Risk factors affecting fatal bus accident severity: Their impact on different types of bus drivers

Accident Analysis and Prevention 86 (2016) 29–39

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Risk factors affecting fatal bus accident severity: Their impact on different types of bus drivers Shumin Feng a , Zhenning Li a , Yusheng Ci a,∗ , Guohui Zhang b a b

School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, China Department of Civil Engineering, University of New Mexico, Albuquerque 87131, USA

a r t i c l e

i n f o

Article history: Received 30 January 2015 Received in revised form 4 September 2015 Accepted 30 September 2015 Keywords: Bus fatal accident Risk factors Accident severity Cluster analysis Ordered logistic model

a b s t r a c t While the bus is generally considered to be a relatively safe means of transportation, the property losses and casualties caused by bus accidents, especially fatal ones, are far from negligible. The reasons for a driver to incur fatalities are different in each case, and it is essential to discover the underlying risk factors of bus fatality severity for different types of drivers in order to improve bus safety. The current study investigates the underlying risk factors of fatal bus accident severity to different types of drivers in the U.S. by estimating an ordered logistic model. Data for the analysis are retrieved from the Buses Involved in Fatal Accidents (BIFA) database from the USA for the years 2006–2010. Accidents are divided into three levels by counting their equivalent fatalities, and the drivers are classified into three clusters by the K-means cluster analysis. The analysis shows that some risk factors have the same impact on different types of drivers, they are: (a) season; (b) day of week; (c) time period; (d) number of vehicles involved; (e) land use; (f) manner of collision; (g) speed limit; (h) snow or ice surface condition; (i) school bus; (j) bus type and seating capacity; (k) driver’s age; (l) driver’s gender; (m) risky behaviors; and (n) restraint system. Results also show that some risk factors only have impact on the “young and elder drivers with history of traffic violations”, they are: (a) section type; (b) number of lanes per direction; (c) roadway profile; (d) wet road surface; and (e) cyclist–bus accident. Notably, history of traffic violations has different impact on different types of bus drivers. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction For public transportation, safety is a basic attribute and is one of the reasons why passengers choose to travel by bus. However, in the U.S. over 60,000 buses are involved in traffic accidents each year. Among these accidents, about 14,000 involve non-fatal injuries and about 300 involve at least one fatal injury (Blower and Green, 2010). During the five year period of 2006–2010, these fatal accidents caused an estimated average of 320 civilian deaths 550 civilian serious injuries per year. Although the number of bus accidents is less than 1% of all the traffic accidents, because the passenger capacity of buses is much greater than that of cars, it is more serious in terms of property loss and personal injury when a bus accident occurs. While the bus is generally considered a relatively safe means of transportation, the property losses and casualties caused by bus accidents are far from being negligible (Chimba et al., 2010).

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (Y. Ci). http://dx.doi.org/10.1016/j.aap.2015.09.025 0001-4575/© 2015 Elsevier Ltd. All rights reserved.

Since 2003, the number of bus accidents has grown steadily, and there is no sign that this trend will slow down. The social and economic impact of bus accidents is becoming more and more serious. Through an analysis of the National Transit Database (NTD), FTA found that the accident, injury, and fatality rates, respectively, rose 171%, 37.8%, and 5.1% from 2003 to 2007. At the same time, the loss of property caused by bus accidents is also increasing steadily; for example, in 2010, the total inflation-adjusted value of property damage rose to about 30 million US dollars from about 20 million dollars in 2000. Bus safety therefore deserves systematic and in-depth consideration. The positive news is that the degree of attention paid by society and scholars is increasing; however, research into bus safety lags far behind that on car safety, which means that there still exist many problems to be solved in the study of bus safety. Current research into bus safety mostly concerns the analysis of the risk factors associated with the bus accidents, measured by vehicle related factors, road environmental factors or driver factors. As for vehicle related factors, a study of bus crashes in five states in the U.S. showed that older buses were overrepresented in injury

