Investigating the injury severity of single-vehicle truck crashes in a developing country

Accident Analysis and Prevention 137 (2020) 105444

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Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap

Investigating the injury severity of single-vehicle truck crashes in a developing country

T

Ehsan Rahimia,*, Ali Shamshiripoura, Amir Samimib, Abolfazl (Kouros) Mohammadiana a b

Department of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, IL, USA Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

ARTICLE INFO

ABSTRACT

Keywords: Truck crashes Injury severity Heterogeneity Developing countries Random threshold Random parameters HOPIT

Trucking plays a vital role in economic development in every country, especially countries where it serves as the backbone of the economy. The fast growth of economy in Iran as a developing country has also been accompanied by an alarming situation in terms of fatalities in truck-involved crashes, among the drivers and passengers of the trucks as well as the other vehicles involved. Despite the sizable efforts to investigate the truck-involved crashes, very little is known about the safety of truck movements in developing countries, and about the singletruck crashes worldwide. Thus, this study aims to uncover significant factors associated with injury severities sustained by truck drivers in single-vehicle truck crashes in Iran. The explanatory factors tested in the models include the characteristics of drivers, vehicles, and roadways. A random threshold random parameters hierarchical ordered probit model is utilized to consider heterogeneity across observations. Several variables turned out to be significant in the model, including driver’s education, advanced braking system deployment, presence of curves on roadways, and high speed-limit. Using those results, we propose safety countermeasures in three categories of 1) educational, 2) technological, and 3) road engineering to mitigate the severity of single-vehicle truck crashes.

1. Introduction

kilometer in 2011 (Samimi et al., 2018, 2019). Moreover, according to the World Health Organization (2015), the drivers and passengers of heavy trucks represent 11 % of road traffic deaths in Iran from 2013 to 2014. To propose efficient countermeasures, evidence suggests dichotomizing single-vehicle and multi-vehicle crashes, in general (Chen and Chen, 2011; Dong et al., 2018; Geedipally and Lord, 2010; Lord et al., 2005; Wu et al., 2014) and specific to the trucks (Zou et al., 2017). Dong et al. (2018) highlight the inherent differences between the mechanisms of single-vehicle and multi-vehicle crashes. Focusing specifically on trucks, Zou et al. (2017) finds a substantial difference between factors affecting the injury severity of the incidents in which only a single truck is involved (hereafter, single-vehicle truck crashes) and rest of the truck-involved crashes. Such a dichotomy is also understandable given the distinct nature of the two types of truck-involved crashes. In an incident where a truck and a personal vehicle are involved, the injury severity is most probably controlled by the injuries incurred to the personal vehicle’s driver and passengers. Whereas in a single-vehicle truck crash, for instance when a truck loses control and goes down the hill, the injury severity is merely sustained by the truck driver and the truck passengers.

Road traffic deaths have become a major public health concern worldwide (World Health Organization, 2015). The World Health Organization (WHO) reports that 90 % of road traffic deaths occur in developing countries, even though those countries account for only 54 % of the world’s registered vehicles (World Health Organization, 2015). As the 18th populous nation worldwide with 82 million inhabitants (The World Bank, 2019), Iran has one of the highest death risks caused by road crashes in the world (World Health Organization, 2015). Among various types of road crashes, mitigating the truck-involved crashes is important due not only to the safety of drivers and passengers of the vehicles involved in the accident, but also to its association with the economic development of societies (Zou et al., 2017). Evidence also shows that the former also contributes to the latter. Uddin and Huynh (2017) showed that providing a safe, reliable, and efficient flow of commodities has a positive influence on economic productivity of shippers and carriers. The truck safety improvement efforts become important, especially in contexts like Iran where trucks serve as the backbone of the commodity movement. Per Iran’s Department of Transportation, trucks moved around 89 % of the commodities by ton-

⁎

Corresponding author. E-mail address: [email protected] (E. Rahimi).

https://doi.org/10.1016/j.aap.2020.105444 Received 19 October 2019; Received in revised form 15 January 2020; Accepted 22 January 2020 0001-4575/ © 2020 Elsevier Ltd. All rights reserved.

Accident Analysis and Prevention 137 (2020) 105444

E. Rahimi, et al.

A profound body of literature exists on the injury severity of truckinvolved crashes in general and/or multi-vehicle truck crashes (Azimi et al., 2020; Behnood and Mannering, 2019; Islam and Hernandez, 2013a; Osman et al., 2016; Uddin and Huynh, 2017, 2018; Zhu and Srinivasan, 2011). Despite the high importance of the subject, however, very little is known about the factors affecting the severity of singlevehicle truck crashes. To the best of our knowledge, Naik et al. (2016) and Zou et al. (2017) are among the very few instances in the literature that focus on the severity of single-vehicle truck crash explicitly. However, both studies are based on the context of U.S., and their results may not be transferable to a developing country such as Iran. The present study aims to contribute to the literature by analyzing single-vehicle truck crashes in Iran as a developing country, and disclose the factors characterizing severity of such incidents. Our findings help policymakers to develop more cost-effective safety countermeasures for preventing such crashes and understanding the contextual differences. To the best of our knowledge, this is the first attempt to analyze the injury severity of single-vehicle truck crashes in a developing country. To do so, a random thresholds random parameters hierarchical ordered probit (random thresholds random parameters HOPIT) model was developed to account for the underlying heterogeneity in multiple ways. To the best of our knowledge, the present study is also the first to use the random thresholds random parameters HOPIT formulation for analyzing the severity of truck-involved crashes in general. The rest of this paper is organized as follows: Section 2 reviews the existing literature on the severity of truck involved crashes and highlights the gaps. This section also discusses in more details various insights from the existing literature, including on the necessity of distinguishing between single-vehicle truck crashes and multi-vehicle truck involved crashes. Section 3, then, describes the single-vehicle truck crash data in Iran’s inter-city roads. Next, the model structure and its methodological background are discussed in Section 4. Section 5 presents the estimated results along with a statistical analysis. Finally, the paper concludes with Section 6 to discuss the policy implementation of the study and Section 7 to summarize key findings as well as limitations of the study.

