (1 = age ≤ 30; 0 = otherwise) Female (1 = female; 0 = male) Safety equipments (1 = with safety equip.; 0 = no safety equip.) Ejection (1 = ejected from vehicle; 0 = not ejected from vehicle) Number of lanes Curved road (1 = curved; 0 = straight)

1.51 0.003 0.32 0.29 0.43 0.05 0.06 −0.64 1.14 −0.02 0.08

<0.0001 0.02 0.001 0.003 <0.0001 0.02 0.01 <0.0001 <0.0001 <0.0001 0.004

Variance Young Safety equipment Ejection

−0.07 −0.78 0.89

0.06 <0.0001 <0.0001

1.52 3.27 −15146 0.02 13277

<0.0001 <0.0001

1 2 Log likelihood at convergence (L*(ˇ)) Log likelihood ratio index (2 ) Number of observations

A GOL model is applied when the relationships between a pair of response groups are different (Long, 1997) (e.g. the relationship between fatal/major and minor injuries is different from the relationship between minor and minimal injury). In spite of different assumptions in the models, Quddus et al. (2010) found that GOL and HOL models equally fitted the observed injury severity data and the results of the two models were consistent. However, the HOL model is more effective than the GOL model in reflecting the effect of missing variables (e.g. actual speed of vehicles) because the effect can be potentially captured by a variance in unobserved effects of proxy (or surrogate) variables (e.g. the posted speed limit). The HOL model can also reflect the difference in variability of effects between direct and indirect variables. A MOL model is analogous to a HOL model in a sense that both models account for heterogeneous effects of a variable on injury level among different observations. Their fundamental difference is a functional specification of choice (or response) probabilities. However, the calculation of choice probabilities using the MOL model requires extensive simulation as the log-likelihood function is described in a multi-dimensional integral (Eluru et al., 2008). On the other hand, the heteroscedastic logit model describes choice probabilities in a one-demensional integral and they can be calculated effectively using Gaussian quadrature instead of simulation (Bhat, 1995; Train, 2002). Thus, the HOL model was chosen in this study. From the observed injury severity levels in crash records, Ui * is determined as follows:

Ui∗ =

⎧ 1 if Ui∗ ≤ 0 (No injury) ⎪ ⎨ ∗

where  (.) = cumulative distribution function of the logistic distribution and  i = standard deviation of driver i’s random error term (εi ). The above parameter ˇ shows the effect of explanatory variables on injury severity. A positive sign of ˇ indicates higher injury severity as the value of the associated variable X increases and vice versa. The variance of driver i’s random error term (i2 ) is described in a function of the variables associated with the variance, Zi , as follows (Wang and Kockelman, 2005): i2 = [exp(Zi )]2 where  = coefficients for variable Zi . The coefficients ˇ and  are estimated using the maximum likelihood method. In the conventional ordered models, the coefficient  is set to zero. If  is statistically different from zero, the variance is significant and thus heteroscedasticity exists for variable Zi . Higher variance indicates higher uncertainty with driver’s injury severity for a given value of the variable Zi (Lemp et al., 2011). 5. Results and discussion HOL models were developed for single-vehicle and two-vehicle crashes separately using SAS 9.2 (SAS Institute, 2012). In SAS, the variable(s) with heteroscedasticity can be specified separately in the “qlim” procedure. Tables 2–5 show significant variables associated with injury severity and their coefficients for the single- and two-vehicle crash models.

1 if 0 ≤ Ui ≤ 1 (Minimal injury)

5.1. Single-vehicle crash model

4 if 2 ≤ Ui ≤ ∞ (Fatal/Major injury)

The model result for single-vehicle crashes shows that all variables except the variance of random effects for young drivers are significant at a 95% significance level as shown in Table 2.

