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Modeling and comparing injury severity of at-fault and not at-fault drivers in crashes
Accident Analysis and Prevention 120 (2018) 55–63
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Modeling and comparing injury severity of at-fault and not at-fault drivers in crashes Venkata R. Duddua, Praveena Penmetsab, Srinivas S. Pulugurthaa,
T
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a Civil & Environmental Engineering Department / IDEAS Center, The University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, NC, 282230001, USA b Alabama Transportation Institute, The University of Alabama, 201 7th Avenue, Tuscaloosa, AL, 35487, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Injury severity Crash At-fault Not at-fault Partial proportional odds model Driver
This paper examines and compares the effect of selected variables on driver injury severity of, both, at-fault and not at-fault drivers. Data from the Highway Safety Information System (HSIS) for the state of North Carolina was used for analysis and modeling. A partial proportional odds model was developed to examine the effect of each variable on injury severity of at-fault driver and not at-fault driver, and, to examine how each variable affects these two drivers’ injury severity differently. Road characteristics, weather condition, and geometric characteristics were observed to have a similar effect on injury severity in a crash to at-fault and not at-fault drivers. Age of the driver, physical condition, gender, vehicle type, and, the number and type of traffic rule violations were observed to play a significant role in the injury severity of not at-fault drivers when compared to at-fault drivers in the crash. Moreover, motorcyclists and drivers 70 years or older are observed to be the most vulnerable road users.
1. Introduction Road crashes affect the society in numerous ways; they impede development, pose threat to public health, and result in economic losses. Each year, approximately 1.24 million people are killed, and 50 million people are injured in traffic crashes worldwide (World Health Organization (WHO), 2009). Over the last two decades, researchers have used several methods to analyze and understand the causes of crashes. Undoubtedly, the results have provided valuable insights about the contributing factors related to road geometry, driver characteristics, weather and environment, vehicle features, etc. associated with crash frequency and severity. These insights are useful in selecting and implementing countermeasures that help transportation officials reach the “zero deaths on roads” vision. Since the year 1966, with a 7.2% increase, year 2015 had the largest increase in traffic fatalities compared to year 2014 (Brown, 2016). The early trends of fatalities predicted a similar increase for year 2016. Therefore, there is a need to better understand the causes and factors associated with road crashes. Human factors play a predominant role among various factors associated with crashes (Blanco, 2013). Aberrant driving behavior is a vital human factor that contributes to road crashes; they can be either intended deviations or unforced errors. Deviations of drivers from safe practices are not recommended since they increase the chances of
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getting involved in crashes. Safe practices are put forward as traffic rules by transportation system managers. For example, drivers are required to come to a complete stop at a stop light. Similarly, drivers should be traveling at or below the posted speed limit under ideal conditions. Such kind of traffic rules ensure a smooth traffic flow while ensuring safety on roads. However, drivers deviate from these safe practices and get involved in crashes. For instance, speeding and driving under the influence of alcohol accounted for 58% of the road deaths in the United States in year 2014 (National Center for Statistics and Analysis, 2016). More than 50% of the drivers involved in crashes committed some type of violation (Penmetsa and Pulugurtha, 2017a). To reduce, both, crash frequency and crash severity, a thorough understanding of factors that contribute to crashes and severity of crashes is necessary. Discrete choice models are widely used in traffic safety area to identify the effect of independent variables on dependent variable such as driver injury severity, crash severity, or occupant severity. Wang and Kockelman (2005), Savolainen and Mannering (2007), and Chen and Chen (2011) identified the need for developing separate injury severity models for single-vehicle and multi-vehicle crashes. Further, a study by Abdelwahab and Abdel-Aty (2001) concluded that at-fault drivers are less likely to succumb a severe injury when compared to not at-fault drivers, showing the need for examining these two drivers separately. Penmetsa and Pulugurtha (2017b)
Corresponding author. E-mail addresses: [email protected] (V.R. Duddu), [email protected] (P. Penmetsa), [email protected] (S.S. Pulugurtha).
https://doi.org/10.1016/j.aap.2018.07.036 Received 6 February 2018; Received in revised form 22 June 2018; Accepted 30 July 2018 0001-4575/ © 2018 Elsevier Ltd. All rights reserved.
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Table 1 Frequency of Variables and Categories. Variable
Categories
Not At-Fault (%)
At-fault (%)
Driver Injury Severity (Dependent Variable)
PDO Moderate Injury Severe Injury Rural Urban Dry Wet Water Standing/Moving (WSM) Ice Snow Slush Sand, Mud, Dirt, Gravel (SMDG) Fuel, Oil Other Clear Cloudy Rain Snow Fog, Smog, Smoke (FSS) Sleet, Hall, Freezing Rain/Drizzle (SHFR) Severe Crosswinds (SC) Blowing Sand, Dirt, Snow (BSDS) Other Daylight Dusk Dawn Dark – Lighted Road (DLR) Dark – Road Not Lighted (DRL) Dark – Unknown Lighting (DUL) Other Straight – Level Straight – Hillcrest (SH) Straight – Grade (SG) Straight – Bottom (SB) Curve – Level (CL) Curve – Hillcrest (CH) Curve – Grade (CG) Curve – Bottom (CB) Other Interstate (IN) US Route (USR) NC Route (NCR) State Secondary Route (SSR) Local Street (LS) Public Vehicular Area (PVA) Private Road, Driveway (PRD) Other One-Way, Not Divided Two-Way, Not Divided (TWND) Two-Way, Divided, Unprotected Median (TWDUM) Two-Way, Divided, Positive Median Barrier (TWDPM) Unknown No Access Control Partial Control (PC) Full Control (FC) One Two Male Female < = 18 years 19–25 years 26–40 years 41–55 years 56–70 years > 70 years Passenger Car (PC) Pickup/Light Truck/Van (PLTV) Sports Utility Vehicle (SUV) Bus Truck/Tractor or Truck/Tractor Trailer (TT) Farm Vehicle (FV) Two-wheeler (TW) Other
270,249 (77.33) 77,781 (22.26) 1424 (0.41) 130,068 (37.22) 219,386 (62.78) 289,401 (82.82) 54,740 (15.66) 1560 (0.45) 1601 (0.46) 1565 (0.45) 452 (0.13) 68 (0.02) 8 (< 0.01) 59 (0.02) 252,372 (71.82) 60,652 (17.36) 32,286 (9.64) 1908 (0.55) 1091 (0.31) 890 (0.25) 30 (0.01) 15 (< 0.01) 210 (0.06) 283,238 (81.05) 8060 (2.31) 4097 (1.17) 29,679 (8.49) 23,931 (6.85) 364 (0.10) 85 (0.02) 268,266 (76.77) 10,597 (3.03) 46,655 (13.35) 2485 (0.71) 11,368 (3.25) 1560 (0.45) 8060 (2.31) 407 (0.12) 56 (0.02) 33,144 (9.48) 62,984 (18.02) 59,108 (16.91) 57,854 (16.56) 133,301 (38.15) 2588 (0.74) 76 1(0.02) 399 (0.11) 14,490 (4.15) 201,622 (57.70) 81,499 (23.32) 51,660 (14.78) 183 (0.05) 246,193 (70.45) 62,615 (17.92) 40,646 (11.63) – – 180,861 (51.76) 168,593 (48.24) 15,568 (4.45) 54,902 (15.71) 108,858 (31.15) 99,583 (28.50) 55,744 (15.95) 14,799 (4.23) 191,833 (54.90) 73,967 (21.17) 67,842 (19.41) 1784 (0.51) 9848 (2.82) 0 (0.00) 3016 (0.86) 1164 (0.33)
303,576 (86.87) 44,286 (12.67) 1592 (0.42)
Location Road Surface Condition
Weather Condition
Light Condition
Road Characteristics
Road Classification
Road Configuration
Access
Number of Violations Committed by Fault Driver Drivers’ Gender Drivers’ Age
Vehicle Type
249,555 (71.41) 88,239 (25.25) 191,893 (54.91) 157,561 (45.09) 35,308 (10.10) 82,604 (23.64) 93,577 (26.78) 69,591 (19.91) 44,503 (12.74) 23,871 (6.83) 200,982 (57.51) 73,730 (21.10) 60,040 (17.18) 979 (0.28) 10,785 (3.09) 4 (< 0.01) 2071 (0.59) 863 (0.25)
(continued on next page)
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Table 1 (continued) Variable
Categories
Not At-Fault (%)
At-fault (%)
Drivers’ Violation
Disregarded Traffic Signs/Signals/Markings (DTS) Exceeded Speed Limit (ESL) Exceeded Safe Speed Limit for Conditions (ESSL) Followed Closely (FC) Improper Maneuver (IM) Improper Passing (IP) Failed to Yield the Right-of-Way (FYRW) Inattention/Distraction (ID) Aggressive/Reckless Driving (ARD) Impaired Driving (IMPD) Crossed Centerline/Going Wrong Way (WW) Other < = 25 mph. 26–45 mph. 46–55 mph. > 55 mph. Apparently Normal Illness Fatigue Fell Asleep, Fainted, Loss of Consciousness (FFLC) Impairment Due to Medications, Drugs, Alcohol (IMDA) Medical Condition (MC) Other Physical Impairment (OPI) Restriction Not Complied with (RNC) Other Undivided Road Rigid Barrier (RB) Continuous Turn Lane (CTL) Paved Mountable (PM) Curb Grass Positive Barrier (POB) Parkland, Business (PB) Couplet Flexible Barrier (FB) Striped Semi-Rigid Barrier (SRB) Flat Rolling Mountainous (MOUN) PC (At-Fault) with PC (Not At-Fault) PC (At-Fault) with PLTV (Not At-Fault) PC (At-Fault) with SUV (Not At-Fault) PLTV (At-Fault) with PC (Not At-Fault) PLTV (At-Fault) with PLTV (Not At-Fault) PLTV (At-Fault) with SUV (Not At-Fault) SUV (At-Fault) with PC (Not At-Fault) SUV (At-Fault) with PLTV (Not At-Fault) SUV (At-Fault) with SUV (Not At-Fault) Other
– – – – – – – – – – – – 5279 (1.51) 205,700 (58.86) 109,097 (31.22) 29,378 (8.41) 348,929 (99.85) 104 (0.03) 31 (0.01) 20 (0.01) 186 (0.05)
20,040 (5.73) 898 (0.26) 6067 (1.74) 135,581 (38.80) 39,054 (11.18) 2598 (0.74) 77,452 (22.16) 45,134 (12.92) 2733 (0.78) 3319 (0.95) 7324 (2.10) 9254 (2.65)
Speed Limit
Drivers’ Physical Condition
Median Type
Terrain
Interactions between At-Fault Driver Vehicle Type and Not At-Fault Driver Vehicle Type
64 (0.02) 62 (0.02) 17 (< 0.01) 41 (0.01) 201,105 (57.55) 6549 (1.87) 40,143 (11.49) 12,482 (3.57) 11,142 (3.19) 49,627 (14.20) 20,628 (5.90) 144 (0.04) 1413 (0.40) 2617 (0.75) 401 (0.11) 3203 (0.92) 67,114 (19.21) 259,604 (74.29) 22,736 (6.51) 113,086 (32.36) 38,985 (11.16) 31,788 (9.10) 40,699 (11.65) 17,583 (5.03) 12,736 (3.64) 38,644 (11.06) 13,759 (3.94) 13,155 (3.76) 29,019 (8.30)
337,901 (96.69) 247 (0.07) 773 (0.22) 1397 (0.40) 7321 (2.09) 1135 (0.32) 285 (0.08) 82 (0.02) 313 (0.09)
The effect of independent variables on injury severity of drivers was well documented in the past. However, past studies on at-fault and not at-fault driver injury severities are comparatively limited. Except Chiou et al. (2013) which focused on crashes at signalized intersections, there is no other notable research on comparing driver injury severity of atfault and not at-fault drivers. The question that remains unanswered is “how does an independent variable effect at-fault and not at-fault driver injury severities in the same crash”. Hence, this study aims to extend the body of knowledge corresponding to driver injury severity of atfault and not at-fault drivers by developing separate injury severity models for both the drivers, and, examining as well as comparing how a given independent variable affects these two drivers differently.