on the severity of truck-involved crashes are not necessarily consistent between different studies, highlighting the significant influence of the context in understanding such factors (Please refer to the last column in Table 1). For instance, Islam and Hernandez (2013b) used U.S. interstates’ truck-involved crash data and found that the severity of crashes increases during the summer. In contrast, Wang and Prato (2019) revealed that the severity of truck-involved crashes decreases during the summers in China. As another example, Osman et al. (2016) showed that a wet surface is associated with less likelihood of serious injuries in truck-involved crashes in the U.S., whereas this factor is found to increase the likelihood of both injuries and fatality in such crashes in China. Thus, current findings and recommendations may not be transferable to developing countries. As another gap in the literature, very few studies have investigated the factors influencing the severity of single-vehicle truck crashes. Although analyzing the truck-involved crashes in general provides valuable insights for policymakers to develop effective countermeasures, the safety countermeasures proposed for multi-vehicle truck-involved crashes may not be adopted to mitigate single-vehicle truck crashes. Zou et al. (2017) found a substantial difference between factors affecting the injury severity of single-vehicle versus multi-vehicle truckinvolved crashes. Naik et al. (2016) is among the very few efforts to explore the severity of single-vehicle truck crashes, explicitly. Focusing on the U.S., the authors found that climate-related variables, road surface condition, and crash types are associated with the severity of single-vehicle truck crashes. 3. Data The present study is conducted using a dataset of intercity truck crashes in Iran. Iran is a developing country with Human Development Index of 0.774 and per capita income of $15,440 (UNDP, 2019) a year. With respect to the vehicle-miles traveled, trucks have traveled around 8 million miles in Iran (WFP, 2019), while this value for the state of Illinois has been around 27.8 million miles in 2014 (FHWA, 2014). Besides, the length of public roads in Iran is around 139 K miles (WFP, 2019), while this value for the state of Illinois is around 146 K miles (FHWA, 2014). The dataset consists of crashes from March 2011 to March 2012 provided by the Iranian Traffic Police. This one-year data has 13,043 single-vehicle truck crash records in two separate files. The first file includes crash-specific variables such as time, location, crash severity, crash type, weather conditions, roadway geometry, roadway surface conditions, and some built environment variables. The second file has information about the people and vehicles involved, such as vehicle type, vehicles’ equipment, and drivers’ socio-demographics. Since the focus of this study is on the single-vehicle truck crashes, only such records are considered. After removing observations with missing values, the final dataset used for model estimation comprises of 4,359 records. Each crash record represents the maximum level of injury severity sustained by the truck driver based on three categories: 1 property damage only PDO, 2 body injury, and 3 fatal. According to the data, 277 records are fatal 6.3 %, 1,530 records are body injury 35.1 %, and 2,552 records are PDO 58.6 %). In the modeling process, the above three injury categories are coded as 0 for PDO, 1 for body injury, and 2 for fatal. Table 2 presents the explanatory variables, cross-tabulated by the injury-severity outcomes. The explanatory variables are classified into five general categories: driver, crashes, truck, roadway, and temporal characteristics. In the table, row percentages are shown next to the PDO, body injury, and fatal severity frequencies in the parentheses. Column percentages are presented in the last column.

2. Literature review Trucks contribute to a large number of severe crashes due to their unique characteristics such as body size, weight, and operating system (Zheng et al., 2018; Zhu and Srinivasan, 2011), and truck-involved crashes, in addition to physical and emotional problems, impose considerable economic losses to the society (Zou et al., 2017). Table 1 presents a summary of previous studies (It should be noted that this table is not an exhaustive review of previous studies, however we tried to provide the majority of studies focusing on truck involved crashes) on the severity of truck crashes, in terms of geographical context, severity categories, the analysis method, and the influential factors. For instance, Al-Bdairi and Hernandez (2017) investigated the severity of run-of-road truck-involved crashes in Oregon, U.S. They found that the presence of curves on the roadway, speeding, lack of control, and fatigue increase the severity of such crashes, while usage of a seatbelt, the existence of median on the roadway, and adverse weather conditions decrease the likelihood of more severe injuries. Zhu and Srinivasan (2011) estimated an ordered probit model using a sample of large-truck crashes in the U.S. to analyze the injury severity of large-truck crashes. They showed that number of lanes, road type, road surface condition, darkness, day of the week, and crash type were associated with the severity of such crashes. In another study, Uddin and Huynh (2018) found road type, road slope, accident type, speed limit, vehicle maneuver, and driver age influential on the severity of HAZMAT truck-involved crashes. Table 1 also highlights a few gaps in the literature. First, studies are mostly focused on the U.S., while developing countries are overlooked. This becomes a serious concern given the fact that the influential factors

4. Method Several methodological approaches are proposed in the literature to 2

3

King County, Washington State, U.S. California, U.S.

U.S.

U.S.

Iowa State, USA

Nebraska, U.S.

Minnesota State, U.S.

New York City, U.S.

Oregon State, U.S.

Ohio State, USA

California, U.S.

U.S.

China

Los Angeles, U.S.

Florida, U.S.

(Chang and Mannering, 1999) (Khorashadi et al., 2005)

(Zhu and Srinivasan, 2011)

(Islam and Hernandez, 2013b)

(Cerwick et al., 2014)

(Naik et al., 2016)

(Osman et al., 2016)

(Zou et al., 2017)

(Al-Bdairi and Hernandez, 2017)

(Uddin and Huynh, 2017)

(Uddin and Huynh, 2018)

(Taylor et al., 2018)

(Wang and Prato, 2019)

(Behnood and Mannering, 2019)

(Azimi et al., 2020)

PDO/ Injury/ Fatal

PDO/ Minor injury/ Sever injury

PDO/ Injury/ Fatal

PDO/ possible injury/ Noncapacitating injury/ Incapacitating injury/ Fatal

PDO/ Minor injury/ Major injury

PDO/ Minor injury/ Major injury

PDO/ Minor injury/ Severe injury

PDO/ Non-capacitating injury/ Capacitating injury/ Fatal

PDO/ Injury/ Severe injury

PDO/ Possible injury/ visible injury/ Sever injury

PDO/ Minor or possible injury / Fatal or major injury

PDO/ Non-capacitating injury/ Capacitating injury/ Fatal

MNL

PDO/ Complaint of pain/ Visible injury/ Major injury PDO/ Minor injury/ Major injury