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and fatal crashes compared to newer buses (Zegeer et al., 1993). Chimba et al. (2010) found that the size of buses was associated with the rates of bus accidents. Yang et al. (2009) figured out that school bus crash fatality and injury rates were 3.5 and 5.4 times lower than overall all vehicle crash fatality and injury rates, respectively. In terms of road environmental factors, several roadway geometric and traffic variables are known to influence occurrence of crashes. For instance, crash frequency has been found to increase with traffic volume per lane (Miaou, 1994), the number of lanes (Noland and Oh, 2004), and lane and shoulder widths (Lee and Mannering, 2002). Experts in Canada detected that the bus accident occurrence is related to bus operating conditions; factors in their study included traffic volumes, pedestrian volumes, position of stops, signal timing of intersections and turning restrictions (Shahla et al., 2009). A study on bus-involved accidents in Melbourne along roads where bus priority measures had been applied suggested that the bus priority in addressing maneuverability issues for buses (Goh et al., 2014). Research into bus accidents in relation to bus driver factors has revealed some interesting insights. Through an analysis of nearly 9000 commercial bus crashes in the U.S., Zegeer et al. (1993) did not find any association between accidents and the basic characteristics of the driver, for instance, gender and age. Similarly, gender, age and education level were found to be insignificant in explaining at-fault accident rates of bus drivers (Tseng, 2012). However, drivers’ socio-economic characteristics, speeding and suspensions were found associated with bus fatal accidents (Blower and Green, 2010). In Sri Lanka, drivers’ disagreements about working hours and low salaries were also found to be significant risk factors for private bus crashes by a case–control study (Jayatilleke et al., 2009). Research into driver’s driving behavior too have been undertaken: A series studies in Sweden investigated the relationship between traffic accident frequency and acceleration behavior (Af Wåhlberg, 2000, 2004, 2006, 2007, 2008) and drivers’ absence behavior (Af Wåhlberg and Dorn, 2009). In addition, a number of studies have attempted to identify groups of drivers with greater risk of being injured or killed in accidents. Most of these studies identify the drivers by age; for example, Marottoli et al. (1994) selected 283 elder persons from a representative cohort of community-living persons in Connecticut to identify the factors associated with automobile crashes, moving violations, and being stopped by police for them. Mao et al. (1997) and Zhang et al. (2000) used the method of multivariate unconditional logistic regression to examine factors affecting the severity of motor vehicle traffic crashes (MVTCs) involving young and elderly drivers in Ontario, respectively. Thompson et al. (2012) examined distracted driving performance in an instrumented vehicle in 86 elderly and 51 middle-aged drivers and found that the elderly drove slower and showed decreased speed variability during distraction compare to middle-aged drivers. Other studies applied gender (Jehle et al., 2012; Møller and Haustein, 2014), working experience (Mulder et al., 2008; Underwood et al., 2003), education level (Engström et al., 2003; Robertson, 1980) and other characteristics to classify the drivers who involved in crashes. Though a great amount of research focused on classification of drivers, more research is needed since most of previous studies only applied a few variables or dichotomous variables (i.e., male or female, young or not, elder or not) for classification instead of taking multiple characteristics of drivers into consideration. Focusing on accident severity, most of studies reviewed divide accidents into three categories: property damage only (PDO), injury, and fatal (Abellán et al., 2013; De Lapparent, 2006; Golob et al., 1987; Zhang et al., 2013) or five categories: property damage only, possible injury, non-incapacitating injury, incapacitating injury, and fatal injury (Al-Ghamdi, 2002; Kaplan and Prato, 2012; Shankar and Mannering, 1996). However, there is also a lack of