provided insights about how at-fault drivers and not at-fault drivers are affected (in terms of injury severity) by type of traffic rule violation committed by the at-fault driver. However, their study ignored several variables that could influence the injury severity of at-fault and not atfault driver, such as; characteristics of the at-fault and not at-fault driver, type of vehicle of the at-fault and not at-fault driver, road characteristics, etc. Overcoming this limitation, Penmetsa et al. (2017) studied how not at-fault drivers’ injury severity is affected by several crash, vehicle, driver, and other characteristics (includes characteristics of at-fault and not at-fault driver, at-fault and not at-fault vehicle type, at-fault drivers’ violation, etc.). Fararouei et al. (2017) studied human, vehicle, and environmental factors that are associated with at-fault drivers in crashes. Chiou et al. (2013) modeled injury severity of both drivers involved in two-vehicle crashes, simultaneously using a bivariate ordered probit model. Their study used police reported at-fault and not at-fault driver information from the crash database to study crash severity of both drivers. However, their study was constrained to crashes that occurred at signalized intersections.
2. Data North Carolina crash data was requested from the Highway Safety Information System (HSIS) from 2009 to 2013. All the necessary information corresponding to a crash are provided in four different files (accident, road, vehicle, and occupant) which can be joined using the 57
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vehicle closely, failing to yield the right-of-way, and inattention/distraction are the three most frequently violated traffic rules. Passing over a stopped school bus, passing on a hill, passing on curve, etc. are grouped under improper passing category. Overcorrected or oversteered, right turn on red, improper backing or parking or signaling, improper turn, improper lane change, improper lane use, etc. are grouped under improper maneuver category. The percentage distribution of at-fault and not at-fault drivers’ vehicle types remained almost the same. Two-lane divided and undivided roads had around 80% of the two-vehicle crashes. Majority of the twovehicle crashes occurred on roads with speed limits between 26–45 mph. The physical condition of not at-fault drivers is apparently normal 99% of the time, whereas, at-fault drivers are normal 97% of the time. At-fault drivers committed one violation 71% of the time and committed two violations 25% of the time. Roads with rolling terrain accounted for 75%, while interstates accounted for 10% of the two-vehicle crashes.
unique identification number. Between 2009–2013, the combined database had information of 791,245 crashes involving 1,315,059 vehicles that occurred on North Carolina roads. For each vehicle involved in a crash, the crash contributing factor was carefully noted by the police officer after investigation of the crash site or through interviewing the drivers/occupants who were involved in the crash. For example, consider a crash involving two vehicles where one vehicle violated a red light and had a collision with another vehicle which had the right-of-way. The vehicle that had violated the red-light violation will have the crash contributing factor as “disregarded traffic signal” and the other vehicle will be assigned “no contributing factor”. For this study, a driver at-fault or not at-fault is decided based on this contributing factor. In the above example, the driver of the disregarded traffic signal vehicle is at-fault and the other driver is not at-fault of the crash. As mentioned earlier, the objective of this study is to develop injury severity models for at-fault and not atfault drivers, separately, to see how several variables affect injury severity differently. While studying the injury severity of at-fault drivers, characteristics corresponding to not at-fault driver, not at-fault vehicle type, etc. are incorporated in the model as independent variables, to see how they affect the at-fault driver injury severity, and vice versa. To study how one affects the other, there should be at least two vehicles involved in the crash, one being at-fault and the other being not atfault. Among the multi-vehicle crashes, only crashes involving two vehicles can be used for this study. Hence, from the database, only twovehicle crashes were retained and the other crash records (single-vehicle and more than two vehicles involved crashes) were removed from the database. Pedestrian and bicycle crashes were also not considered in this research. The crash database was processed such a way that each row represents a crash. Several characteristics of the crash were considered as independent variables in the model; road, environment, vehicle, and driver characteristics. Table 1 summarizes all the variables and categories that were considered for injury severity analysis. The frequency and percentages are also shown for each variable and category in the Table. Crashes with unknown or unreported information for the variables mentioned in Table 1 were removed from the database. The final dataset for developing the injury severity models consisted of 349,454 crashes (349,454 at-fault and 349,454 not at-fault driver injury severities). The dependent variables in the study are at-fault driver injury severity, and not at-fault driver injury severity. The injury severity is defined as fatal, incapacitating injury, capacitating injury, possible injury, and property damage only (PDO). The injury severity for this study is reclassified into three levels; severe injury, moderate injury, and PDO. Severe injury is created by combining fatal and incapacitating injury, while moderate injury is created by combining capacitating injury and possible injury. About 12.67% and 22.26% of at-fault and not at-fault drivers sustained moderate injuries, respectively. The not at-fault drivers are more likely to succumb moderate injuries when compared to at-fault drivers. The likelihood of resulting in PDO is higher for at-fault drivers when compared to not at-fault drivers. Majority of the two-vehicle crashes (63%, 83%, 72%, and 81%) occurred on urban roads, dry surface condition, clear weather condition, and during daylight condition, respectively. Male drivers contributed to 55% of at-fault drivers and 52% of not at-fault drivers. Driver involved in crashes are classified into six categories; novice (< = 18 years), young (19–25 years), 26–40 years, 41–55 years, 56–70 years, and elderly (> = 70 years). Drivers 26–40 years old accounted for the highest portion of at-fault and not at-fault drivers in the selected crash records. Drivers 41–55 years old are not at-fault more frequently than they are at-fault in the selected crash records. There are more than 30 traffic rule violations under the contributing factor variable. They are reclassified into 12 categories to examine their effect on at-fault and not at-fault driver injury severity. Following
3. Method Savolainen et al. (2011) outlined different methods that were adopted by researchers for modelling injury severity in crashes. The nature of the dependent variable plays an important role in choosing a method for modeling. The levels of injury severity of the driver are ordinal in nature, but the distance between these variables is unknown. A bivariate ordered probit or simultaneous equation joint model is preferred if the injury severity levels of drivers and passengers involved in the same crash are correlated with each other (Savolainen et al., 2011). The joint model is particularly suitable when modeling injury severities of driver and passengers in the same vehicle, when modeling injury severities of drivers involved in the same crash at a location (say, merging areas on freeways), etc., and will help minimize computation of biased parameter estimates (Huang et al., 2008). Therefore, the correlation between injury severity levels of at-fault driver and not atfault driver was first tested. The computed Pearson correlation coefficient between the injury severity levels of at-fault driver and not atfault driver was observed to be low (∼0.3) at a 95% confidence level. Therefore, independent ordered probit models, which are also known as proportional odds models were considered appropriate and developed to evaluate the injury severity of both the at-fault driver and not at-fault driver in this research. The proportional odds model is a class of generalized linear models used for modeling the dependence of an ordinal response on discrete or continuous covariates. This model assumes the effect of the independent variables to be identical across the categories of the dependent variable (proportional odds or parallel lines assumption). Let Y denote response category in the range 1, 2, 3, …., j, with j > 1, and let yk = pr (Y ≤ k / x ) be the cumulative response probability when covariate is held at x. The mathematical formulation of a general linear logistic model for kth response probability is shown as Eq. (1) (McCullagh, 1980). The predicted logits can be transformed to odds and probability using Eq. (2) (Wang and Abdel-Aty, 2008; Williams, 2006).
logit (yi ) = αi−βit x i
P (yi > j ) =
(1)
exp(αi−βit x i ) 1 + exp(αi−βit x i )
(2)
The intercept α and the coefficient β depend on the category ‘i’. However, the proportional odds model is a linear logistic model in which the intercepts depend on ‘i’, but all slopes are equal. Thus, the general form of proportional odds model is shown as Eq. (3). The predicted logits can be transformed to odds and probability using Eq. (4).