No

Yes

No

No

No

No

No

Focused on single-vehicle truck crashes explicitly

RORP

Partial proportional odds model RORL

RORL

RORP/ ORP

ML

RORP

No

No

No

No

No

No

No

Spacial GORL, RORL Yes

RORP/ ORP

RORP/ ML

MNL/ ML

RORP

ORP

NL

Model structure

PDO/ Possible injury/ Major injury

Severity categories

Speed limit (↑), Dry surface (↑), Night (↑), Opposite direction crash (↑), Off-the-road crash (↑), no restraint system was used (↑), Speed not involved (↓), Inattention (↓), Male (↓) Number of lanes (↑), Terrain rolling surface (↓), Congested flow (↓), Peak hour (↓), Dawn/Dusk (↑), Rear-end accident (↑), Making turn (↑), Speeding (↑) Interstate roadway (↓), Highway (↓), Number of lanes (↓), Speed limit (↑), Wet surface (↓), Weekday (↓), Dark lighted condition (↑), Rear end accident (↓), Fix-object accident (↑), Over-turn accident (↓), Fire exist (↑) Curved road (↑), Summer (↑), Weekday (↑), Dark (↑), Single-vehicle accident (↑), Over-turn accident (↓), Straight maneuver (↓), Making turn (↑), Lane-change maneuver (↓), Speeding (↑), Age (↑) Speed limit (↑), Snowy surface (↓), Summer (↑↓), Fall (↑), Rainy weather (↑), Peak hour (↓), Evening (↑), Weekday (↑), Dark-unlighted condition (↑), Van involved (↑), Passenger car (↑), Sidewipe accident (↓), Head-on accident (↑), Cargo type (↑), Heavy truck (↑), Age (↑) Curved road (↑), Number of lanes (↑), Snow on road surface (↓), Concrete road (↓), Rainy weather (↑), Temperature (↑), Wind speed (↑), Dark unlighted condition (↓), Fix-object accident (↓), accident with animals (↓), Urban land-use (↓), DUI (↑) Urban major road (↑), Urban minor road (↑), Rural major road (↑),Curved road (↑), Two-lane road (↑), No control (↑), Speed limit (↑), Wet surface (↓), Weather adverse (↑), Peak hour (↓), Day time (↑), Evening time (↓), Single-vehicle accident (↓), On-bridge accident (↑), Large truck (↑) Curved road (↑), Traffic signal (↓), Traffic sign (↓), Single-occupancy traffic flow (↓), Highoccupancy traffic flow (↑), Truck flow (↑), Commercial van (↓), Wet surface (↑), Snowy weather (↓), Rainy weather (↓), Evening time (↓), Dawn (↓), Dusk (↓), Pedestrian involved (↑), Bicycle involved (↑), Truck weight (↑), Service job density (↓), Entertainment land-use (↑) Curved road (↑), The existence of median (↓), Dry surface (↑), Fall/ Winter (↓), Single-vehicle accident (↑), Over-turn accident (↑), Straight maneuver (↑), Lost vehicle control (↑), Using seatbelt (↓), Speeding (↑), DUI (↑), Driver fatigue (↑) Seating position (↓), Traffic volume (↓),Weather adverse (↓), Male (↓), Single-unit truck (↑), Speed limit (↑), Early morning and late night (↑), accident with animals (↓),Curved road (↑), Driver’s age between 55–64 (↓↑), Fix-object accident (↑), Weekday (↓), Number of lanes () Rural road (↑), Non-interstate road (↓), Flat (↓), Speed limit (↑), Weekday (↑), Dark-unlighted condition (↑), Dark-lighted condition (↑), Rear end accident (↓), Fix-object accident (↓), Making turn (↓), Male (↑), Age (↓), The presence of passenger (↓) Summer (↓), Dust storm (↑), Dark light conditions (↑), Fix-object accident (↑), Rollover (↑), Single vehicle (↓), Head on (↑), Sideswipe same direction (↓), Sideswipe opposite direction (↑), Run-offroad (↑), Age 24 or less (↓), Age 65 or up (↑), Female (↑), Safety device used (↓), Drugs or alcohol used (↑), Median width (↑), high-flow of trucks (↑), Flat (↓) Curved road (↑), Wet surface (↑), Weather adverse (↑), Winter (↑), Fall (↑), Summer (↓), Night (↑), Rear end accident (↑), Break failure (↑), Commercial transport (↓), loaded truck (↑) Black driver (↓), White driver (↓), Hispanic driver (↑), Male (↑), Young-aged driver (↓), middleaged driver (↑↓), Drunk (↑), Stopped driver (↓), Proceeding straight driver (↓), Backing (↓), Making U-turn (↑↓), Making left turn (↑↓), Passing another vehicle (↑↓), Sideswipe (↓), Head-on (↓), Hit object (↓), Rear end (↓), Parked motor vehicle (↓), Pedestrian (↑↓), Fixed object (↓), Traffic signals and signs (↑↓), Improper passing (↓), Unsafe lane change (↓), Daylight (↓), Dark – street lights (↑), Weekday (↑↓), Dry surface (↑), Wet surface (↓), Rainy (↑↓), Intersection (↑), Old truck (↑), New truck (↑↓) Dry surface (↑), Local road (↓), Unpaved road (↑), Downhill (↑), Curve Right (↑), The presence of person as a traffic control (↑), Hazardous Material Released (↑), Defected tire (↑), Airbag deployed (↑), Ran Red Light (↑), Asleep or Fatigued (↑), Ill or fainted (↑), Restraint System is not used (↑), Month of Jun (↑), Month of July (↑)

Explanatory variables (effect on the severity)

Notes: NL: Nested logit model, MNL: Multinomial logit model, ML: Mixed logit model, ORP: Ordered probit model, RORP: Random parameter ordered probit model, RORL: Random parameter ordered logit model, GORP: Generalized order probit model. (↑): The presence of a condition (for dummy variables) or increasing a variable (for continuous variables) increase the severity of the accidents. (↓): The presence of a condition (for dummy variables) or increasing a variable (for continuous variables) decrease the severity of the accidents.