specialized research into fatal accidents severity, especially fatal bus accidents. The current study investigates the underlying risk factors affecting fatal bus accident severity and their impact on different types of bus drivers in the U.S. Risk factors associated with bus fatal accidents from bus level, vehicle level, and bus driver level have been taken into consideration. Data for the analysis are retrieved from the Bus Involved in Fatal Accidents (BIFA) database from 2006 to 2010 years. First of all, since impact of fatality is our primary concern, we defined fatal bus accident severity into three levels by utilizing the method raised by Association for the advancement of Automotive Medicine (AAAM) to calculating equivalent fatalities. Then, by taking multiple characteristic factors of the bus drivers into consideration, drivers were divided into three clusters by K-means cluster analysis. Next, an ordered logistic model was estimated in order to determine the odds ratios of these risk factors, in other word, their positively or negatively associated with bus accident severity. Model results provide insights regarding the different effect of the various risk factors on fatal bus accident to different types of drivers. The remainder of the paper is organized as follows. Section 2 presents the bus accident data and the classification of fatal accident severity. Section 3 makes the classification of drivers. Section 4 describes the methodology applied for analyzing risk factors associated with accident severity. Section 5 presents model estimates and marginal effects. Last, Section 6 discusses the major findings of this study and stimulates thoughts about policy implications for enhancing bus safety.

2. Data Since this article is mainly concerned with analyzing fatalities, the data are retrieved from the Buses Involved in Fatal Accidents (BIFA) database. The BIFA files contain records for all buses that were involved in fatal traffic accidents in the 50 states and the District of Columbia. A bus is defined as a vehicle designed to carry at least nine people, which means that the bus is not used for personal transportation. All the vehicles described are also contained in the Fatality Analysis Reporting System (FARS) files compiled by the National Highway Traffic Safety Administration (NHTSA) for the respective years. The BIFA file is a census file, meaning there is one record for each bus involved in a fatal accident. Each record in the BIFA data includes virtually all variables from the FARS files at the Accident, Vehicle, and Person (bus driver) level, plus data collected through the BIFA survey process describing the vehicle, company, driver, trip, and crash. That is to say, one record contains the information of one accident, the bus involved, the other road user(s) involved, the bus driver and other variables concerned with the accidents. The accident file reports the details of each accident, including accident date, accident time, the number of vehicles and persons involved, the manner of collision, the environmental characteristics, and the roadway conditions. In the vehicle file, there are several variables concerning the vehicle, such as body type, vehicle maneuver, most harmful event, and number of deaths in vehicle. The driver and occupant files describe each driver involved in the accident, with records of age, sex, number of previous accidents, drivers’ demographics characteristics, and injury severity. Given the current focus of this study, the accidents that occurred in the period of 2006–2010 are considered. The data presented in this paper is focused on bus involvements only. Involvements; counts of buses involved in a fatal accident. Fatalities; counts of fatalities of occupants of bus and/or other vehicle involved. Bus; an entity providing passenger transportation over fixed, scheduled routes, within urban or rural area geographical areas. By

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Table 1 Variable definitions and descriptions. Variable The crash level Accident severity Number of K-injury Number of A-injury

Number of B-injury

Year

Season Day of week Time period Number of vehicles involved Land use Manner of collision

Section type Number of lanes per direction Speed limit

Roadway alignment Roadway profile Roadway surface type Roadway surface condition Traffic control The vehicle level Bus service type Bus vehicle type Bus vehicle age Bus seating capacity Bus maneuver Other road users involved The bus driver level Gender Age

License History of crashes History of convictions Behavior

Restraint system

Categories

Percentage

Categories

Level 1 Level 2 1 2 0 1 2 0 1 2 3 2006 2007 2008 Spring Summer Weekday Morning Afternoon 1 2 Urban area Rear-end Head-on Angle Non-junction 1 2 ≤25 30–35 40–45 Straight Level Concrete Blacktop Dry Wet Functioning

88.5% 7.2% 89.9% 6.6% 79.5% 10.9% 3.0% 69.8% 13.8% 5.9% 2.3% 21.7% 19.2% 21.7% 29.0% 17.2% 71.3% 37.2% 42.0% 32.5% 52.5% 56.4% 16.0% 17.2% 21.9% 52.3% 1.6% 64.7% 9.8% 23.8% 20.8% 85.3% 75.4% 9.9% 86.4% 85.3% 11.2% 41.0%