∗ ⎪ ⎩ 3 if 1 ≤ Ui∗ ≤ 2 (Minor injury)

where ’s are thresholds. Then the probability that driver i’s injury severity level is equal to N (=1, 2, 3 or 4), Pi (N), can be calculated as Pi (1) = P(Ui = 1) = P(Ui∗ ≤ 0) = P(ˇXi + εi ≤ 0) = P(εi ≤ −ˇXi ) Pi (2) = P(Ui = 2) = P(0 ≤ Ui∗ ≤ 1 ) = P(εi ≤ 1 − ˇXi ) − P(εi ≤ −ˇXi ) follows: Pi (3) = P(Ui = 3) = P(1 ≤ Ui∗ ≤ 2 ) = P(εi ≤ 2 − ˇXi ) − P(εi ≤ 1 − ˇXi ) Pi (4) = P(Ui = 4) = P(2 ≤ Ui∗ ≤ ∞) = 1 − P(εi ≤ 2 − ˇXi ) In general, the probability Pi (N) can be calculated using the following equation (Wang and Kockelman, 2005): In general, the injury severity is higher on the roads with higher



Pi (N) = 

n − ˇXi i





−

n−1 − ˇXi i



posted speed limit. Higher speed limit implies higher actual speed of vehicle when the crash occurred. Those drivers in vehicles with higher speed are likely to experience higher impact of collision and

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Table 3 Comparison of heavy-truck-involved two-vehicle crash models with car–car crash model. Parameter

C–C

C–H(C)

Estimate Intercept Female Young (≤30) Middle1 (31–45) Middle2 (46–60) Daytime Safety equipments Abnormal condition Improper action Vehicle age Angle Head-on Sideswipe Asphalt over concrete Wet surface Median width (m) Surface width (m) Variance Female Head-on Angle Abnormal condition 1 2 L*(ˇ) 2 No. of observations a

Pr > t

Estimate

C–H(H) Pr > t

Estimate

H–H Pr > t

Estimate

2.33 0.71 −0.24 −0.23 −0.20 −0.29 −1.92 0.16 −0.61 0.01 0.49 1.62 0.53 −0.28 0.13 −0.01 −0.01

<0.0001 <0.0001 0.009 0.02 0.05 <0.0001 <0.0001 0.006 <0.0001 0.05 <0.0001 <0.0001 <0.0001 <0.0001 0.07 0.01 <0.0001

4.52 –a – – – – −2.58 – – – 0.87 3.89 – – – – –

<0.0001 – – – – – <0.0001 – – – 0.006 <0.0001 – – – – –

−0.91 – – – – – −1.19 – −0.81 – 0.81 1.47 – – – – –

0.08 – – – – – 0.02 – <0.0001 – 0.01 <0.0001 – – – – –

0.24 0.69 – –

0.004 <0.0001 – –

– 1.66 0.80 –

– <0.0001 0.001 –

– −0.82 – –

– 0.065 – –

– – – –

0.83 3.22 −5318 0.07 5532

<0.0001 <0.0001

2.05 4.72 −2025 0.06 1757

<0.0001 <0.0001

0.52 3.14 −672 0.05 1757

<0.0001 <0.0001

0.90 2.34 −216 0.04 170

2.15 – – – – – −1.89 0.73 – – – – −0.87 – – – –

Pr > t 0.01 – – – – – 0.02 0.01 – – – – 0.02 – – – – – – – – <0.0001 <0.0001

A variable is excluded due to statistically insignificance of the variable at a 90% significance level.