Geographical context

Study

Table 1 A summary of studies on the severity of truck-involved crashes.

E. Rahimi, et al.

Accident Analysis and Prevention 137 (2020) 105444

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E. Rahimi, et al.

Table 2 Descriptive statistics of the explanatory variables. a

Explanatory variable

PDO

Total accident Driver characteristics Age Younger (< 30) Middle-aged (30–59) Senior (> 60) Education Middle school and less High school Collage degree and more Accident characteristics Collision type Run-off-road Fixed object Animals Over-turn Truck characteristics Weight Light weight (< 8500 lbs.) Heavy weight (> 8500 lbs.) ABS status Deployed Not deployed Vehicle malfunction Yes No Roadway characteristics Roadway classification Highway Major urban Minor urban Rural Surface condition Dry Wet/ snowy/ icy Geometry condition Flat Horizontal curve Vertical curve Horizontal & vertical curve Number of lanes (each direction) 2 lanes and less More than 2 lanes Speed limit ≤ 90 km/h > 90 km/h Temporal characteristics Season Spring Summer Fall Winter Time of day Daylight Nightlight Dawn/Dusk

2,552

(58.6 %)

1,530

(35.1 %)

277

(6.3 %)

4359

(100 %)

693 1,778 81

(56.07 %) (59.76 %) (54.73 %)

452 1,020 58

(36.57 %) (34.29 %) (39.19 %)

91 177 9

(7.36 %) (5.95 %) (6.08 %)

1,236 2,975 148

(28.36 %) (68.25 %) (3.40 %)

953 1,341 58

(50.30 %) (56.68 %) (59.18 %)

733 863 34

(40.79 %) (36.48 %) (34.69 %)

209 162 6

(11.03 %) (6.85 %) (6.12 %)

1,895 2,366 98

(43.47 %) (54.28 %) (2.25 %)

491 444 226 1,391

(62.87 (75.90 (90.40 (50.71

257 121 22 1,130

(32.91 %) (20.68 %) (8.80 %) (41.20 %)

33 20 2 222

(4.23 (3.42 (0.80 (8.09

%) %) %) %)

781 585 250 2,743

(17.92 %) (13.42 %) (5.74 %) (62.93 %)

940 1,612

(47.50 %) (67.73 %

889 641

(44.92 %) (26.93 %)

150 127

(7.58 %) (5.34 %)

1,979 2,380

(45.40 %) (54.60 %)

98 2,454

(60.87 %) (58.46 %)

51 1,479

(31.68 %) (35.23 %)

12 265

(7.45 %) (6.31 %)

161 4,198

(3.69 %) (96.31 %)

250 3,071

(74.62 %) (76.32 %)

63 788

(18.80 %) (19.60 %)

24 165

(7.16 %) (4.1 %)

335 4,024

(7.69 %) (92.31 %)

655 1,142 610 145

(62.14 (60.62 (53.42 (51.97

343 647 433 107

(32.54 (34.34 (37.92 (38.35

56 95 99 27

(5.31 (5.04 (8.67 (9.68

%) %) %) %)

1,054 1,884 1,142 279

(24.18 %) (43.22 %) (26.20 %) (6.40 %)

2,210 342

(57.60 %) (65.52 %)

1,373 157

(35.78 %) (30.08 %)

254 23

(6.62 %) (4.41 %)

3,837 522

(88.02 %) (11.98 %)

1,782 405 159 256

(60.81 (59.56 (54.83 (55.77

1,034 240 102 154

(35.29 (35.29 (35.17 (33.55

%) %) %) %)

114 35 29 49

(3.89 %) (5.15 %) (10.00 %) (10.68 %)

2,930 680 290 459

(67.22 %) (15.60 %) (6.65 %) (10.53 %)

1,562 1,004

(60.98 %) (55.92 %)

860 659

(33.57 %) (36.65 %)

140 134

(5.45 %) (7.43 %)

2,562 1,797

(58.77 %) (41.22 %)

979 1,573

(58.83 %) (58.37 %)

600 930

(36.06 %) (34.51 %)

85 192

(5.11 %) (7.12 %)

1,664 2,695

(38.17 %) (61.83 %)

671 747 570 564

(58.65 (57.73 (57.11 (61.11

399 456 367 308

(34.88 (35.24 (36.77 (33.37

74 91 61 51

(6.47 (7.03 (6.11 (5.53

%) %) %) %)

1,144 1,294 998 923

(26.24 (29.69 (22.90 (21.17

1,725 701 126

(57.35 %) (61.76 %) (58.33 %)

1,085 368 77

(36.07 %) (32.42 %) (35.65 %)

198 66 13

(6.58 %) (5.81 %) (6.02 %)

3,008 1,135 216

(69.01 %) (26.04 %) (4.96 %)

a

Injury

%) %) %) %)

%) %) %) %)

%) %) %) %)

%) %) %) %)

Fatal

%) %) %) %)

%) %) %) %)

Total

%) %) %) %)

PDO: Property damage only.

model the severity of crashes. Mannering and Bhat (2014) extensively reviewed the application of those methodologies. The crash-injury severity data is ordinal in nature and considering this feature is essential in modeling injury severity (Fountas and Anastasopoulos, 2017; Mannering and Bhat, 2014). Accordingly, traditional ordered probability models (both probit and logit) have been widely employed in the literature (Arvin et al., 2019; Feizi et al., 2019; Eluru, 2013; Jalayer et al., 2018; Khattak and Rocha, 2003; Mergia et al., 2013; Pai and Saleh, 2007; Quddus et al., 2010; Yasmin and Eluru, 2013; Ye and Lord, 2014, 2011). The ordered probit models are more utilized than the ordered logit models since ordered probit models assume a normal distribution for error terms and avoid the estimation difficulties associated with the multinomial probit model (Washington et al., 2010).