Level 3

4.3%

3 ≥4 3 4 ≥5 4 5 ≥6

1.7% 1.9% 1.7% 0.4% 4.5% 2.5% 1.1% 4.6%

School bus Van-based ≤5 years 6–10 years 9–16 seats Going straight Turning left Pedestrian Cyclist Male ≤25 26–35 36–45 Valid Yes Suspensions Speeding Drowsy Ill, blackout Alcohol/drugs Belted

eliminating some incomplete data, we obtain 1380 valid data records from 1472. The specific variable definitions and descriptions are illustrated in Table 1. There are three levels presented in Table 1; in the crashes levels, we focused on accident severity, road conditions, traffic environment and other variables; in the vehicle level, service type, vehicle type, vehicle age and other variables in regards to bus are our mainly concerns; and in the bus driver level, bus drivers’ age, gender, driving histories and driving behaviors are considered in the analysis.

Percentage

2009 2010

19.2% 18.2%

Autumn Winter Weekend Evening Night ≥3

26.2% 27.6% 28.7% 14.2% 6.6% 15.1%

Rural area Sideswipe Not with a motor vehicle

43.6% 4.3% 39.8%

Intersection ≥3

47.7% 33.7%

50–55 60–65 ≥70 Curve Grade Other

23.1% 12.3% 10.2% 14.7% 24.6% 3.8%

Snow or ice

3.6%

No controls

59.0%

36.3% 14.1% 46.9% 33.5% 10.3% 55.1% 15.2% 26.2% 2.0%

Other bus Regular bus ≥11 years

63.7% 85.9% 19.6%

>16 seats Turning right Other Motor vehicle

89.7% 4.3% 25.4% 71.8%

62.0% 2.1% 11.7% 24.6% 90.6% 27.7% 5.4% 10.9% 0.5% 1.2% 0.2% 86.7%

Female 46–55 56–65 ≥66 Not valid No Other convictions

38.0% 30.1% 24.4% 7.1% 9.4% 72.3% 11.2%

Careless Speeding Distracted Not belted

4.3% 4.7% 13.4% 13.3%

Since impact of fatality or injury is our primary concern, and as we noted above, there is a lack of specialized research into bus fatal accidents severity level, so we defined accident severity by the number of equivalent fatalities per accident. The equivalent fatality captures the equivalent impact of an injury relative to a fatality. There are several methods of calculating equivalent fatality worldwide; for instance, In China mainland, 1 slight injury is equivalent to 0.1 fatalities, and 1 major injury is equivalent to 0.33 fatalities; In Taiwan, 1 injury is equivalent to 0.368 fatalities (Hu et al., 2010); In

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Britain, 1 major injury is equivalent to 0.1 fatalities (Evans, 1994), and 1 slight injury is equivalent to 0.0088 fatalities (O’Reilly et al., 1994). In current study, the method raised by Association for the Advancement of Automotive Medicine (AAAM) were used to calculating equivalent fatality. AAAM first created the code of Abbreviated Injury Scale (AIS) in 1969 with several major updates, which is an anatomical-based coding system to classify and describe the severity of injuries in the traffic accident area (Palmer et al., 2013). It represents the threat to life associated with the injury rather than the comprehensive assessment of the severity of the injury. The AIS can therefore be considered as an interdisciplinary and universal code of injury severity. The AIS classifies each injury by body region according to its relative importance on a 6-point ordinal scale (1 = minor and 6 = maximal). The maximum AIS (MAIS) is the highest single AIS code for an occupant with multiple injuries. According to “The Economic and Societal Impact of Motor Vehicle Crashes, 2010” published by NHSTA (Blincoe et al., 2014), the comprehensive fatality and injury relative values are as follows; 1 MAIS1 injury is equivalent to 0.0047 fatalities, similarly, 1 MAIS2, MAIS3, MAIS4, MAIS5 injury, and Fatal are equivalent to 0.0484, 0.1183, 0.2790, 0.6209, and 1 fatalities, respectively. However, the MAIS levels are not presented in BIFA database directly, injury severity in it is classified into KABCO scale as K – killed, A – incapacitating injury, B – non-incapacitating injury, C – possible injury, and O – no apparent injury. Hence, it is necessary to translate KABCO scale into MAIS scheme, and by applying the translator presented in “The Economic and Societal Impact of Motor Vehicle Crashes, 2010”, we obtained the equivalent rule in KABCO scale; 1 O-injury, C-injury, B-injury, A-injury, and K-injury are equivalent to 0.0049, 0.0148, 0.0310, 0.1107, and 1 fatalities, respectively. By this means, the equivalent fatalities of the records from BIFA database can be readily calculated, and the cumulative frequency distribution of equivalent fatalities is presented in Fig. 1. As shown in Fig. 1, the minimum, maximum, average, and median of equivalent fatalities are 1, 19.962, 1.373, and 1.031, respectively. Besides, 88.49% records have less than 2 equivalent fatalities and 4.27% records have more than 3 ones. So we classified accident severity levels into 3 levels designated 1–3: higher the severity level, more severe the accident. Accordingly, a severity of level 1 means less than 2 equivalent fatalities; level 2 implies greater than 2 but smaller than 3 fatalities; level 3 denotes 3 or more equivalent fatalities. Significantly, accident severity is an ordinal three-level response variable and the frequency of it is also presented in Table 1.