they are more likely to be severely injured. However, drivers are less likely to be severely injured on the road with higher number of lanes. This is because the roads with higher number of lanes usually have better safety facilities (e.g. well-paved surface) than those with only one or two lanes. Also, drivers can avoid severe collisions when more space is available in the roadway with higher number of lanes. These results are consistent with Zhu and Srinivasan (2011). However, drivers are more likely to be severely injured on curved roads than straight roads due to higher likelihood of losing control and hitting fixed objects on the roadside. Drivers in passenger cars, light trucks and heavy trucks are more likely to be severely injured compared to motorcycle riders. This result contradicts the past studies that motorcycle drivers are more likely to be severely injured than passenger car and truck drivers (e.g. Savolainen and Mannering, 2007). It was observed that motorcycle riders have higher proportion of fatal/major injury but lower proportion of minor injury (the next highest injury severity level) than car and truck drivers. Thus, there was no consistent trend of more severe injury for motorcycle riders. It was also observed that heavy truck drivers sustain higher injury severity than car and light truck drivers. The result of the model also shows that young drivers (≤30) are more likely to be severely injured compared to older drivers (>30) in single-vehicle crashes. This is consistent with the finding of the past studies (e.g. Chang and Yeh, 2007). Thus, they are more likely to make errors and be involved in severe single-vehicle crashes. Compared to male drivers, female drivers are more likely to be severely injured. Safety equipments reduce the injury severity whereas ejection from vehicles increases injury severity. It was observed that the variance of random effects for safety equipments and ejection were significant at a 95% significance level. This indicates that the variance of random effects must be considered in the model. HOL models also provided better model fit than OL models based on higher log likelihood ratio index. The result of variance indicates that there is the largest variance in injury

severity for ejection. This is potentially because injury severity can greatly vary depending on whether drivers are fully or partially ejected and whether ejected drivers hit the fixed objects (e.g. tree) or not. Similarly injury severity significantly varies with safety equipments as the levels of human body protection are different for various types of equipments (e.g. seat belt, helmet, air bag). 5.2. Two-vehicle crash models In the two-vehicle crash models, the effects of variables on injury severity are generally similar to the effects in the single-vehicle crash model as shown in Tables 3–5. Female drivers and no use of safety equipments increase injury severity. Due to rare occurrence of driver’s ejection from vehicles in two-vehicle crashes, ejection was not included in the models. In Table 3, it is interesting to note that young drivers are less likely to be severely injured in two-vehicle C–C crashes than old drivers (>61) unlike single-vehicle crashes. These opposite effects reflect that compared to old drivers, young drivers are more likely to take evasive actions to avoid crashes with another vehicle in high traffic volume conditions where two-vehicle crashes occur more frequently. The result also indicates that old drivers are more susceptible to injury than younger driver groups (≤60) when their vehicles collide with another vehicle. In the C–C crash model, abnormal driver conditions (e.g. alcohol use, fatigue) increase injury severity. However, proper driving actions also increase injury severity of two-vehicle crashes. This reflects that when the driver with proper driving actions is hit by the driver with improper driving actions, he/she cannot usually anticipate the crash occurrence and cannot take actions to avoid crashes. Consequently, this results in the driver’s higher injury severity. Injury severity is also higher for crashes at nighttime than daytime. This reflects that drivers make more errors in poor lighting conditions and they tend to drive faster when traffic volume is low at nighttime. Injury severity is lower for newer vehicles as they

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Table 4 Comparison of light-truck-involved two-vehicle crash models with car–car crash model. Parameter

C–C Estimate

C–L(C) Pr > t

Estimate

C–L(L) Pr > t

L–L

Estimate

Pr > t

Estimate

Intercept Female Young Middle1 Middle2 Daytime Safety Equipments Abnormal condition Improper action Vehicle age Angle Head-on Sideswipe Asphalt over concrete Wet surface Median width (m) Surface width (m) Weekend Undivided

2.33 0.71 −0.24 −0.23 −0.20 −0.29 −1.92 0.16 −0.61 0.01 0.49 1.62 0.53 −0.28 0.13 −0.01 −0.01 – –

<0.0001 <0.0001 0.009 0.02 0.05 <0.0001 <0.0001 0.006 <0.0001 0.05 <0.0001 <0.0001 <0.0001 <0.0001 0.07 0.01 <0.0001 – –

3.67 0.57 –a – – – −2.99 0.22 −0.97 – 0.43 1.61 0.24 – – – – −0.25 0.40

<0.0001 <0.0001 – – – – <0.0001 0.03 <0.0001 – 0.0006 <0.0001 0.03 – – – – 0.004 <0.0001