The probabilities of ordinal outcomes in the ordered probit model is driven by considering an unobserved variable, y*, which is typically specified as a linear function for each observation (Greene, 2003; Washington et al., 2010), as in Eq. (1). Where X is a vector of explanatory variables, is a vector of parameters to be estimated, and is the error term which is normally distributed across observations with mean = 0 and variance = 1.

y* = X

+

(1)

The dependent variable ( y ) that is observed in the data is defined as in Eq. (2) (Greene, 2003; Washington et al., 2010). Where, µ1, …, µJ 1 are threshhold parameters to be estimated jointly with . 4

Accident Analysis and Prevention 137 (2020) 105444

E. Rahimi, et al.

y= y= y= … y= … y=

term with mean zero and variance one. To estimate the models’ parameters efficiently, we employed a simulated maximum likelihood estimator using Halton sequences rather than random draws (Fountas and Anastasopoulos, 2017; Greene and Hensher, 2010). A practical challenge in ordered models is the interpretation of the effect of explanatory variables for interior-outcome categories (i.e., injury in this study), where this effect could be either positive or negative (Washington et al., 2010). Therefore, marginal effects are computed for each category to reveal the accurate effect of the explanatory variables. The marginal effects are defined for the indicator variables as the change in the estimated probabilities when the indicator variable shifts from zero to one, with all other variables equal to their means (Rahimi et al., 2019b; Nazari et al., 2019; Washington et al., 2010). The marginal effects for continuous variables are computed using Eq. (6) (Greene, 2012; Washington et al., 2010).

0 if y * 0 1 if 0 y * µ1 2 if µ1 y * µ 2 i if

µi

1

y*

J if

µJ

1

y*

µi (2)

The observed variable ( y) corresponds to an integer ordering, and J N (0, 1) , the estimation is the highest ordered integer. Assuming problem is to determine the probability of J for each observation (Greene, 2003; Washington et al., 2010), as shown in Eq. (3). Where (.) is the standard normal cumulative density function.

P (y = 0|X) = P (y = 1|X) =

( X ) ( µ1 X )

( X )

P (y = 2|X) = (µ 2 X ) ( µ1 … P (y = i|X) = (µi X ) ( µi 1 … P (y = J|X) = 1 (µJ 1 X ).

X ) X )

P (y = 0|X) = (X ) X P (y = 1|X) =[ ( X ) X P (y = 2|X) = (µ X ) X

(3)

Traditional ordered probability models have two major constraints. First, the threshold parameters are constrained to be fixed across all the observations. Accounting for heterogeneity of crash data (Azimi et al., 2020; Jin et al., 2018; Rahimi et al., 2019a), this constraint can cause inconsistent estimation of the model parameters (Azimi et al., 2019; Eluru et al., 2008). The random parameters ordered probit model relaxes this constraint and allows the parameters to vary across observations (Greene and Hensher, 2010). Second, traditional ordered probit models assume that the same set of explanatory variables affect all injury-severity outcomes (Fountas and Anastasopoulos, 2017). To relax the constraint, the generalized ordered logit model (Quddus et al., 2010; Wang and Abdel-Aty, 2008) and its extension, the mixed generalized ordered logit model (Eluru, 2013; Eluru et al., 2008; Yasmin et al., 2015) are proposed in the literature. However, the generalized ordered logit models sometimes predict negative probabilities (Fountas and Anastasopoulos, 2017; Greene and Hensher, 2010). In this paper, we adopted random thresholds random parameters hierarchical ordered probit (random thresholds random parameters HOPIT) model as an extension of the HOPIT model. In the context of crash severity, Fountas and Anastasopoulos (2017) showed the superiority of this structure as compared with other ordered probability models. The random thresholds random parameters HOPIT model allows the threshold parameters to be a function of a set of unique explanatory variables (which do not necessarily influence directly the ordinal outcomes) and to vary across observations, while simultaneously allows the explanatory variables that determine the probability of injury-severity outcomes to vary across observations (Fountas and Anastasopoulos, 2017; Greene and Hensher, 2010). Also, this structure assures that the thresholds are positive and ordered which results in predicting positive probabilities (Fountas and Anastasopoulos, 2017; Greene and Hensher, 2010). Considering the random thresholds random parameters HOPIT model assumptions, the threshold parameters (µi ) in Eqs. (1)–(3) are defined as in Eq. (4) (Greene, 2012; Greene and Hensher, 2010). Where, j is the intercept term, z i is the vector of explanatory variables, is the vector of estimable variables in the threshold parameters, j is the standard deviation of the threshold intercept, and uij is a normally distributed term with mean zero and standard deviation one.

µij = µi, j

1

+ exp (

j

+

zi +

j uij )

=

+ wi

X )] (6)

5. Results In order to analyze the crash records, a random threshold random parameters HOPIT model was developed. As it was mentioned in the Section 4, we employed a simulated maximum likelihood estimator using Halton sequences to estimate the parameters and threshold. Previous studies suggested that although, in general, 200 Halton draws provide adequate numerical integrations for parameter stability and accuracy (Bhat, 2003; Kashani et al., 2019; Fountas and Anastasopoulos, 2017; Train, 2009), random threshold random parameters HOPIT model requires 500 Halton draws as it is suggested by Fountas and Anastasopoulos (2017). Thus, this study used 500 Halton draws to estimate all parameters. Also, with respect to the previous literature (Fountas and Anastasopoulos, 2017), we adopted normal distribution functional form for the parameter density function of the estimable parameters. Table 3 presents the estimation results for the random threshold random parameters HOPIT model including parameters, standard deviations, distributional effect of the random threshold and random parameters across observations, t-statistics, and goodness-of-fit measures. All the coefficients are assured to be statistically significant in the model within a 90 % confidence interval. Also, Table 4 lists the marginal effects of each explanatory variable in the model which are complementary to the estimated parameters which help better interpret the results. 5.1. Driver characteristics As shown in Tables 3 and 4, the model indicates that being a younger driver (i.e., aged less than 30 years) increases the probability of body injury and fatal by 0.020 and 0.005, respectively. This is in-line with previous studies that explained it by a gradual improvement in driving experience and skills (Carr et al., 1992; Lee and Li, 2014; López et al., 2014; Wang and Prato, 2019). Besides, this parameter was found to be a fixed parameter across the observations. Also, the education of truck drivers is significant and fixed parameter across the observations. Per the results, when a truck driver has a college degree, the probabilities of injury and fatal crashes are decreased by 0.003 and 0.001, respectively. One possible reason for the result is that less-educated drivers are expected to be more likely to engage in speeding behavior, resulting in more severe crashes. Similar findings are also reported by Tseng et al. (2016) who analyzed the