3. The classification of the drivers How to identify the drivers properly has already been a considerable stumbling block in the analysis of accident risk factors. As we noted above, previous research into classifying drivers who involved in accidents mainly concerned with age, gender, working experience or other characteristics, individually. By this means, drivers were classified into young and old, male and female, novice and experienced or other types. While significant differences are found in these population segments, there is a lack of research that taking these characteristics into consideration together. The drivers, as human beings, have numerous factors associated with their driving behaviors not only just age, gender and other basic indices of them, in other word, multiple factors should be taken into consideration. In this section, cluster analysis is carried out to answer the question of ‘who is the problem driver’, that is to say, to identify the drivers into several types according to their characteristic variables shown in Table 1. Cluster analysis is a multivariate statistical methodology aimed at partitioning N observations into K disjoint groups in a such way that they are both maximally internally homogeneous and externally heterogeneous (Everitt et al., 2001). Ward’s method for hierarchical clustering is undertaken to determine the number of clusters, or subgroups, present in the data. Although the hierarchical clustering method is advantageous for determining the number of clusters present, it cannot produce the most optimal cluster solution pertaining to between-cluster heterogeneity (Lucidi et al., 2010). This is because the method is unable to separate clusters created at previous steps. Thus, it is recommended to run a K-means cluster analysis after the number of clusters has been determined, using the centroids generated from the hierarchical analysis as a starting point (Milligan and Sokol, 1980). Therefore, K-means cluster analysis is carried out to calculate the optimal cluster solution in this study. The AIC (Akaike’s information criterion) and BIC (Schwarz’s Bayesian criterion) rules are applied to determine the proper amount of clusters in the cluster model. These statistical figures measure the model fit and simultaneously correct for the model’s complexity (a more parsimonious model is better) (Depaire et al., 2008). When cluster the drivers into three subtypes, both AIC and BIC get the lowest amount, suggesting that the three-cluster is enough to make the cluster analysis well. Furthermore, the entropy criterion (McLachlan and Peel, 2004) as in Eq. (1) is used to assess the quality of the clustering solution. In Eq. (1) where pik denotes the posterior probability that case i belongs to cluster K and with

Fig. 1. Cumulative frequency distribution of equivalent fatalities.

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Table 2 Results of the classification of the drivers. Factors

Variables

Sample (N = 1380)

Cluster1 (N = 425)

Cluster2 (N = 302)

Cluster3 (N = 653)

Gender

Male** Female** ≤25* 26–35** 36–45*** 46–55*** 56–65*** ≥66* Valid = yes* Crashes = yes*** Suspensions = yes*** Speeding = yes*** Other convictions = yes** Drowsy = yes* Ill, blackout = yes* Alcohol/drugs = yes* Careless = yes* Speeding = yes* Distracted = yes* Belt = yes* Level 1*** Level 2*** Level 3***