logit (yi ) = αi−β t x i 58
(3)
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categories that are observed to be statistically significant at a 95% confidence level (indicated with asterisk “*” sign in the tables) were only included in the final model. The categories of road surface condition variable (water standing/ moving and ice) affect the injury severity of at-fault and not at-fault drivers in the same way. Water standing or moving of road is 1.19 times likely to result in severe injury for both at-fault and not at-fault drivers. Snow is 0.69 and 0.65 times likely to result in a severe injury for at-fault and not at-fault drivers when compared to dry road condition in twovehicle crashes. All the weather conditions have similar effect on atfault driver injury severity. For not at-fault drivers, snow and cloudy weather condition have higher odds when compared to clear weather condition, while rest all are insignificant. Dark and not lighted road are 1.7 and 1.55 times likely to result in severe injury to not at-fault and atfault drivers when compared to daylight condition. On the other hand, dark and lighted roads are 1.28 and 1.31 likely to result in severe injury to not at-fault and at-fault drivers when compared to daylight condition. The type of terrain has similar effect on at-fault and not at-fault driver injury severity. Two-way divided and undivided roads are around 1.31 times likely to result in severe injury to not at-fault driver when compared to one-way roads. For at-fault drivers, the odds are approximately 1.8, indicating that at-fault drivers have higher odds of getting severely injured on two-way roads when compared to not atfault drivers. At-fault drivers’ physical condition influences not at-fault driver injury severity. If at-fault driver fell asleep, fainted, or lost consciousness, they are going to increase the odds of having a severe injury for not at-fault driver by 2.11 times when compared to at-fault drivers’ apparently normal physical condition. At-fault drivers’ falling asleep, fainting, or losing consciousness increase the odds of having a severe injury and moderate injury for at-fault driver by 3.18 times. At-fault drivers’ physical condition influences their own injury severity more than not at-fault drivers’ injury severity. The role of “Other” category (with high odds) in case of not at-fault driver physical condition could not be explored further due to lack of details in the obtained crash database. Vehicle type has a significant effect on their own driver injury severity as well as the other driver injury severity. A not at-fault driver driving a bus and truck are 0.11 and 0.21 times likely to get severely injured compared to a not at-fault driver driving a passenger car, respectively. A not at-fault driver driving a bus and truck are 2.68 and 3.75 times likely to result in a severe injury compared to an at-fault driver driving a passenger car. A not at-fault two-wheeler driver is 40.60 and 27.04 times likely to result in a severe injury and moderate injury to himself/herself when compared to a not at-fault passenger car driver, respectively. A not at-fault two-wheel driver is 0.27 and 0.69 times likely to result in a severe injury and moderate injury to the atfault driver when compared to passenger car at-fault driver. The effect of at-fault drivers’ vehicle types on not at-fault driver injury severity is different than that of a not at-fault drivers’ vehicle type on at-fault drivers’ injury severity. For example, a two-wheeler driver not at-fault is 40.60 times likely to severely injury himself/herself, whereas, a twowheeler driver at-fault is 29.02 times likely to severely injury himself/ herself. An at-fault driver driving a truck and two-wheeler are 2.85 and 0.28 times likely to result in a severe injury for not at-fault driver compared to at-fault driver of a passenger car. The severity of the crash could also depend on the type of vehicles colliding with each other. Therefore, at-fault and not at-fault drivers’ vehicle type interactions between passenger car, pickup / light truck / van, and sports utility vehicle (SUV) were also considered as a variable in the modeling process. The considered nine interactions account for ∼92% of the considered data. The results obtained indicate that atfault drivers are more likely to be moderately injured while driving a passenger car and colliding with a passenger car (not at-fault) compared to most vehicle type interactions considered in this research. The odds of severe injury to at-fault drivers driving passenger car is higher than severe injury to not at-fault drivers driving pickup / light truck /
Table 2 Results of Brant Test for Individual Independent Variables. Variable
Not At-fault
Location Road Surface Condition Weather Condition Light Condition Road Characteristics Road Classification Road Configuration Access Terrain Median Type Speed Limit Fault Drivers’ Physical Condition Not at Fault Drivers’ Physical Condition Fault Drivers’ Gender Not at Fault Drivers’ Gender Fault Drivers’ Age Not at Fault Drivers’ Age Fault Drivers’ Vehicle Type Not at Fault Drivers’ Vehicle Type Fault Drivers’ Violation Number of Violations Committed by Fault Driver Interactions (Fault Drivers’ Vehicle Type VS Not at Fault Drivers’ Vehicle Type)
P (yi > j ) =
exp(αi−β t x i ) 1 + exp(αi−β t x i )
At- fault
Wald ChiSquare
p-value
Wald ChiSquare
p-value
8.28 4.45 7.58 22.69 28.22 27.49 4.75 1.42 0.69 10.40 26.60 10.15 24.46
< 0.01 0.81 0.37 < 0.01 < 0.01 < 0.01 0.31 0.49 0.70 0.49 < 0.01 0.25 < 0.01
21.63 9.16 4.54 11.71 30.45 21.65 6.93 3.76 2.26 18.65 14.13 25.57 19.22
< .0001 0.33 0.71 0.06 < 0.01 < 0.01 0.14 0.15 0.32 0.06 < 0.01 < 0.01 0.01
0.00 4.08 17.13 138.19 5.25 19.88 466.23 39.80
0.97 0.04 < 0.01 < 0.01 0.51 < 0.01 < 0.01 < 0.01
50.55 0.00 99.64 8.07 7.96 12.37 301.05 11.90
< .0001 0.95 < .0001 0.15 0.24 0.05 < .0001 < 0.01
14.78
0.09
30.85
< 0.01
(4)
where yi is the latent and continuous measure of driver’s injury severity in a crash, x i is a vector of explanatory variables, and β is a vector of coefficients to be estimated. Brant test was performed before developing the model to check if the data satisfies the underlying proportionality assumption. Among the independent variables considered, if few failed Brant test, a partial proportional odds model is preferred. The underlying formulation for partial proportional model is same as proportional odds model or generalized ordered logit model, except that variables which failed Brant test will have different coefficients for categories of a dependent variable.
4. Results Independent variables such as road surface condition, weather condition, light condition, road configuration, access, terrain, median type, not at-fault drivers’ gender and age, at-fault drivers’ vehicle type have p-values greater than 0.05 in the proportional odds test for the atfault drivers (Table 2). This indicates that the null hypothesis cannot be rejected for these variables. The null hypothesis for this test is that all the categories of a given dependent variable has only one coefficient. Hence, for these variables, there exist only one coefficient which explains the effect across the categories of the dependent variable. Similarly, independent variables that failed Brant test for not at-fault driver injury severity model are also identified and shown in Table 2. The variables that failed proportional odds assumption were relaxed to have different coefficients for different driver injury severity levels. A partial proportional odds model was developed for driver injury severity of at-fault drivers and not at-fault drivers, separately. The results obtained are presented in Table 3. The reference category of a categorical variable is typically the normal condition. For example, for road surface condition variable, ‘dry’ was chosen as the reference category. All independent variables with a minimum of one or more of its 59
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Table 3 Partial Proportional Odds Model for Not At-Fault and At-Fault Driver Injury Severity. Variable
Road Surface Condition ®-Dry
Weather Condition ®-Clear
Light Condition ®-Daylight
Terrain ®-Flat Road Configuration ®-One Way Not Divided
At-Fault Drivers’ Physical Conditions ®-Apparently Normal
Not At-Fault Drivers’ Vehicle Type ®-Passenger Car
At-Fault Drivers’ Age ®-26-40 years
At-Fault Drivers’ Vehicle Type ®-Passenger Car
Categories
Wet Water Standing/Moving (WSM) Ice Snow Slush Sand, Mud, Dirt, Gravel (SMDG) Fuel, Oil Other Cloudy Rain Snow Fog, Smog, Smoke (FSS) Sleet, Hall, Freezing Rain/Drizzle (SHFR) Severe Crosswinds (SC) Blowing Sand, Dirt, Snow (BSDS) Other Dusk Dawn Dark – Lighted Road (DLR) Dark – Road Not Lighted (DRL) Dark – Unknown Lighting (DUL) Other Rolling Mountainous (MOUN) Two-Way, Not Divided (TWND) Two-Way, Divided, Unprotected Median (TWDUM) Two-Way, Divided, Positive Median Barrier (TWDPM) Unknown Illness Fatigue Fell Asleep, Fainted, Loss of Consciousness (FFLC) Impairment Due to Medications, Drugs, Alcohol (IMDA) Medical Condition (MC) Other Physical Impairment (OPI) Restriction Not Complied with (RNC) Other Pickup/Light Truck/Van (PLTV) Sports Utility Vehicle (SUV) Bus Truck/Tractor or Truck/Tractor Trailer (TT) Two-wheeler (TW) Other < = 18 years 19–25 years 41–55 years 56–70 years > 70 years Pickup/Light Truck/Van (PLTV) Sports Utility Vehicle (SUV) Bus Truck/Tractor or Truck/Tractor Trailer (TT) Farm Vehicle (FV) Two-wheeler (TW) Other
Not At-fault Driver Injury Severity Model
At-fault Driver Injury Severity Model
Severe Injury
Severe Injury
Moderate Injury
0.95* 1.19* 0.69* 0.64* 0.87 0.73 1.43 1.69 1.04* 1.02 0.78* 1.10 1.17
0.97 1.19* 0.65* 0.55* 0.64* 0.40 2.69 2.21* 1.02 0.98 0.85 1.13 0.95
0.32 1.22 0.82 1.50* 1.51 1.28* 1.70* 0.33 0.69 0.95* 0.78* 1.36* 1.31*
0.47 2.37 0.92 1.26 1.67* 1.31* 1.55* 1.60 0.08 0.94* 0.76* 1.89* 1.81*
1.05 1.11* 1.10* 1.22* 1.00 1.00
1.31*
1.88*
1.26 0.96 1.36* 2.11*
1.09 2.43* 1.52* 3.18*
1.58*
1.99*
1.53* 1.38* 1.74*
4.87* 1.51* 2.16*
Moderate Injury
1.02 1.08 1.15* 1.25* 1.21 1.13
1.25 1.29 1.06 0.11* 0.21*
0.89* 0.82* 0.42* 0.44*
2.36* 1.17 0.76 2.68* 3.85*
1.51* 1.22* 2.42* 3.9*
40.60* 1.10 1.05 1.13 0.95 0.74* 1.15 1.29 1.34 2.40 2.85*
27.04* 1.19* 1.01 1.01 1.01 0.99 1.03 1.10 1.17* 1.55 2.00*
0.27* 1.06 0.92 0.90 1.17* 1.36* 2.54* 1.29 1.13 0.001 0.38*
0.69* 1.49* 0.92* 1.0 1.01 1.06* 1.19* 0.91 0.90 0.31* 0.36*
0.61 0.28* 1.86
4.30 0.34* 1.59
– 29.02* 0.90
– 39.9* 1.60*
(continued on next page)
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Table 3 (continued) Variable
Median Type ®-Undivided Road
Access ®-No Access Control At-Fault Drivers’ # Violations ®-One At-Fault Drivers’ Gender®-Male At-Fault Drivers’ Violation ®-Disregarding Traffic Signs/Signals/ Markings
Road Characteristics ®-Straight Level
Not At-Fault Drivers’ Age ®-26-40 years
Location ®-Rural Speed Limit ®-46-55 mph
Road Classification ®-Interstate
Not At-Fault Drivers’ Physical Conditions ®-Apparently Normal
Not At-Fault Drivers’ Gender ®-Male
Categories
Rigid Barrier (RB) Continuous Turn Lane (CTL) Paved Mountable (PM) Curb Grass Positive Barrier (POB) Parkland, Business (PB) Couplet Flexible Barrier (FB) Striped Semi-Rigid Barrier (SRB) Partial Access Control Full Access Control Two Three Female Exceeding Speed Limit (ESL) Exceeding Safe Speed Limit for Conditions (ESSL) Followed Closely (FC) Improper Maneuver (IM) Improper Passing (IP) Failure to Yield the Right-of-Way (FYRW) Inattention/Distraction (ID) Aggressive/Reckless Driving (ARD) Impaired Driving (IMPD) Crossed Centerline/Going Wrong Way (WW) Other Straight – Hillcrest (SH) Straight – Grade (SG) Straight – Bottom (SB) Curve – Level (CL) Curve – Hillcrest (CH) Curve – Grade (CG) Curve – Bottom (CB) Other < = 18 years 19–25 years 41–55 years 56–70 years > 70 years Urban < = 25 mph. 26–45 mph. > 55 mph. US Route (USR) NC Route (NCR) State Secondary Route (SSR) Local Street (LS) Public Vehicular Area (PVA) Private Road, Driveway (PRD) Other Illness Fatigue Fell Asleep, Fainted, Loss of Consciousness (FFLC) Impairment Due to Medications, Drugs, Alcohol (IMDA) Medical Condition (MC) Other Physical Impairment (OPI) Restriction Not Complied with (RNC) Other Female
Not At-fault Driver Injury Severity Model
At-fault Driver Injury Severity Model
Severe Injury
Severe Injury