(4)

The effect of explanatory variables also can vary across observationthen the form of estimable parameters as in Eq. (5): i

(µ

(5)

where is the vectors of the mean of random parameters, is a diagonal matrix of standard deviations, and wi is a normally distributed 5

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Table 3 (continued)

Table 3 Results of the estimated random threshold random parameters HOPIT model. Explanatory variables

Constant Driver characteristics Age Younger (< 30) Education Collage degree and more Accident characteristics Collision type Over-turn (base) Run-off-road Standard deviation of parameter Fixed object Animals Truck characteristics Weight Heavy weight Standard deviation of parameter ABS status Deployed Vehicle malfunction Yes

Random threshold random parameters HOPIT model

Distributional effect of the random threshold and random parameters across observations

Coefficient

t-stat

Below zero

−0.563***

−7.85

0.178***

4.14

−0.027***

−3.45

Threshold covariates Winter Dawn/ Dusk Model Statistics Number of observations Restricted loglikelihood

Above zero

Log-likelihood at convergence McFadden Pseudo Rsquared Number of parameters (p) AIC BIC

Random threshold random parameters HOPIT model

Distributional effect of the random threshold and random parameters across observations

Coefficient

Below zero

t-stat

Above zero

−7228.30 0.16 28 14512.6 14691.23

*, **, and *** mean 90 %, 95 %, and 99 % level of confidence, respectively.

−0.591*** 0.662**

−7.81 2.16

−1.083*** −1.426***

−19.10 −9.80

−0.932*** 0.548***

−10.72 3.68

0.001**

2.10

0.0571***

4.70

Roadway characteristics Roadway classification Highway −0.348*** Major urban −0.082** Minor urban 0.714*** Surface condition Wet & snowy/icy −0.026*** Standard deviation of 0.105* parameter Geometry condition Horizontal curve (base) Straight −0.326*** Vertical curve 0.153** Both horizontal and 0.247*** vertical curve Standard deviation of 0.365** parameter Number of lanes (each direction) More than 2 lanes 0.512*** Standard deviation of 1.580*** parameter Speed limit > 90 km/h 1.913*** Standard deviation of 2.215** parameter Threshold parameters μ0 (normalized to 0) Intercept for μ1 Standard deviation of parameter

Explanatory variables

81.4 %

Table 4 Marginal effects of the random threshold random parameters HOPIT model.

18.6 %

Explanatory variables

PDO

95.5 %

4.5 %

59.78 %

40.22 %

2.45

24.93 %

75.07 %

7.30 6.45

37.29 %

69.71 %

10.24 2.10

19.39 %

80.61 %

5.71 7.65

5.53 %

Fatal

0.020

0.005

0.004

−0.003

−0.001

Accident characteristics Collision type Run-off-road Fixed object Animals

0.065 0.115 0.163

−0.050 −0.100 −0.125

−0.019 −0.033 −0.046

0.122

−0.091

−0.029

−0.001

0.000

0.000

−0.01

0.005

0.002

0.045 0.011 −0.075

−0.037 −0.008 0.061

−0.015 −0.005 0.020

0.004

−0.003

−0.002

0.041 −0.020 −0.027

−0.035 0.012 0.016

−0.019 0.005 0.006

−0.062

0.038

0.011

−0.210

0.164

0.035

a

0.308*** 0.193***

Injury

−0.025

Roadway characteristics Roadway classification Highway Major urban Minor urban Surface condition Wet & snowy/icy Geometry condition Straight Vertical curve Both horizontal and vertical Number of lanes (each direction) More than 2 lanes Speed limit > 90 km/h.

−7.11 2.25 3.18

a

Driver characteristics Age Younger (< 30) Education Collage degree and more

Truck characteristics Weight Heavy weight ABS status Deployed Vehicle malfunction Yes

−8.75 −2.30 5.45 −4.01 1.75

Marginal effects

PDO: Property damage only.

crashes involving large trucks in Taiwan.

94.47 %

5.2. Crash characteristics 0.132** −0.001**

The over-turn crashes are considered as the base of crash types in the model. As can be seen in Table 3, collision with fixed object and collision with animals were found to be fixed parameters that have negative and significant effects on the injury-severity outcomes. The run-off-road crash type is found to have a normally distributed random parameter with a mean of −0.591 and standard deviation of 0.662. our findings support the hypothesis that drivers in those crashes are less likely to sustain severe injuries compared to over-turn crashes. The

2.25 −6.41

4,359 −8649.75

6

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results are in good agreement with Al-Bdairi and Hernandez (2017) who showed that overturning causes more severe injuries in the run-offroad truck-involved crashes. Naik et al. (2016) also argued that hitting fixed objects or animals are found to decrease injury severity in singlevehicle truck crashes. As shown in Table 3, the effect of crash types on injury severity in single-vehicle truck crashes might be different. Per the marginal effects, fixed objects, run-off-roads, and the hitting of animals decrease the likelihood of fatal crashes respectively by 0.033, 0.019, and 0.046.