62.0% 38.0% 2.1% 11.7% 24.6% 30.1% 24.4% 7.1% 90.6% 27.7% 5.4% 10.9% 11.2% 0.5% 1.2% 0.2% 4.3% 4.7% 13.4% 86.7% 77.8% 14.0% 8.2%

61.4% 38.6% 1.4% 4.2% 38.5% 38.1% 13.6% 4.2% 99.5% 53.4% 9.1% 21.5% 20.5% 0.1% 0.7% 0.0% 2.6% 2.4% 5.9% 94.8% 95.3% 4.2% 0.5%

61.6% 38.4% 3.3% 19.3% 2.1% 4.9% 53.1% 17.3% 76.2% 50.6% 10.5% 18.8% 19.2% 1.3% 2.2% 0.7% 9.5% 8.5% 15.8% 73.2% 51.3% 30.3% 18.4%

62.5% 37.5% 2.0% 13.0% 26.0% 36.5% 18.2% 4.3% 91.4% 0.3% 0.6% 0.4% 1.5% 0.4% 1.0% 0.1% 3.1% 4.5% 17.2% 87.7% 78.7% 12.8% 8.5%

Age

License History of crashes History of convictions

Behavior

Restraint system Accident severity

* ** ***

Significant at the 0.1 level. Significant at the 0.05 level. Significant at the 0.01 level.

the convention that pik ln(pik ) = 0 if pik = 0. In case of perfect classification the criterion equals to 1 and for the worst case clustering the value of the criterion is 0 (Depaire et al., 2008). For our data, I(3) = 0.94, which indicates a very good separation among the clusters. Hence, the three-cluster is selected as our final model. By the method of K-means, drivers are classified into three clusters, and the number of them in each cluster is 425, 302 and 653, respectively. Pearson’s Chi-square test is used to analyze the significance of these variables, and the specific results are illustrated in Table 2:

n k I(K) = 1 −

i=1

p j=1 ik

ln(pik )

n ln(1/k)

(1)

As shown in Table 2, cluster 1 is characterized by a greatly high ratio in middle age (36–55 years). Besides, the drivers also have extremely high ratios in the variables concerning in history of crashes and convictions, suggesting that the drivers have violations or even illegal driving histories during their previous driving time. The results also show that the drivers attach great importance to buckling belts and license validity. Besides, the lowest percentages presented in bad behavior variables indicate that cluster 1 drivers behave best among all the drivers. Based on these characteristics, we label the drivers in cluster 1 “middle-aged drivers with history of driving violations”. It is worth noting too that the impact of the accidents they involved, known as accident severity, presented extremely low ratios in more severe accidents (levels 2 and 3). Cluster 2 is characterized by high percentages in the young (≤35 years) and elderly ones (≥56 years). Similarly to the cluster 1, most drivers also got involved in crashes or traffic convictions in their driving histories. Nevertheless, there are several differences between clusters 1 and 2; for instance, drivers in cluster 2 behave the worst of the overall sample with the lowest percentages of license validity and belt use. Moreover, they have the highest ratios in more severe accidents, that is to say, they are the most dangerous drivers. Based on these characteristics, cluster 2 is labeled as “young and elderly drivers with history of driving violations”. Cluster 3 is characterized by the lowest percentages in the variables concerned with driving violations (almost none). Besides, there are no significant differences in other variables between

cluster 3 and the overall sample. Therefore, cluster 3 is named as “drivers without history of driving violations”. 4. Methodology In this study, fatal accident severity is divided into three levels, known as levels 1, 2 and 3, and higher the level, more severe the accident. The classification was confirmed by calculating the equivalent fatalities, hence, accident severity can be regarded as a linear variable. Moreover, since divided into three levels, the accident severity also can be treated as an ordered variable. In this field, the ordered logistic model is generally used to analyze situations in which the dependent coordinate is an ordered variable and the number of independent variables is large. The ordered logistic model, originally proposed by Walker and Duncan (1967) and later called the proportional odds model (McCullagh, 1980), relates the covariates Xi = (X1 , X2 , . . ., Xp ) to the cumulative probabilities of the distribution of Y and is given by log(Pj ) = ln

 P(Y ≥ j|X )  i i 1 − P(Yi ≥ j|X i )