0.88* 0.96* 1.02 1.03 0.96* 0.91* 1.30 1.15 0.86* 0.66* 0.89* 0.99 0.98 1.67* 2.83* 0.98* 2.28* 0.81
Moderate Injury
Moderate Injury
1.05 0.69*
0.99 0.93* 0.89* 0.96 0.97 0.93* 0.99 1.47* 0.88 0.70* 0.91 0.96* 0.96* 1.31* 2.34* 1.64* 3.79* 1.10
0.09* 0.21* 0.28* 0.50*
0.47* 0.26* 0.29* 0.67*
0.13* 0.32* 0.43* 0.53*
0.28* 0.26* 0.28* 0.64*
0.18* 1.36*
0.41* 0.73*
0.19* 1.29
0.26* 0.80*
0.81 0.31*
0.64* 0.29*
0.96 0.42*
0.49* 0.35*
2.28* 1.26 1.13 2.36* 1.89* 1.64* 1.50* 0.45 8.89* 0.54* 0.78* 1.25* 1.44* 2.83* 0.63* 0.57 0.60* 0.95 1.79* 1.80* 1.30 1.13 0.07 4.97 0.40 0.60 7.22 0.50
0.89* 1.17* 1.15* 1.36* 1.27* 1.23* 1.22* 0.91 0.73 0.67* 0.90* 1.09* 1.09* 0.95* 0.86* 0.56* 0.83* 0.84* 1.17* 1.18* 1.06 1.12* 0.41* 0.66 0.87 0.93 1.46 1.35
2.34* 1.20 1.36* 1.33 2.05* 1.62* 1.42* 1.15 0.09 1.12 1.05 1.08 1.16* 1.26 0.49* 0.25* 0.64* 0.91 1.97* 2.02* 1.5* 1.19 0.24 0.12 0.01 0.02 7.65* 0.001
0.97 1.18* 1.15* 1.51* 1.32* 1.2* 1.32* 1.13 0.68 0.96 1.03* 0.99 1.0 0.97 0.81* 0.48* 0.78* 0.87* 1.20* 1.21* 1.01 1.13* 0.36* 0.31* 0.66 0.86 2.08 0.94
5.90*
1.88*
5.63*
2.01*
8.05* 14.13* 14.41
3.02* 3.82* 1.19
0.99 5.44 0.69
0.91 1.30 2.10
17.44* 1.35*
3.28* 1.53*
0.03 0.92
1.78 0.93*
1.22* 1.48*
1.27* 1.56* 1.28* 0.69*
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Table 3 (continued) Variable
Interactions (At-Fault Drivers’ Vehicle Type VS Not At-Fault Drivers’ Vehicle Type) ®- Passenger Car (At-Fault) with Passenger Car (Not At-Fault)
Categories
PC (At-Fault) with PLTV (Not AtFault) PC (At-Fault) with SUV (Not AtFault) PLTV (At-Fault) with PC (Not AtFault) PLTV (At-Fault) with PLTV (Not At-Fault) PLTV (At-Fault) with SUV (Not At-Fault) SUV (At-Fault) with PC (Not AtFault) SUV (At-Fault) with PLTV (Not At-Fault) SUV (At-Fault) with SUV (Not AtFault) Other
Not At-fault Driver Injury Severity Model
At-fault Driver Injury Severity Model
Severe Injury
Moderate Injury
Severe Injury
Moderate Injury
1.23
1.01
0.47*
0.73*
1.21
0.91
0.65
0.79*
0.60*
0.88*
1.64
0.83*
0.74
0.92
0.82
0.65*
0.67
0.84
0.82
0.72*
0.59
0.86*
2.33*
0.94
0.51
0.95
1.16
0.79*
0.78
0.87
1.14
0.80
1.36
0.60*
1.06
*
0.62
Note: ® indicates reference or base category. * Indicates significant odds ratio value at a 95% confidence level.
drivers’ injury severity differently. Road characteristics, weather and geometric characteristics such as road surface condition, weather condition, lighting condition, terrain, road configuration, speed limit, median type, location, road classification, and access control are observed to have a similar effect on injury severity to, both, at-fault and not at-fault drivers. At-fault driver’s age and physical condition are observed to play a dominant role on injury severity of at-fault drivers. The results obtained indicate that the injury severity of at-fault drivers is more likely to increase with an increase in age. Older drivers (> 70 years old) are observed to be the highest risk group compared to all other age groups. Similarly, at-fault drivers with restriction not complied physical condition were observed to have the highest risk when compared to other physical conditions. An increase in the number of traffic violations tends to increase the likelihood of severe injury to, both, at-fault and not at-fault drivers. However, not at-fault drivers are more likely to be severely injured (1.67 times due to drivers with two traffic violations and 2.83 times due to drivers with three traffic violations when compared to drivers with single traffic violation) compared to at-fault drivers (1.31 times due to drivers with two traffic violations and 2.34 times due to drivers with three traffic violations when compared to drivers with single traffic violation). Similarly, traffic violations such as aggressive/reckless driving are more likely to result in severe injury to not at-fault drivers (1.36 times for aggressive/reckless driving violation when compared to disregarded traffic signs violation) when compared to at-fault drivers (1.29 times for aggressive/reckless driving violation when compared to disregarded traffic signs violation). Drivers tend to react more quickly to the incidents that they expect when compared to the incidents that they do not expect. The higher injury severity to not at-fault drivers compared to at-fault drivers could be attributed to this expectancy. The not at-fault drivers may not expect aggressive/reckless driving, crossed centerline, going wrong way or disregarding traffic violation, which could have a bearing on their reaction time resulting in a severe injury. At-fault drivers are more likely to be severely injured when driving passenger car, while not at-fault drivers driving passenger car, pickup / light truck / van, or SUV are more likely to be severely injured when atfault driver is driving a SUV. Driver’s gender is also observed to play an important role in the severity of a crash. Female at-fault drivers (1.13 times when compared to male at-fault drivers) are more like to be severely injured than not at-fault female drivers (0.98 times when compared to male at-fault drivers). Female not at-fault drivers (1.35 times
van or SUV. On the other hand, the odds of severe injury to at-fault drivers driving SUV is lower than severe injury to not at-fault drivers driving passenger car, pickup / light truck / van, or SUV. At-fault driver age has no significant effect on the not at-fault driver injury severity and vice versa. However, at-fault drivers’ age affects his/ her own injury severity and vice versa. At-fault drivers above 70 years are 2.54 and 1.19 times likely to result in a severe and moderate injury to himself/herself when compared to drivers of age 26–40 years. A not at-fault driver above 70 years is 2.83 times likely to result in a severe injury to himself/herself when compared to drivers of age 26–40 years. Significant categories of median type, road characteristics, road classification, and access control variables have almost equal odds ratios of at-fault and not at-fault driver injury severity. At-fault drivers with two violations increase the odds of having a serious injury by 1.67 and 1.31 times for a not at-fault driver and at-fault driver, respectively. At-fault drivers with three violations further increase the odds by 2.83 and 2.34 for not at-fault and at-fault driver when compared to at-fault driver with one violation. Compared to male at-fault drivers, female atfault drivers are 0.98 and 1.64 times likely to result in a severe injury for not at-fault and at-fault drivers. Female at-fault drivers are less likely to severely injury other drivers but more likely to severely injure themselves when compared to males. The type of violation committed by the at-fault driver influence atfault driver and not at-fault driver differently. Aggressive or reckless driving violations are 1.36 times likely to result in a severe injury to not at-fault driver. Exceeding speed limit has higher odds of resulting in a severe injury to at-fault driver (3.79 times) when compared to not atfault drivers (2.28). Not at-fault drivers are more likely to get severely injured on urban roads when compared to at-fault drivers. 5. Conclusions Several independent variables contribute to injury severity sustained by drivers that are involved in crashes. A comprehensive crash data from the Highway Safety Information System (HSIS) for the state of North Carolina was used for examination of the effect of each independent variable on driver injury severity of both at-fault and not atfault drivers. The partial proportional odds model developed for driver injury severity of at-fault drivers and not at-fault drivers not only allows to investigate the effect of each independent variable on injury severity of at-fault and not at-fault drivers, but also helps compare one with another to examine how each independent variable affects these two 62
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when compared to male not at-fault drivers) are more likely to be severely injured than at-fault female drivers (0.93 times when compared to male at-fault drivers). Motorcycles are observed to be the most vulnerable road users’ in both at-fault and not at-fault conditions. Overall, the effect of various independent variables on, both, atfault and not at-fault driver’s injury severity was examined and compared in this research. Engineering solutions and advancement of technologies such as sensors and short-range communications could be adopted to detect and avoid or minimize unsafe situations contributed by at-fault drivers to enhance safety of drivers on roads. Additionally, the findings from this research can be used to educate at-fault drivers about risk to themselves and other drivers due to traffic violations or errors that result in crashes. The findings from this research can also be used make policy decisions such as fines and points for at-fault drivers based on relative risk to themselves and other drivers. While a comprehensive list of independent variables was considered for modeling and analysis of relative risk to at-fault and not at-fault drivers, the interaction between all the levels within each independent variable type (for example, all vehicle types as the severity may be severe if a two-wheeler is hit by a truck) on both at-fault and not atfault driver’s injury severity was not explored due to data limitations. Also, the role of independent variables could differ from one city/town to another city/town. Expanding and exploring interactions between all the categories within each independent variable type using data for multiple cities/towns merits further investigation.
Blanco, R.L., 2013. Percepción del riesgo y de seguridad ante la conducción de vehículos. Carreteras: Revista técnica de la Asociación Española de la Carretera, pp. 48–56. Brown, B., 2016. (Accessed 28 March 2017) at. U.S. Traffic Fatalities Up 7.2 Percent in 2015, The Biggest Increase Since 1966. Digital Trends (2016). http://www. digitaltrends.com/cars/traffic-deaths-up-biggest-rise-since-1966/. Chen, F., Chen, S., 2011. Injury severities of truck drivers in single-and multi-vehicle accidents on rural highways. Accid. Anal. Prev. 43, 1677–1688. Chiou, Y.C., Hwang, C.C., Chang, C.C., Fu, C., 2013. Modeling two-vehicle crash severity by a bivariate generalized ordered probit approach. Accid. Anal. Prev. 51, 175–184. Fararouei, M., Sedaghat, Z., Sadat, S.J., Shahraki, G., 2017. Risk factors for being the atfault driver: a case–control study. Traffic Inj. Prev. 18, 262–266. Huang, H., Chin, H.C., Haque, M.M., 2008. Severity of driver injury and vehicle damage in traffic crashes at intersections: a Bayesian hierarchical analysis. Accid. Anal. Prev. 40 (1), 45–54. McCullagh, P., 1980. Regression models for ordinal data. J. R. Stat. Soc. Ser. B (Methodol.) 109–142. National Center for Statistics and Analysis, 2016. Traffic Safety Facts 2014. Report No. DOT HS 812 261. National Highway Traffic Safety Administration, Washington, DC. Penmetsa, P., Pulugurtha, S.S., 2017a. Methods to rank traffic rule violations resulting in crashes for allocation of funds. Accid. Anal. Prev. 99, 192–201. Penmetsa, P., Pulugurtha, S.S., 2017b. Risk drivers pose to themselves and other drivers by violating traffic rules. Traffic Inj. Prev. 18, 63–69. Penmetsa, P., Pulugurtha, S.S., Duddu, V.R., 2017. Examining injury severity of not-atfault drivers in two-vehicle crashes. Transp. Res. Rec. 2659, 164–173. Savolainen, P.T., Mannering, F.L., 2007. Probabilistic models of motorcyclists’ injury severities in single-and multi-vehicle crashes. Accid. Anal. Prev. 39, 955–963. Savolainen, P.T., Mannering, F.L., Lord, D., Quddus, M.A., 2011. The statistical analysis of highway crash-injury severities: a review and assessment of methodological alternatives. Accid. Anal. Prev. 43, 1666–1676. Wang, X., Abdel-Aty, M., 2008. Analysis of left-turn crash injury severity by conflicting pattern using partial proportional odds models. Accid. Anal. Prev. 40, 1674–1682. Wang, W., Kockelman, K., 2005. Use of heteroscedastic ordered logit model to study severity of occupant injury: distinguishing effects of vehicle weight and type. Transp. Res. Rec. 1908, 195–204. Williams, R., 2006. Generalized ordered logit/partial proportional odds models for ordinal dependent variables. Stata J. 6, 58–82. World Health Organization (WHO), 2009. Global Status Report on Road Safety: Time for Action. World Health Organization, Geneva.