severe conditions are, in overall, scarce in the U.S., and that drivers who are used to driving in regions with few instances of severe weather conditions might not realize how much caution is truly enough. In Iran, there is heavy precipitation throughout the country during winter seasons which is contextually similar to the weather in Minnesota, U.S. Compared to level and straight roadways, curvy segments on roadways contributed substantially to the severity of injuries sustained by truck drivers in single-vehicle truck crashes. Per the results, straight and level segments of roadways decrease the likelihood of injury and fatal by 0.035 and 0.019, respectively. Besides, the parameters turned out to be constant across observations. Our findings are in good agreement with several previous studies (Islam and Hernandez, 2013a, 2012; Mahmoudzadeh et al., 2019; Naik et al., 2016; Razi-Ardakani et al., 2018; Zou et al., 2017). Moreover, our results indicate that the severity of single-vehicle truck crashes in Iran also varies by types of curves on roadways. The importance of such differences is also emphasized in a study of Wang and Prato (2019) in China. According to Table 3, we found that the presence of both vertical and horizontal curves at the same time is associated with the more severe injuries in single-vehicle truck crashes. As can be seen in Table 4, the probabilities of injury and fatal increase by 0.016 and 0.006, respectively, where both horizontal and vertical curves exist on roadways. Also, this parameter is found to be random across the observations. Furthermore, the presence of vertical curves on roadways is associated with the increase in the probabilities of injury and fatal by 0.012 and 0.005, respectively. It is noteworthy that this parameter is fixed across the crash records, with statistically insignificant standard deviation. With respect to the roadway width, our results uncover a significant relationship between the number of lanes in each direction and the severity of single-vehicle truck crashes. Also, the result shows that this parameter varies across the observations. According to Table 4, crashes occurring on roadways with more than two lanes in each direction are more likely by 0.038 and 0.011, respectively, to be injury and fatal. This is in line with Naik et al. (2016) who showed for Nebraska, U.S. that the likelihood of severe injuries increase on roadways with a higher number of lanes. Also, the model suggests that higher speed limits have higher risk propensity relative to lower speed limits. To be specific, the indicator of speed limits of 90 km/h or higher is found to be a normally distributed random parameter that has a positive and significant effect on the injury-severity outcomes. Per the result, truck drivers in such conditions are more likely to sustain severe injuries. According to Table 4, driving in such condition increases the likelihood of sustaining injury and fatal by 0.165 and 0.035, respectively. Understandably, driving at higher speeds could lead to crashes with more severe outcomes. These results are consistent with previous studies (e.g., Cerwick et al., 2014; Chang and Mannering, 1999; Osman et al., 2016; Zhu and Srinivasan, 2011).

5.3. Truck characteristics With respect to the truck weight, the estimated parameter is found to have a normally distributed random parameter with a mean of -0.932 and standard deviation of 0.548. Also, this parameter has a negative and significant effect on the injury-severity outcomes. Per the result, a driver in a heavyweight truck is less likely to sustain injury and fatal. This is possibly because the heavier- or larger-body trucks can provide more protection to their drivers (Bédard et al., 2002; and Kahane, 2003). Further, due to more restricting rules for the heavy trucks, the drivers tend to involve themselves in more risk compensating behaviors such as avoiding speeding and paying more attention to the roadway surroundings, which result in less severe injury crashes. According to marginal effects, the involvement of a heavy truck decreases the probability of injury and fatal by 0.091 and 0.029, respectively. Also, we found that the deployment of the anti-lock braking system (ABS), as a fixed parameter across the observations, is associated with the reduction of 0.001 in the probability of PDO in single-vehicle truck crashes. According to the marginal effects, however, the results do not reveal any relationship between deploying ABS and injury or fatal crashes. Furthermore, our results show that the presence of vehicle malfunction increases the severity of single-vehicle crashes. As a fixed parameter across observations, this parameter is associated with increases of 0.005 and 0.002 in probabilities of injury and fatal, respectively. 5.4. Roadway characteristics The severity of single-vehicle truck crashes also varies by the location of crashes. The both highway and major urban indicator parameters are found to be constant across observations that have negative and significant effects on the injury-severity outcomes. More specifically, crashes occurring in highways are associated with reductions of 0.037 and 0.015 in probabilities of injury and fatal, respectively. These results are in good agreement with the findings of Zhu and Srinivasan (2011). Also, crashes occurring in major urban roadways decrease the likelihood of injury and fatal by 0.008 and 0.005, respectively. Moreover, the minor urban roadway, as another roadway classification indicator, turned out to be fixed and significant in the severity of singlevehicle truck crashes with a positive sign. Per the result, crashes in minor urban roadways increase the probability of injury and fatal by 0.061 and 0.020, respectively. This is in line with Osman et al. (2016). Regarding road-surface conditions, we found wet and snowy indicator to have a normally distributed random parameter with a mean of -0.026 and standard deviation of 0.105. This result suggests that the truck drivers sustain less severe injuries in around 60 % of crashes on a wet and snowy/icy surface, and higher injury outcomes rest of crashes in such situations. This is in agreement with previous studies (Chen and Chen, 2011; Mousavi et al., 2019a, 2019b; Naik et al., 2016; Parsa et al., 2020; Zhu and Srinivasan, 2011). Osman et al. (2016), for instance, evidenced that crashes on wet surfaces in Minnesota, U.S. are associated with lower chances of serious injury compared to no injury. In contrast to such findings, Lemp et al. (2011) found that the presence of snowy or icy road conditions substantially increases the likelihood of fatality in the U.S. The authors justified their result arguing that such

5.5. Threshold covariates The values of thresholds turned to vary across the observations as the function of the two explanatory variables including the winter and the two-way divided roadway indicators which are significant at least within a 90 percent confidence interval. Besides, the intercept of threshold is found to be a normally distributed random parameter with the mean of 0.308 and the standard deviation of 0.193. Since the indicator of winter season has a positive and significant parameter in the threshold function, this variable increases the threshold values and consequently decreases the probabilities of more severe-injury crashes. It might be because the winter season is usually associated with the adverse weather and road surface conditions which might increase drivers’ risk compensation (Fountas and Anastasopoulos, 2017; Russo et al., 2014). Furthermore, the dusk-dawn time of day indicator – which is possibly associated with drivers’ fatigue and the poor visibility (Rowden et al., 2008)– is found to be negatively significant in the threshold function indicating that driving in such conditions increases 7

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the likelihood of more severe crashes across the observations regardless of the effect of the other explanatory variables.