1.41 0.85 – – – – −1.64 – −1.30 0.03 – 0.95 – – – – – – –

0.001 <0.0001 – – – – <0.0001 – <0.0001 <0.0001 – <0.0001 – – – – – – –

Variance Female Head-on Vehicle age Asphalt over concrete Improper action Sideswipe Abnormal condition

−0.24 0.69 – – – – –

0.004 <0.0001 – – – – –

– 1.16 – – – 0.33 0.26

– <0.0001 – – – 0.007 0.02

0.28 0.69 −0.02 – 0.44 – –

0.01 <0.0001 0.04 – 0.0003 – –

– – – – – – –

0.83 3.22 −5318 0.07 5532

<0.0001 <0.0001

1.29 4.16 −3694 0.06 3132

<0.0001 <0.0001

0.88 3.45 −3113 0.07 3128

<0.0001 <0.0001

0.92 2.78 −657 0.09 639

1 2 L*(ˇ) 2 No. of observations a

2.93 0.38 −0.58 −0.76 – – −2.67 – – – – 1.08 −1.34 – – – – – –

Pr > t <0.0001 0.04 0.003 <0.0001 – – <0.0001 – – – – <0.0001 <0.0001 – – – – – – – – – – – – – <0.0001 <0.0001

A variable is excluded due to statistically insignificance of the variable at a 90% significance level.

have better safety equipments and design features which protect drivers. The type of collisions between two vehicles is significantly related to injury severity of two-vehicle crashes. Angle, head-on and sideswipe collisions produce more severe injury than the other types of collisions (e.g. rear-end, turning) for most two-vehicle crashes. It should be noted that the effects of sideswipe collisions are different between C–C crashes and H–H crashes as shown in Table 3. The result shows that sideswipe collisions between cars result in higher injury severity but sideswipe collisions between heavy trucks result in lower injury severity compared to the other types of collisions. These opposite effects are potentially because when sideswipe crashes occur between heavy trucks, long trailers are more likely to collide each other from the sides whereas drivers in tractors are less influenced by the impact of the collision. Some geometric and environmental factors were also significant for C–C crashes. Injury severity was higher on the road with narrower median and travel lanes, but lower on the asphalt over concrete pavement. Injury severity was also higher in wet surface conditions than the other surface conditions. It was observed that the variance of random effects for head-on collisions was significant at a 95% significance level for the C–C and C–H(C) models. This implies that injury severity of drivers involved in head-on collisions significantly vary among different two-vehicle crashes. Thus, their injury largely depends on the variance in the unobserved effects (e.g. point of impact). The result also shows a significant variance of random effects for angle collisions when car drivers are involved in C–H crashes. This indicates that larger differences in size and weight between two vehicles contribute to greater variation in injury severity of the driver in a smaller and lighter vehicle for multiple crash types.

C–C crashes were also compared with light-truck-involved two-vehicle crashes as shown in Table 4. Similar to heavy-truckinvolved crashes, the effects of nighttime, safety equipments, improper action, and head-on collisions are significant. It was observed in C–L crash models that car driver’s injury severity is higher for angle and sideswipe crashes, not only head-on crashes, than the other crash types unlike light truck drivers. This indicates that car drivers are more vulnerable than light truck drivers in various crash types. The effect of sideswipe collisions was also negative for L–L crashes similar to H–H crashes due to stronger resistance to impacts of collisions with more rigid vehicle body. Table 5 Comparison of L-H crashes between light truck and heavy truck drivers. Parameter

L–H(L) Estimate

Intercept Angle Head-on Safety Equipments Curved Daytime Variance Head-on 1 2 L*(ˇ) 2 No. of observations

4.39 0.74 3.06 −2.59 −1.17 –a 1.02 1.93 4.01 −442 0.09 372

L–H(H) Pr > t <0.0001 0.03 <0.0001 <0.0001 0.0003 – 0.03 <0.0001 <0.0001

Estimate 0.54 – 1.71 −2.00 – −0.67 – 0.70 2.82 −205 0.07 370

Pr > t 0.53 – <0.0001 0.01 – 0.05 – <0.0001 <0.0001

a A variable is excluded due to statistically insignificance of the variable at a 90% significance level.