References Abdelwahab, H., Abdel-Aty, M., 2001. Development of artificial neural network models to predict driver injury severity in traffic accidents at signalized intersections. Transp. Res. Rec. 1746, 6–13.
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Modeling and comparing injury severity of at-fault and not at-fault drivers in crashes Venkata R. Duddua, Praveena Penmetsab, Srinivas S. Pulugurthaa,
T
⁎
a Civil & Environmental Engineering Department / IDEAS Center, The University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, NC, 282230001, USA b Alabama Transportation Institute, The University of Alabama, 201 7th Avenue, Tuscaloosa, AL, 35487, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Injury severity Crash At-fault Not at-fault Partial proportional odds model Driver
This paper examines and compares the effect of selected variables on driver injury severity of, both, at-fault and not at-fault drivers. Data from the Highway Safety Information System (HSIS) for the state of North Carolina was used for analysis and modeling. A partial proportional odds model was developed to examine the effect of each variable on injury severity of at-fault driver and not at-fault driver, and, to examine how each variable affects these two drivers’ injury severity differently. Road characteristics, weather condition, and geometric characteristics were observed to have a similar effect on injury severity in a crash to at-fault and not at-fault drivers. Age of the driver, physical condition, gender, vehicle type, and, the number and type of traffic rule violations were observed to play a significant role in the injury severity of not at-fault drivers when compared to at-fault drivers in the crash. Moreover, motorcyclists and drivers 70 years or older are observed to be the most vulnerable road users.
1. Introduction Road crashes affect the society in numerous ways; they impede development, pose threat to public health, and result in economic losses. Each year, approximately 1.24 million people are killed, and 50 million people are injured in traffic crashes worldwide (World Health Organization (WHO), 2009). Over the last two decades, researchers have used several methods to analyze and understand the causes of crashes. Undoubtedly, the results have provided valuable insights about the contributing factors related to road geometry, driver characteristics, weather and environment, vehicle features, etc. associated with crash frequency and severity. These insights are useful in selecting and implementing countermeasures that help transportation officials reach the “zero deaths on roads” vision. Since the year 1966, with a 7.2% increase, year 2015 had the largest increase in traffic fatalities compared to year 2014 (Brown, 2016). The early trends of fatalities predicted a similar increase for year 2016. Therefore, there is a need to better understand the causes and factors associated with road crashes. Human factors play a predominant role among various factors associated with crashes (Blanco, 2013). Aberrant driving behavior is a vital human factor that contributes to road crashes; they can be either intended deviations or unforced errors. Deviations of drivers from safe practices are not recommended since they increase the chances of
⁎
getting involved in crashes. Safe practices are put forward as traffic rules by transportation system managers. For example, drivers are required to come to a complete stop at a stop light. Similarly, drivers should be traveling at or below the posted speed limit under ideal conditions. Such kind of traffic rules ensure a smooth traffic flow while ensuring safety on roads. However, drivers deviate from these safe practices and get involved in crashes. For instance, speeding and driving under the influence of alcohol accounted for 58% of the road deaths in the United States in year 2014 (National Center for Statistics and Analysis, 2016). More than 50% of the drivers involved in crashes committed some type of violation (Penmetsa and Pulugurtha, 2017a). To reduce, both, crash frequency and crash severity, a thorough understanding of factors that contribute to crashes and severity of crashes is necessary. Discrete choice models are widely used in traffic safety area to identify the effect of independent variables on dependent variable such as driver injury severity, crash severity, or occupant severity. Wang and Kockelman (2005), Savolainen and Mannering (2007), and Chen and Chen (2011) identified the need for developing separate injury severity models for single-vehicle and multi-vehicle crashes. Further, a study by Abdelwahab and Abdel-Aty (2001) concluded that at-fault drivers are less likely to succumb a severe injury when compared to not at-fault drivers, showing the need for examining these two drivers separately. Penmetsa and Pulugurtha (2017b)
Corresponding author. E-mail addresses: [email protected] (V.R. Duddu), [email protected] (P. Penmetsa), [email protected] (S.S. Pulugurtha).
https://doi.org/10.1016/j.aap.2018.07.036 Received 6 February 2018; Received in revised form 22 June 2018; Accepted 30 July 2018 0001-4575/ © 2018 Elsevier Ltd. All rights reserved.
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Table 1 Frequency of Variables and Categories. Variable
Categories
Not At-Fault (%)
At-fault (%)
Driver Injury Severity (Dependent Variable)
PDO Moderate Injury Severe Injury Rural Urban Dry Wet Water Standing/Moving (WSM) Ice Snow Slush Sand, Mud, Dirt, Gravel (SMDG) Fuel, Oil Other Clear Cloudy Rain Snow Fog, Smog, Smoke (FSS) Sleet, Hall, Freezing Rain/Drizzle (SHFR) Severe Crosswinds (SC) Blowing Sand, Dirt, Snow (BSDS) Other Daylight Dusk Dawn Dark – Lighted Road (DLR) Dark – Road Not Lighted (DRL) Dark – Unknown Lighting (DUL) Other Straight – Level Straight – Hillcrest (SH) Straight – Grade (SG) Straight – Bottom (SB) Curve – Level (CL) Curve – Hillcrest (CH) Curve – Grade (CG) Curve – Bottom (CB) Other Interstate (IN) US Route (USR) NC Route (NCR) State Secondary Route (SSR) Local Street (LS) Public Vehicular Area (PVA) Private Road, Driveway (PRD) Other One-Way, Not Divided Two-Way, Not Divided (TWND) Two-Way, Divided, Unprotected Median (TWDUM) Two-Way, Divided, Positive Median Barrier (TWDPM) Unknown No Access Control Partial Control (PC) Full Control (FC) One Two Male Female < = 18 years 19–25 years 26–40 years 41–55 years 56–70 years > 70 years Passenger Car (PC) Pickup/Light Truck/Van (PLTV) Sports Utility Vehicle (SUV) Bus Truck/Tractor or Truck/Tractor Trailer (TT) Farm Vehicle (FV) Two-wheeler (TW) Other
270,249 (77.33) 77,781 (22.26) 1424 (0.41) 130,068 (37.22) 219,386 (62.78) 289,401 (82.82) 54,740 (15.66) 1560 (0.45) 1601 (0.46) 1565 (0.45) 452 (0.13) 68 (0.02) 8 (< 0.01) 59 (0.02) 252,372 (71.82) 60,652 (17.36) 32,286 (9.64) 1908 (0.55) 1091 (0.31) 890 (0.25) 30 (0.01) 15 (< 0.01) 210 (0.06) 283,238 (81.05) 8060 (2.31) 4097 (1.17) 29,679 (8.49) 23,931 (6.85) 364 (0.10) 85 (0.02) 268,266 (76.77) 10,597 (3.03) 46,655 (13.35) 2485 (0.71) 11,368 (3.25) 1560 (0.45) 8060 (2.31) 407 (0.12) 56 (0.02) 33,144 (9.48) 62,984 (18.02) 59,108 (16.91) 57,854 (16.56) 133,301 (38.15) 2588 (0.74) 76 1(0.02) 399 (0.11) 14,490 (4.15) 201,622 (57.70) 81,499 (23.32) 51,660 (14.78) 183 (0.05) 246,193 (70.45) 62,615 (17.92) 40,646 (11.63) – – 180,861 (51.76) 168,593 (48.24) 15,568 (4.45) 54,902 (15.71) 108,858 (31.15) 99,583 (28.50) 55,744 (15.95) 14,799 (4.23) 191,833 (54.90) 73,967 (21.17) 67,842 (19.41) 1784 (0.51) 9848 (2.82) 0 (0.00) 3016 (0.86) 1164 (0.33)
303,576 (86.87) 44,286 (12.67) 1592 (0.42)
Location Road Surface Condition
Weather Condition
Light Condition
Road Characteristics
Road Classification
Road Configuration
Access
Number of Violations Committed by Fault Driver Drivers’ Gender Drivers’ Age
Vehicle Type
249,555 (71.41) 88,239 (25.25) 191,893 (54.91) 157,561 (45.09) 35,308 (10.10) 82,604 (23.64) 93,577 (26.78) 69,591 (19.91) 44,503 (12.74) 23,871 (6.83) 200,982 (57.51) 73,730 (21.10) 60,040 (17.18) 979 (0.28) 10,785 (3.09) 4 (< 0.01) 2071 (0.59) 863 (0.25)
(continued on next page)
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Table 1 (continued) Variable
Categories
Not At-Fault (%)
At-fault (%)
Drivers’ Violation
Disregarded Traffic Signs/Signals/Markings (DTS) Exceeded Speed Limit (ESL) Exceeded Safe Speed Limit for Conditions (ESSL) Followed Closely (FC) Improper Maneuver (IM) Improper Passing (IP) Failed to Yield the Right-of-Way (FYRW) Inattention/Distraction (ID) Aggressive/Reckless Driving (ARD) Impaired Driving (IMPD) Crossed Centerline/Going Wrong Way (WW) Other < = 25 mph. 26–45 mph. 46–55 mph. > 55 mph. Apparently Normal Illness Fatigue Fell Asleep, Fainted, Loss of Consciousness (FFLC) Impairment Due to Medications, Drugs, Alcohol (IMDA) Medical Condition (MC) Other Physical Impairment (OPI) Restriction Not Complied with (RNC) Other Undivided Road Rigid Barrier (RB) Continuous Turn Lane (CTL) Paved Mountable (PM) Curb Grass Positive Barrier (POB) Parkland, Business (PB) Couplet Flexible Barrier (FB) Striped Semi-Rigid Barrier (SRB) Flat Rolling Mountainous (MOUN) PC (At-Fault) with PC (Not At-Fault) PC (At-Fault) with PLTV (Not At-Fault) PC (At-Fault) with SUV (Not At-Fault) PLTV (At-Fault) with PC (Not At-Fault) PLTV (At-Fault) with PLTV (Not At-Fault) PLTV (At-Fault) with SUV (Not At-Fault) SUV (At-Fault) with PC (Not At-Fault) SUV (At-Fault) with PLTV (Not At-Fault) SUV (At-Fault) with SUV (Not At-Fault) Other
– – – – – – – – – – – – 5279 (1.51) 205,700 (58.86) 109,097 (31.22) 29,378 (8.41) 348,929 (99.85) 104 (0.03) 31 (0.01) 20 (0.01) 186 (0.05)
20,040 (5.73) 898 (0.26) 6067 (1.74) 135,581 (38.80) 39,054 (11.18) 2598 (0.74) 77,452 (22.16) 45,134 (12.92) 2733 (0.78) 3319 (0.95) 7324 (2.10) 9254 (2.65)
Speed Limit
Drivers’ Physical Condition
Median Type
Terrain
Interactions between At-Fault Driver Vehicle Type and Not At-Fault Driver Vehicle Type
64 (0.02) 62 (0.02) 17 (< 0.01) 41 (0.01) 201,105 (57.55) 6549 (1.87) 40,143 (11.49) 12,482 (3.57) 11,142 (3.19) 49,627 (14.20) 20,628 (5.90) 144 (0.04) 1413 (0.40) 2617 (0.75) 401 (0.11) 3203 (0.92) 67,114 (19.21) 259,604 (74.29) 22,736 (6.51) 113,086 (32.36) 38,985 (11.16) 31,788 (9.10) 40,699 (11.65) 17,583 (5.03) 12,736 (3.64) 38,644 (11.06) 13,759 (3.94) 13,155 (3.76) 29,019 (8.30)
337,901 (96.69) 247 (0.07) 773 (0.22) 1397 (0.40) 7321 (2.09) 1135 (0.32) 285 (0.08) 82 (0.02) 313 (0.09)
The effect of independent variables on injury severity of drivers was well documented in the past. However, past studies on at-fault and not at-fault driver injury severities are comparatively limited. Except Chiou et al. (2013) which focused on crashes at signalized intersections, there is no other notable research on comparing driver injury severity of atfault and not at-fault drivers. The question that remains unanswered is “how does an independent variable effect at-fault and not at-fault driver injury severities in the same crash”. Hence, this study aims to extend the body of knowledge corresponding to driver injury severity of atfault and not at-fault drivers by developing separate injury severity models for both the drivers, and, examining as well as comparing how a given independent variable affects these two drivers differently.