conditions significantly affect the severity of single-vehicle truck crashes. According to the results of random parameters, the presence of a wet/snowy road surface increases ends up in lower injury outcomes in around 60 % of intercity crashes in Iran, and more severe injuries in rest of crashes occurred in wet/snowy conditions. The marginal effects are also computed to understand which factors are associated with a higher probability of severe injuries. Accounting for the marginal effects of significant variables in the model as well as contextual characteristics of Iran, we proposed several safety countermeasures comprising educational, technological, and road engineering. The proposed countermeasures help transportation authorities to mitigate the severity of single-vehicle truck crashes. Also, the results of the model provide knowledge of the potential risk factors influencing the severity of such crashes to be presented in future educational programs. Like any other research, this study has some limitations and could be further improved through future work. As the data used in this study cover a relatively old period (March 2011–March 2012), there could be a temporal instability associated with the data which may negatively affect the reliability of the model and results (Behnood and Mannering, 2019, 2015; Mannering, 2018; Mannering and Bhat, 2014). Moreover, we utilized a national-level severity data to investigate single-vehicle truck crashes. Although our geographical context is not diverse in terms of infrastructure, roadway settings and traffic law, the possible effect of special instability of the model as it mentioned in (Mannering, 2018; Mannering and Bhat, 2014) should be considered for the interpretation of the results.

6. Policy implementation This section is dedicated to proposing countermeasures for improving the safety of truck movements in Iran and other contexts like Iran and discussing how using models transferred from developed countries could mislead the analyst. Based on the results of this study, our proposed safety countermeasures can be divided into three major categories of: Education, technology improvement, and road engineering. Even though driver’s education is not suggested as an influential factor on the severity of truck-involved crashes in most of the studies for the U.S., this variable turned out to be significant in our model. Most truck drivers in Iran are less educated and from low-income families. In addition, truck drivers’ licensing procedures do not include professional training programs focusing on unique characteristics of trucks. Thus, educational countermeasures must include updating the truck driver’s licensing procedure. More specifically, professional training programs should be developed and added to the licensing process. More importantly, truck drivers’ knowledge regarding road safety hazards should also be increased through awareness campaigns, media, and mandatory workshops (Ebnali et al., 2019a, 2019b). Also, our model showed that fitting ABS as a safety feature into trucks might reduce the severity of crashes. The presence of this variable in the model highlights another source of difference between Iran and other developed countries like the U.S. The truck manufacturing industry in Iran is highly outdated; essential safety features such as modern braking systems, airbags, electronic stability controls, and speed limiters are not typically fitted to the trucks. Besides, the vehicle malfunction, as another underlying cause of severe single-vehicle truck crashes, indicates another issue in the context of the truck manufacturing industry. In Iran, trucks are used more than their optimal life (the average truck fleet age in Iran is around 20 years old) due to the high ratio of truck to fuel prices (Moradi et al., 2015), causing more risk of safety issues. Accordingly, technological countermeasures must include not only renewal of the old fleet, but also enhancement of the truck manufacturing industry in terms of using safety-features. Finally, in terms of road design characteristics, the results suggested that the amount of speed limit, as well as the presence of curvy segments on roadways, substantially contribute to the severity of singlevehicle truck crashes. Despite developed countries, road safety audit programs in Iran are not effectively implemented especially in the roads where truck volume is high. Also, in Iran, speed limits are mostly established based on roadway types, regardless of other road characteristics such as 85th percentile speed, traffic volume, and crash history. This evidence, along with the statistical model developed in this study, suggested that the road engineering countermeasures should primarily focus on roads design improvementat curves, infrastrucutre monitoring (Abedin et al., 2019; Abedin and Mehrabi, 2019), and the assessment of speed limits on different segments of roadways.

Author contributions The authors confirm contribution to the paper as follows: study conception and design: Ehsan Rahimi, Ali Shamshiripour; data collection: Amir Samimi; analysis and interpretation of results: Ehsan Rahimi, Ali Shamshiripour, Amir Samimi, Abolfazl (Kouros) Mohammadian; draft manuscript preparation: Ehsan Rahimi, Ali Shamshiripour, Amir Samimi. All authors reviewed the results and approved the final version of the manuscript. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Abedin, M., Farhangdoust, S., Mehrabi, A., 2019. Fracture detection in steel girder bridges using self-powered wireless sensors. Proceedings of the In Risk-Based Bridge Engineering: Proceedings of the 10th New York City Bridge Conference. Abedin, M., Mehrabi, A.B., 2019. Novel approaches for fracture detection in steel girder bridges. Infrastructures 4 (3). https://doi.org/10.3390/infrastructures4030042. Al-Bdairi, N.S.S., Hernandez, S., 2017. An empirical analysis of run-off-road injury severity crashes involving large trucks. Accid. Anal. Prev. 102, 93–100. https://doi. org/10.1016/J.AAP.2017.02.024. Arvin, R., Kamrani, M., Khattak, A.J., 2019. The role of pre-crash driving instability in contributing to crash intensity using naturalistic driving data. Accid. Anal. Prev. 132, 105226. https://doi.org/10.1016/j.aap.2019.07.002. Azimi, G., Asgari, H., Rahimi, A., Jin, X., 2019. Investigation of heterogeneity in severity analysis for large truck crashes. In: Present. 98th Annu. Meet. Transp. Res. Board. Washington, D.C.. Azimi, G., Rahimi, A., Asgari, H., Jin, X., 2020. Severity analysis for large truck rollover crashes using a random parameter ordered logit model. Accid. Anal. Prev. 135. https://doi.org/10.1016/j.aap.2019.105355. Bédard, M., Guyatt, G.H., Stones, M.J., Hirdes, J.P., 2002. The independent contribution of driver, crash, and vehicle characteristics to driver fatalities. Accid. Anal. Prev. 34, 717–727. https://doi.org/10.1016/S0001-4575(01)00072-0.

7. Summary and conclusion This study aimed to analyze the severity of single-vehicle truck crashes in Iran as a developing country, where freight movement is crucial for economic development. We used 2011 Iran intercity crash data provided by Iranian Traffic Police and developed random threshold random parameters hierarchical ordered probit model to reveal the factors that contribute to the severity of single-vehicle truck crashes, while accounting for the underlying heterogeneity in multiple ways. Our result suggested that factors including driver age, driver education, collision types, truck weight, ABS deployment, vehicle malfunction, surface conditions, roadway classification, roadway geometry, number of lanes, speed limit, and seasons with adverse weather 8

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