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293

Table 6 Comparison of two-vehicle crashes among car, light truck and heavy truck drivers. (a) Parameters of HOL model Parameter

Car drivers only

Light truck drivers only

Heavy truck drivers only

Estimate

Pr > t

Estimate

Pr > t

Estimate

Pr > t

Intercept Female Young Daytime Safety equipments Abnormal condition Angle Head-on Sideswipe Asphalt over concrete Median width (m) Surface width (m) Improper action Vehicle age Weekend Undivided Collision with light truck Collision with heavy truck Collision with car

2.55 0.44 −0.08 −0.18 −1.94 0.15 0.43 1.61 0.20 −0.18 −0.01 −0.01 –a – – – 0.70 1.28 N/Ab

<0.0001 <0.0001 0.02 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0002 <0.0001 – – – – <0.0001 <0.0001 −0.19

1.54 0.37 – – −1.47 – 0.14 0.59 – – – – −0.48 0.01 −0.10 0.10 N/A 0.59 0.002

<0.0001 <0.0001 – – <0.0001 – 0.02 <0.0001 – – – – <0.0001 0.03 0.01 0.01 −2.53 <0.0001 −3.00

2.61 – – – −1.78 – – 1.24 – – – – −0.55 – – – <0.0001 N/A <0.0001

<0.0001 – – – <0.0001 – – <0.0001 – – – – 0.0002 – – –

Variance Female Head-on Safety equipments Collision with light truck Collision with heavy truck Collision with car 1 2 L*(ˇ) 2 No. of observations

0.24 1.00 – −0.31 −0.62 N/A 0.99 3.09 −11252 0.11 10412

<0.0001 <0.0001 – <0.0001 <0.0001 – <0.0001 <0.0001

−0.20 0.68 −1.37 N/A – – 0.48 1.69 −4316 0.09 4139

0.039 <0.0001 0.001 – – – <0.0001 <0.0001

– – – – N/A – 0.65 2.63 −1116 0.13 2297

– – –

<0.0001 <0.0001

(b) Marginal effects of partner vehicle types on driver’s injury severity Injury severity

No injury Minimal injury Minor injury Fatal a b

Car drivers (compared to C–C crashes)

Light truck drivers (compared to L–L crashes)

Heavy truck drivers (compared to H–H crashes)

Collision with

Collision with

Collision with

Light truck

Heavy truck

Car

Heavy truck

Car

Light truck

−0.16 0.01 0.12 0.03

−0.30 0.02 0.21 0.06

0.08 −0.02 −0.05 −0.01

−0.25 0.05 0.16 0.04

0.31 −0.10 −0.16 −0.05

0.26 −0.08 −0.13 −0.04

A variable is excluded due to statistically insignificance of the variable at a 90% significance level. A dummy variable is excluded as collisions between same vehicle types are set to the base case.

The result also shows that the variance of random effects for head-on collisions was significant in C–L crash models at a 95% significance level. However, there were more variables with heteroscedasticity for C–L crashes than C–H crashes. This indicates that uncertainty with driver’s injury severity increases with smaller difference in size and weight between two different types of vehicles. Two L–H crash models were compared between light truck and heavy truck drivers as shown in Table 5. The result shows that angle crashes significantly increase light truck driver’s injury severity but not heavy truck driver’s. Since angle crashes also significantly increase car driver’s injury severity but not light truck driver’s as shown in Table 4, angle crashes tend to increase injury severity of drivers in smaller and lighter vehicles only. Alternate HOL models were also developed to analyze effects of partner vehicle types on car, light truck and heavy truck drivers’ injury severity separately as shown in Table 6(a). The effects of explanatory variables on injury severity in these models are generally similar to the results of the previous two-vehicle crash models. The only difference is that these alternative models can capture the effect of partner vehicle types using dummy variables. The base case