provided insights about how at-fault drivers and not at-fault drivers are affected (in terms of injury severity) by type of traffic rule violation committed by the at-fault driver. However, their study ignored several variables that could influence the injury severity of at-fault and not atfault driver, such as; characteristics of the at-fault and not at-fault driver, type of vehicle of the at-fault and not at-fault driver, road characteristics, etc. Overcoming this limitation, Penmetsa et al. (2017) studied how not at-fault drivers’ injury severity is affected by several crash, vehicle, driver, and other characteristics (includes characteristics of at-fault and not at-fault driver, at-fault and not at-fault vehicle type, at-fault drivers’ violation, etc.). Fararouei et al. (2017) studied human, vehicle, and environmental factors that are associated with at-fault drivers in crashes. Chiou et al. (2013) modeled injury severity of both drivers involved in two-vehicle crashes, simultaneously using a bivariate ordered probit model. Their study used police reported at-fault and not at-fault driver information from the crash database to study crash severity of both drivers. However, their study was constrained to crashes that occurred at signalized intersections.
2. Data North Carolina crash data was requested from the Highway Safety Information System (HSIS) from 2009 to 2013. All the necessary information corresponding to a crash are provided in four different files (accident, road, vehicle, and occupant) which can be joined using the 57
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vehicle closely, failing to yield the right-of-way, and inattention/distraction are the three most frequently violated traffic rules. Passing over a stopped school bus, passing on a hill, passing on curve, etc. are grouped under improper passing category. Overcorrected or oversteered, right turn on red, improper backing or parking or signaling, improper turn, improper lane change, improper lane use, etc. are grouped under improper maneuver category. The percentage distribution of at-fault and not at-fault drivers’ vehicle types remained almost the same. Two-lane divided and undivided roads had around 80% of the two-vehicle crashes. Majority of the twovehicle crashes occurred on roads with speed limits between 26–45 mph. The physical condition of not at-fault drivers is apparently normal 99% of the time, whereas, at-fault drivers are normal 97% of the time. At-fault drivers committed one violation 71% of the time and committed two violations 25% of the time. Roads with rolling terrain accounted for 75%, while interstates accounted for 10% of the two-vehicle crashes.
unique identification number. Between 2009–2013, the combined database had information of 791,245 crashes involving 1,315,059 vehicles that occurred on North Carolina roads. For each vehicle involved in a crash, the crash contributing factor was carefully noted by the police officer after investigation of the crash site or through interviewing the drivers/occupants who were involved in the crash. For example, consider a crash involving two vehicles where one vehicle violated a red light and had a collision with another vehicle which had the right-of-way. The vehicle that had violated the red-light violation will have the crash contributing factor as “disregarded traffic signal” and the other vehicle will be assigned “no contributing factor”. For this study, a driver at-fault or not at-fault is decided based on this contributing factor. In the above example, the driver of the disregarded traffic signal vehicle is at-fault and the other driver is not at-fault of the crash. As mentioned earlier, the objective of this study is to develop injury severity models for at-fault and not atfault drivers, separately, to see how several variables affect injury severity differently. While studying the injury severity of at-fault drivers, characteristics corresponding to not at-fault driver, not at-fault vehicle type, etc. are incorporated in the model as independent variables, to see how they affect the at-fault driver injury severity, and vice versa. To study how one affects the other, there should be at least two vehicles involved in the crash, one being at-fault and the other being not atfault. Among the multi-vehicle crashes, only crashes involving two vehicles can be used for this study. Hence, from the database, only twovehicle crashes were retained and the other crash records (single-vehicle and more than two vehicles involved crashes) were removed from the database. Pedestrian and bicycle crashes were also not considered in this research. The crash database was processed such a way that each row represents a crash. Several characteristics of the crash were considered as independent variables in the model; road, environment, vehicle, and driver characteristics. Table 1 summarizes all the variables and categories that were considered for injury severity analysis. The frequency and percentages are also shown for each variable and category in the Table. Crashes with unknown or unreported information for the variables mentioned in Table 1 were removed from the database. The final dataset for developing the injury severity models consisted of 349,454 crashes (349,454 at-fault and 349,454 not at-fault driver injury severities). The dependent variables in the study are at-fault driver injury severity, and not at-fault driver injury severity. The injury severity is defined as fatal, incapacitating injury, capacitating injury, possible injury, and property damage only (PDO). The injury severity for this study is reclassified into three levels; severe injury, moderate injury, and PDO. Severe injury is created by combining fatal and incapacitating injury, while moderate injury is created by combining capacitating injury and possible injury. About 12.67% and 22.26% of at-fault and not at-fault drivers sustained moderate injuries, respectively. The not at-fault drivers are more likely to succumb moderate injuries when compared to at-fault drivers. The likelihood of resulting in PDO is higher for at-fault drivers when compared to not at-fault drivers. Majority of the two-vehicle crashes (63%, 83%, 72%, and 81%) occurred on urban roads, dry surface condition, clear weather condition, and during daylight condition, respectively. Male drivers contributed to 55% of at-fault drivers and 52% of not at-fault drivers. Driver involved in crashes are classified into six categories; novice (< = 18 years), young (19–25 years), 26–40 years, 41–55 years, 56–70 years, and elderly (> = 70 years). Drivers 26–40 years old accounted for the highest portion of at-fault and not at-fault drivers in the selected crash records. Drivers 41–55 years old are not at-fault more frequently than they are at-fault in the selected crash records. There are more than 30 traffic rule violations under the contributing factor variable. They are reclassified into 12 categories to examine their effect on at-fault and not at-fault driver injury severity. Following
3. Method Savolainen et al. (2011) outlined different methods that were adopted by researchers for modelling injury severity in crashes. The nature of the dependent variable plays an important role in choosing a method for modeling. The levels of injury severity of the driver are ordinal in nature, but the distance between these variables is unknown. A bivariate ordered probit or simultaneous equation joint model is preferred if the injury severity levels of drivers and passengers involved in the same crash are correlated with each other (Savolainen et al., 2011). The joint model is particularly suitable when modeling injury severities of driver and passengers in the same vehicle, when modeling injury severities of drivers involved in the same crash at a location (say, merging areas on freeways), etc., and will help minimize computation of biased parameter estimates (Huang et al., 2008). Therefore, the correlation between injury severity levels of at-fault driver and not atfault driver was first tested. The computed Pearson correlation coefficient between the injury severity levels of at-fault driver and not atfault driver was observed to be low (∼0.3) at a 95% confidence level. Therefore, independent ordered probit models, which are also known as proportional odds models were considered appropriate and developed to evaluate the injury severity of both the at-fault driver and not at-fault driver in this research. The proportional odds model is a class of generalized linear models used for modeling the dependence of an ordinal response on discrete or continuous covariates. This model assumes the effect of the independent variables to be identical across the categories of the dependent variable (proportional odds or parallel lines assumption). Let Y denote response category in the range 1, 2, 3, …., j, with j > 1, and let yk = pr (Y ≤ k / x ) be the cumulative response probability when covariate is held at x. The mathematical formulation of a general linear logistic model for kth response probability is shown as Eq. (1) (McCullagh, 1980). The predicted logits can be transformed to odds and probability using Eq. (2) (Wang and Abdel-Aty, 2008; Williams, 2006).
logit (yi ) = αi−βit x i
P (yi > j ) =
(1)
exp(αi−βit x i ) 1 + exp(αi−βit x i )
(2)
The intercept α and the coefficient β depend on the category ‘i’. However, the proportional odds model is a linear logistic model in which the intercepts depend on ‘i’, but all slopes are equal. Thus, the general form of proportional odds model is shown as Eq. (3). The predicted logits can be transformed to odds and probability using Eq. (4).