in each model is the collision between the same vehicle types (C–C, L–L or H–H). The result shows that driver’s injury severity is higher when the partner vehicle is larger and heavier. It should be noted that the goodness-of-fit is slightly better for these joint models (Table 6(a)) than the separate models (Tables 3–5) as indicated by higher values of log-likelihood ratio index (2 ). This is expected because of a larger sample size. However, these joint models can overlook the differences in effects of the same variable on driver’s injury severity among different types of crashes, which have been identified from the comparison of the separate models.Based on the results of HOL models, marginal effects of these dummy variables were also estimated as shown in Table 6(b). The result shows that the collisions with smaller and lighter vehicles increase the probability of no injury but the collisions with higher and heavier vehicles increase the probabilities of fatal/major, minor and minimal injuries. As expected, the highest positive marginal effect on fatal/major injury was observed for C–H(C) followed by L–H(L) and C–L(C). This verifies that larger difference in size and weight between two vehicles involved in collisions causes more severe damages to a smaller and lighter vehicle.

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6. Conclusions and recommendations This study analyzed driver’s injury severity in single- and two-vehicle crashes using the 5-year crash records in Ontario, Canada. To account for variations in unobserved effects of variables on injury severity among observations, heteroscedastic ordered logit (HOL) models were developed for identifying the association between injury severity and explanatory variables. For two-vehicle crashes, crash records were separated into nine data sets of different combinations of vehicle types considering the differential impacts of the collision on vehicles due to difference in their size and weight. Vehicles were classified into cars, light trucks, and heavy trucks. There are two noteworthy findings in this study. First, there exist significant variances in unobserved effects of variables among different crashes and drivers, and the HOL model which accounts for these effects can better predict driver’s injury severity than conventional ordered logit model. For instance, a variance in unobserved effects of head-on collisions among different two-vehicle crashes was significant. This indicates that injury severity of drivers involved in head-on collisions highly depends on the other factors such as point of impact and collision force. Second, the models developed using separate two-vehicle crash data sets classified by vehicle type can identify important differences in the effects of the same variables on driver’s injury severity, which could have not been observed in a single joint model for all vehicle types. More specifically, young drivers (≤30) are more likely to be severely injured in single-vehicle crashes but less likely to be severely injured in car–car crashes than older drivers (>60). This indicates that young drivers are more likely to drive faster and make errors in low traffic volume conditions but they are more likely to take evasive actions to avoid crashes in high traffic volume conditions when vehicle interactions are more frequent. Also, the effects of sideswipe collisions were opposite between car–car crashes and truck–truck crashes. This is potentially because larger and more rigid vehicle bodies of trucks than cars are more likely to reduce the impact of sideswipe collisions on truck drivers. The study also found that heavy truck drivers are more likely to be severely injured than car and light truck drivers in single-vehicle crashes. However, motorcycle riders did not have consistently higher injury compared to car and truck drivers. As expected, collisions with larger and heavier vehicles increase the probabilities of all levels of injury for drivers in smaller and lighter vehicles involved in two-vehicle crashes. In particular, the probability of fatal and major injury is higher when the difference in vehicle size and weight between two vehicles is greater. Based on the results in this study, some remedial treatments can be suggested to reduce driver’s injury severity. First, median width and surface width are increased and curvature is reduced to lower driver’s injury severity associated with car–car crashes and single-vehicle crashes, respectively. Second, heavy truck drivers and young drivers are educated and trained to take more caution in low traffic volume conditions where they are more likely to drive fast. Third, a special design consideration is needed for undivided roadways with high truck volume to prevent head-on collisions between passenger cars and heavy trucks. There are some limitations in this study. The analysis results and conclusions from this study may not reflect the changes in recent year’s traffic safety circumstances (e.g., legislation changes) in the study area. In addition, principle variables associated with injury severity such as the impact speed and structural strength of vehicles were missing in the study data. Also, since the exact point of impact is unknown, it is still unclear why a variance in injury severity is higher for certain collision types, particularly head-on collisions. In the future studies, it is recommended to apply nonparametric models to predict driver’s injury severity using the

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