logit (yi ) = αi−β t x i 58
(3)
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categories that are observed to be statistically significant at a 95% confidence level (indicated with asterisk “*” sign in the tables) were only included in the final model. The categories of road surface condition variable (water standing/ moving and ice) affect the injury severity of at-fault and not at-fault drivers in the same way. Water standing or moving of road is 1.19 times likely to result in severe injury for both at-fault and not at-fault drivers. Snow is 0.69 and 0.65 times likely to result in a severe injury for at-fault and not at-fault drivers when compared to dry road condition in twovehicle crashes. All the weather conditions have similar effect on atfault driver injury severity. For not at-fault drivers, snow and cloudy weather condition have higher odds when compared to clear weather condition, while rest all are insignificant. Dark and not lighted road are 1.7 and 1.55 times likely to result in severe injury to not at-fault and atfault drivers when compared to daylight condition. On the other hand, dark and lighted roads are 1.28 and 1.31 likely to result in severe injury to not at-fault and at-fault drivers when compared to daylight condition. The type of terrain has similar effect on at-fault and not at-fault driver injury severity. Two-way divided and undivided roads are around 1.31 times likely to result in severe injury to not at-fault driver when compared to one-way roads. For at-fault drivers, the odds are approximately 1.8, indicating that at-fault drivers have higher odds of getting severely injured on two-way roads when compared to not atfault drivers. At-fault drivers’ physical condition influences not at-fault driver injury severity. If at-fault driver fell asleep, fainted, or lost consciousness, they are going to increase the odds of having a severe injury for not at-fault driver by 2.11 times when compared to at-fault drivers’ apparently normal physical condition. At-fault drivers’ falling asleep, fainting, or losing consciousness increase the odds of having a severe injury and moderate injury for at-fault driver by 3.18 times. At-fault drivers’ physical condition influences their own injury severity more than not at-fault drivers’ injury severity. The role of “Other” category (with high odds) in case of not at-fault driver physical condition could not be explored further due to lack of details in the obtained crash database. Vehicle type has a significant effect on their own driver injury severity as well as the other driver injury severity. A not at-fault driver driving a bus and truck are 0.11 and 0.21 times likely to get severely injured compared to a not at-fault driver driving a passenger car, respectively. A not at-fault driver driving a bus and truck are 2.68 and 3.75 times likely to result in a severe injury compared to an at-fault driver driving a passenger car. A not at-fault two-wheeler driver is 40.60 and 27.04 times likely to result in a severe injury and moderate injury to himself/herself when compared to a not at-fault passenger car driver, respectively. A not at-fault two-wheel driver is 0.27 and 0.69 times likely to result in a severe injury and moderate injury to the atfault driver when compared to passenger car at-fault driver. The effect of at-fault drivers’ vehicle types on not at-fault driver injury severity is different than that of a not at-fault drivers’ vehicle type on at-fault drivers’ injury severity. For example, a two-wheeler driver not at-fault is 40.60 times likely to severely injury himself/herself, whereas, a twowheeler driver at-fault is 29.02 times likely to severely injury himself/ herself. An at-fault driver driving a truck and two-wheeler are 2.85 and 0.28 times likely to result in a severe injury for not at-fault driver compared to at-fault driver of a passenger car. The severity of the crash could also depend on the type of vehicles colliding with each other. Therefore, at-fault and not at-fault drivers’ vehicle type interactions between passenger car, pickup / light truck / van, and sports utility vehicle (SUV) were also considered as a variable in the modeling process. The considered nine interactions account for ∼92% of the considered data. The results obtained indicate that atfault drivers are more likely to be moderately injured while driving a passenger car and colliding with a passenger car (not at-fault) compared to most vehicle type interactions considered in this research. The odds of severe injury to at-fault drivers driving passenger car is higher than severe injury to not at-fault drivers driving pickup / light truck /
Table 2 Results of Brant Test for Individual Independent Variables. Variable
Not At-fault
Location Road Surface Condition Weather Condition Light Condition Road Characteristics Road Classification Road Configuration Access Terrain Median Type Speed Limit Fault Drivers’ Physical Condition Not at Fault Drivers’ Physical Condition Fault Drivers’ Gender Not at Fault Drivers’ Gender Fault Drivers’ Age Not at Fault Drivers’ Age Fault Drivers’ Vehicle Type Not at Fault Drivers’ Vehicle Type Fault Drivers’ Violation Number of Violations Committed by Fault Driver Interactions (Fault Drivers’ Vehicle Type VS Not at Fault Drivers’ Vehicle Type)
P (yi > j ) =
exp(αi−β t x i ) 1 + exp(αi−β t x i )
At- fault
Wald ChiSquare
p-value
Wald ChiSquare
p-value
8.28 4.45 7.58 22.69 28.22 27.49 4.75 1.42 0.69 10.40 26.60 10.15 24.46
< 0.01 0.81 0.37 < 0.01 < 0.01 < 0.01 0.31 0.49 0.70 0.49 < 0.01 0.25 < 0.01
21.63 9.16 4.54 11.71 30.45 21.65 6.93 3.76 2.26 18.65 14.13 25.57 19.22
< .0001 0.33 0.71 0.06 < 0.01 < 0.01 0.14 0.15 0.32 0.06 < 0.01 < 0.01 0.01
0.00 4.08 17.13 138.19 5.25 19.88 466.23 39.80
0.97 0.04 < 0.01 < 0.01 0.51 < 0.01 < 0.01 < 0.01
50.55 0.00 99.64 8.07 7.96 12.37 301.05 11.90
< .0001 0.95 < .0001 0.15 0.24 0.05 < .0001 < 0.01
14.78
0.09
30.85
< 0.01
(4)
where yi is the latent and continuous measure of driver’s injury severity in a crash, x i is a vector of explanatory variables, and β is a vector of coefficients to be estimated. Brant test was performed before developing the model to check if the data satisfies the underlying proportionality assumption. Among the independent variables considered, if few failed Brant test, a partial proportional odds model is preferred. The underlying formulation for partial proportional model is same as proportional odds model or generalized ordered logit model, except that variables which failed Brant test will have different coefficients for categories of a dependent variable.
4. Results Independent variables such as road surface condition, weather condition, light condition, road configuration, access, terrain, median type, not at-fault drivers’ gender and age, at-fault drivers’ vehicle type have p-values greater than 0.05 in the proportional odds test for the atfault drivers (Table 2). This indicates that the null hypothesis cannot be rejected for these variables. The null hypothesis for this test is that all the categories of a given dependent variable has only one coefficient. Hence, for these variables, there exist only one coefficient which explains the effect across the categories of the dependent variable. Similarly, independent variables that failed Brant test for not at-fault driver injury severity model are also identified and shown in Table 2. The variables that failed proportional odds assumption were relaxed to have different coefficients for different driver injury severity levels. A partial proportional odds model was developed for driver injury severity of at-fault drivers and not at-fault drivers, separately. The results obtained are presented in Table 3. The reference category of a categorical variable is typically the normal condition. For example, for road surface condition variable, ‘dry’ was chosen as the reference category. All independent variables with a minimum of one or more of its 59
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Table 3 Partial Proportional Odds Model for Not At-Fault and At-Fault Driver Injury Severity. Variable
Road Surface Condition ®-Dry
Weather Condition ®-Clear
Light Condition ®-Daylight
Terrain ®-Flat Road Configuration ®-One Way Not Divided
At-Fault Drivers’ Physical Conditions ®-Apparently Normal
Not At-Fault Drivers’ Vehicle Type ®-Passenger Car
At-Fault Drivers’ Age ®-26-40 years
At-Fault Drivers’ Vehicle Type ®-Passenger Car
Categories
Wet Water Standing/Moving (WSM) Ice Snow Slush Sand, Mud, Dirt, Gravel (SMDG) Fuel, Oil Other Cloudy Rain Snow Fog, Smog, Smoke (FSS) Sleet, Hall, Freezing Rain/Drizzle (SHFR) Severe Crosswinds (SC) Blowing Sand, Dirt, Snow (BSDS) Other Dusk Dawn Dark – Lighted Road (DLR) Dark – Road Not Lighted (DRL) Dark – Unknown Lighting (DUL) Other Rolling Mountainous (MOUN) Two-Way, Not Divided (TWND) Two-Way, Divided, Unprotected Median (TWDUM) Two-Way, Divided, Positive Median Barrier (TWDPM) Unknown Illness Fatigue Fell Asleep, Fainted, Loss of Consciousness (FFLC) Impairment Due to Medications, Drugs, Alcohol (IMDA) Medical Condition (MC) Other Physical Impairment (OPI) Restriction Not Complied with (RNC) Other Pickup/Light Truck/Van (PLTV) Sports Utility Vehicle (SUV) Bus Truck/Tractor or Truck/Tractor Trailer (TT) Two-wheeler (TW) Other < = 18 years 19–25 years 41–55 years 56–70 years > 70 years Pickup/Light Truck/Van (PLTV) Sports Utility Vehicle (SUV) Bus Truck/Tractor or Truck/Tractor Trailer (TT) Farm Vehicle (FV) Two-wheeler (TW) Other
Not At-fault Driver Injury Severity Model
At-fault Driver Injury Severity Model
Severe Injury
Severe Injury
Moderate Injury
0.95* 1.19* 0.69* 0.64* 0.87 0.73 1.43 1.69 1.04* 1.02 0.78* 1.10 1.17
0.97 1.19* 0.65* 0.55* 0.64* 0.40 2.69 2.21* 1.02 0.98 0.85 1.13 0.95
0.32 1.22 0.82 1.50* 1.51 1.28* 1.70* 0.33 0.69 0.95* 0.78* 1.36* 1.31*
0.47 2.37 0.92 1.26 1.67* 1.31* 1.55* 1.60 0.08 0.94* 0.76* 1.89* 1.81*
1.05 1.11* 1.10* 1.22* 1.00 1.00
1.31*
1.88*
1.26 0.96 1.36* 2.11*
1.09 2.43* 1.52* 3.18*
1.58*
1.99*
1.53* 1.38* 1.74*
4.87* 1.51* 2.16*
Moderate Injury
1.02 1.08 1.15* 1.25* 1.21 1.13
1.25 1.29 1.06 0.11* 0.21*
0.89* 0.82* 0.42* 0.44*
2.36* 1.17 0.76 2.68* 3.85*
1.51* 1.22* 2.42* 3.9*
40.60* 1.10 1.05 1.13 0.95 0.74* 1.15 1.29 1.34 2.40 2.85*
27.04* 1.19* 1.01 1.01 1.01 0.99 1.03 1.10 1.17* 1.55 2.00*
0.27* 1.06 0.92 0.90 1.17* 1.36* 2.54* 1.29 1.13 0.001 0.38*
0.69* 1.49* 0.92* 1.0 1.01 1.06* 1.19* 0.91 0.90 0.31* 0.36*
0.61 0.28* 1.86
4.30 0.34* 1.59
– 29.02* 0.90
– 39.9* 1.60*
(continued on next page)
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Table 3 (continued) Variable
Median Type ®-Undivided Road
Access ®-No Access Control At-Fault Drivers’ # Violations ®-One At-Fault Drivers’ Gender®-Male At-Fault Drivers’ Violation ®-Disregarding Traffic Signs/Signals/ Markings
Road Characteristics ®-Straight Level
Not At-Fault Drivers’ Age ®-26-40 years
Location ®-Rural Speed Limit ®-46-55 mph
Road Classification ®-Interstate
Not At-Fault Drivers’ Physical Conditions ®-Apparently Normal
Not At-Fault Drivers’ Gender ®-Male
Categories
Rigid Barrier (RB) Continuous Turn Lane (CTL) Paved Mountable (PM) Curb Grass Positive Barrier (POB) Parkland, Business (PB) Couplet Flexible Barrier (FB) Striped Semi-Rigid Barrier (SRB) Partial Access Control Full Access Control Two Three Female Exceeding Speed Limit (ESL) Exceeding Safe Speed Limit for Conditions (ESSL) Followed Closely (FC) Improper Maneuver (IM) Improper Passing (IP) Failure to Yield the Right-of-Way (FYRW) Inattention/Distraction (ID) Aggressive/Reckless Driving (ARD) Impaired Driving (IMPD) Crossed Centerline/Going Wrong Way (WW) Other Straight – Hillcrest (SH) Straight – Grade (SG) Straight – Bottom (SB) Curve – Level (CL) Curve – Hillcrest (CH) Curve – Grade (CG) Curve – Bottom (CB) Other < = 18 years 19–25 years 41–55 years 56–70 years > 70 years Urban < = 25 mph. 26–45 mph. > 55 mph. US Route (USR) NC Route (NCR) State Secondary Route (SSR) Local Street (LS) Public Vehicular Area (PVA) Private Road, Driveway (PRD) Other Illness Fatigue Fell Asleep, Fainted, Loss of Consciousness (FFLC) Impairment Due to Medications, Drugs, Alcohol (IMDA) Medical Condition (MC) Other Physical Impairment (OPI) Restriction Not Complied with (RNC) Other Female
Not At-fault Driver Injury Severity Model
At-fault Driver Injury Severity Model
Severe Injury
Severe Injury
0.88* 0.96* 1.02 1.03 0.96* 0.91* 1.30 1.15 0.86* 0.66* 0.89* 0.99 0.98 1.67* 2.83* 0.98* 2.28* 0.81
Moderate Injury
Moderate Injury
1.05 0.69*
0.99 0.93* 0.89* 0.96 0.97 0.93* 0.99 1.47* 0.88 0.70* 0.91 0.96* 0.96* 1.31* 2.34* 1.64* 3.79* 1.10
0.09* 0.21* 0.28* 0.50*
0.47* 0.26* 0.29* 0.67*
0.13* 0.32* 0.43* 0.53*
0.28* 0.26* 0.28* 0.64*
0.18* 1.36*
0.41* 0.73*
0.19* 1.29
0.26* 0.80*
0.81 0.31*
0.64* 0.29*
0.96 0.42*
0.49* 0.35*
2.28* 1.26 1.13 2.36* 1.89* 1.64* 1.50* 0.45 8.89* 0.54* 0.78* 1.25* 1.44* 2.83* 0.63* 0.57 0.60* 0.95 1.79* 1.80* 1.30 1.13 0.07 4.97 0.40 0.60 7.22 0.50
0.89* 1.17* 1.15* 1.36* 1.27* 1.23* 1.22* 0.91 0.73 0.67* 0.90* 1.09* 1.09* 0.95* 0.86* 0.56* 0.83* 0.84* 1.17* 1.18* 1.06 1.12* 0.41* 0.66 0.87 0.93 1.46 1.35
2.34* 1.20 1.36* 1.33 2.05* 1.62* 1.42* 1.15 0.09 1.12 1.05 1.08 1.16* 1.26 0.49* 0.25* 0.64* 0.91 1.97* 2.02* 1.5* 1.19 0.24 0.12 0.01 0.02 7.65* 0.001
0.97 1.18* 1.15* 1.51* 1.32* 1.2* 1.32* 1.13 0.68 0.96 1.03* 0.99 1.0 0.97 0.81* 0.48* 0.78* 0.87* 1.20* 1.21* 1.01 1.13* 0.36* 0.31* 0.66 0.86 2.08 0.94
5.90*
1.88*
5.63*
2.01*
8.05* 14.13* 14.41
3.02* 3.82* 1.19
0.99 5.44 0.69
0.91 1.30 2.10
17.44* 1.35*
3.28* 1.53*
0.03 0.92
1.78 0.93*
1.22* 1.48*
1.27* 1.56* 1.28* 0.69*
(continued on next page)
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Table 3 (continued) Variable
Interactions (At-Fault Drivers’ Vehicle Type VS Not At-Fault Drivers’ Vehicle Type) ®- Passenger Car (At-Fault) with Passenger Car (Not At-Fault)
Categories
PC (At-Fault) with PLTV (Not AtFault) PC (At-Fault) with SUV (Not AtFault) PLTV (At-Fault) with PC (Not AtFault) PLTV (At-Fault) with PLTV (Not At-Fault) PLTV (At-Fault) with SUV (Not At-Fault) SUV (At-Fault) with PC (Not AtFault) SUV (At-Fault) with PLTV (Not At-Fault) SUV (At-Fault) with SUV (Not AtFault) Other
Not At-fault Driver Injury Severity Model
At-fault Driver Injury Severity Model
Severe Injury
Moderate Injury
Severe Injury
Moderate Injury
1.23
1.01
0.47*
0.73*
1.21
0.91
0.65
0.79*
0.60*
0.88*
1.64
0.83*
0.74
0.92
0.82
0.65*
0.67
0.84
0.82
0.72*
0.59
0.86*
2.33*
0.94
0.51
0.95
1.16
0.79*
0.78
0.87
1.14
0.80
1.36
0.60*
1.06
*
0.62
Note: ® indicates reference or base category. * Indicates significant odds ratio value at a 95% confidence level.
drivers’ injury severity differently. Road characteristics, weather and geometric characteristics such as road surface condition, weather condition, lighting condition, terrain, road configuration, speed limit, median type, location, road classification, and access control are observed to have a similar effect on injury severity to, both, at-fault and not at-fault drivers. At-fault driver’s age and physical condition are observed to play a dominant role on injury severity of at-fault drivers. The results obtained indicate that the injury severity of at-fault drivers is more likely to increase with an increase in age. Older drivers (> 70 years old) are observed to be the highest risk group compared to all other age groups. Similarly, at-fault drivers with restriction not complied physical condition were observed to have the highest risk when compared to other physical conditions. An increase in the number of traffic violations tends to increase the likelihood of severe injury to, both, at-fault and not at-fault drivers. However, not at-fault drivers are more likely to be severely injured (1.67 times due to drivers with two traffic violations and 2.83 times due to drivers with three traffic violations when compared to drivers with single traffic violation) compared to at-fault drivers (1.31 times due to drivers with two traffic violations and 2.34 times due to drivers with three traffic violations when compared to drivers with single traffic violation). Similarly, traffic violations such as aggressive/reckless driving are more likely to result in severe injury to not at-fault drivers (1.36 times for aggressive/reckless driving violation when compared to disregarded traffic signs violation) when compared to at-fault drivers (1.29 times for aggressive/reckless driving violation when compared to disregarded traffic signs violation). Drivers tend to react more quickly to the incidents that they expect when compared to the incidents that they do not expect. The higher injury severity to not at-fault drivers compared to at-fault drivers could be attributed to this expectancy. The not at-fault drivers may not expect aggressive/reckless driving, crossed centerline, going wrong way or disregarding traffic violation, which could have a bearing on their reaction time resulting in a severe injury. At-fault drivers are more likely to be severely injured when driving passenger car, while not at-fault drivers driving passenger car, pickup / light truck / van, or SUV are more likely to be severely injured when atfault driver is driving a SUV. Driver’s gender is also observed to play an important role in the severity of a crash. Female at-fault drivers (1.13 times when compared to male at-fault drivers) are more like to be severely injured than not at-fault female drivers (0.98 times when compared to male at-fault drivers). Female not at-fault drivers (1.35 times
van or SUV. On the other hand, the odds of severe injury to at-fault drivers driving SUV is lower than severe injury to not at-fault drivers driving passenger car, pickup / light truck / van, or SUV. At-fault driver age has no significant effect on the not at-fault driver injury severity and vice versa. However, at-fault drivers’ age affects his/ her own injury severity and vice versa. At-fault drivers above 70 years are 2.54 and 1.19 times likely to result in a severe and moderate injury to himself/herself when compared to drivers of age 26–40 years. A not at-fault driver above 70 years is 2.83 times likely to result in a severe injury to himself/herself when compared to drivers of age 26–40 years. Significant categories of median type, road characteristics, road classification, and access control variables have almost equal odds ratios of at-fault and not at-fault driver injury severity. At-fault drivers with two violations increase the odds of having a serious injury by 1.67 and 1.31 times for a not at-fault driver and at-fault driver, respectively. At-fault drivers with three violations further increase the odds by 2.83 and 2.34 for not at-fault and at-fault driver when compared to at-fault driver with one violation. Compared to male at-fault drivers, female atfault drivers are 0.98 and 1.64 times likely to result in a severe injury for not at-fault and at-fault drivers. Female at-fault drivers are less likely to severely injury other drivers but more likely to severely injure themselves when compared to males. The type of violation committed by the at-fault driver influence atfault driver and not at-fault driver differently. Aggressive or reckless driving violations are 1.36 times likely to result in a severe injury to not at-fault driver. Exceeding speed limit has higher odds of resulting in a severe injury to at-fault driver (3.79 times) when compared to not atfault drivers (2.28). Not at-fault drivers are more likely to get severely injured on urban roads when compared to at-fault drivers. 5. Conclusions Several independent variables contribute to injury severity sustained by drivers that are involved in crashes. A comprehensive crash data from the Highway Safety Information System (HSIS) for the state of North Carolina was used for examination of the effect of each independent variable on driver injury severity of both at-fault and not atfault drivers. The partial proportional odds model developed for driver injury severity of at-fault drivers and not at-fault drivers not only allows to investigate the effect of each independent variable on injury severity of at-fault and not at-fault drivers, but also helps compare one with another to examine how each independent variable affects these two 62
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when compared to male not at-fault drivers) are more likely to be severely injured than at-fault female drivers (0.93 times when compared to male at-fault drivers). Motorcycles are observed to be the most vulnerable road users’ in both at-fault and not at-fault conditions. Overall, the effect of various independent variables on, both, atfault and not at-fault driver’s injury severity was examined and compared in this research. Engineering solutions and advancement of technologies such as sensors and short-range communications could be adopted to detect and avoid or minimize unsafe situations contributed by at-fault drivers to enhance safety of drivers on roads. Additionally, the findings from this research can be used to educate at-fault drivers about risk to themselves and other drivers due to traffic violations or errors that result in crashes. The findings from this research can also be used make policy decisions such as fines and points for at-fault drivers based on relative risk to themselves and other drivers. While a comprehensive list of independent variables was considered for modeling and analysis of relative risk to at-fault and not at-fault drivers, the interaction between all the levels within each independent variable type (for example, all vehicle types as the severity may be severe if a two-wheeler is hit by a truck) on both at-fault and not atfault driver’s injury severity was not explored due to data limitations. Also, the role of independent variables could differ from one city/town to another city/town. Expanding and exploring interactions between all the categories within each independent variable type using data for multiple cities/towns merits further investigation.
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