= ˛j + ˇT X i

= ln

P

(Yi ≥ j|X i ) P (Yi < j|X i )



with j = 2, . . ., k; ˛2 ≥ ˛3 ≥ · · · ≥ ˛k

(2)

In this formula, Y denotes a categorical response variable with k categories (1, 2, . . ., k) that has a multinomial distribution. Supposing Y is its value for subject i and Xi is a vector of covariate values for that subject (i = 1, 2, . . ., n). The intercepts (˛j : j = 2, . . ., k) are the log odds of Y to be equal to or greater than j when X is zero,



−1

that is, P(Y ≥ j) = 1 + exp(−˛j ) . The vector of coefficients, ˇ, represents the log odds ratios of Y to be equal to or greater than j when each component of X increases by one unit, respectively, and the other components remain constant. Notice that in this model does not depend on j; thus the model assumes that the association between X and Y is independent of j. McCullagh (1980) referred to the assumption of equality of the log odds ratio over all the cut-off points as the proportional odds assumption, and hence the name “proportional odds” model. The validity of this assumption can be

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ˆ checked by graphical methods. The coefficients are estimated by ˇ ˆ using maximum likelihood, and the odds ratios by exp(ˇ). Most statistical packages employ the Newton–Raphson method with Fisher scoring to find the maximum likelihood solution. The asymptotic ˆ is estimated directly from the variance–covariance matrix, V, of ˇ information  matrix. Wald’s test of H0 : ˇl = 0 is then based on the ˆ l / (V ) and has an asymptotic standard normal distriratio z = ˇ ll bution under the null hypothesis. Thus, the p value for two-sided test against H1 : ˇl = / 0 is given by 2(1 − (|z|)), where  is the cumulative distribution function of a standard normal variable. Focusing on the current study, the lowest accident severity level 1 was chose to be an evoked set so as to study the risk factors of more severe bus fatalities (level 2 and level 3). Investigated observed variables come from three levels, the crash level, the vehicle level and the bus driver level; more particularly, including number of vehicles involved, manner of collision, infrastructure characteristics (i.e., land use, section type, number of lanes per direction, number of lanes, traffic-way type, speed limit, roadway alignment and profile), environmental conditions (i.e., weather, road surface condition, season and day of week), bus service type, vehicle type, vehicle age, driver characteristics (i.e., age and gender), history of crashes and convictions (i.e., suspensions and speeding) and bus driver behavior (i.e., drowsy, ill, blackout, DUI, careless, speeding and distracted). 5. Results The ordered logistic model was estimated with several combinations of the explanatory variables described in the data section, and hypothesis testing was performed for variable significance and category aggregation were conducted. Table 3 presents the estimation results (ER) and the odds ratios (OR) of every category in clusters 1, 2 and 3. Notably, variables with low statistical significance (at the 0.05 significant level) were removed from the model since they are not significant with accident severity; for instance, year, the roadway surface type, and bus vehicle age. The following subsections present the how risk factors affecting fatal bus accident and their impact on the three clusters of bus drivers. 5.1. Time related variables Season is significantly associated with fatal bus accident severity to all the three driver clusters. In comparison with spring, summer lightly decreases the likelihood of more severe accidents (level 2 and level 3) to all the three clusters of drivers. In contrast, autumn and winter are associated with increased accident severity. And notably, it can be seen that autumn (OR = 1.25, 1.48, and 1.30) has higher odds ratios than winter (OR = 1.15, 1.32, and 1.21). Day of week is also associated with accident severity, results show that driving in weekend increases the probability of serious accidents (28%, 67%, and 43%) when compared with weekday. With respect to accidents occurring in the morning, increases in the likelihood of higher severe accidents are observed throughout both evening and night. In particular, it seems that driving in evening (OR = 1.83, 3.45, and 2.21) is more likely to result in more severe accidents than in night (OR = 1.67, 2.66, and 1.83). And no significant downward or upward trend is observed in afternoon. 5.2. Collision related variables Relative to only one vehicle involved, two and three or more vehicles involved sharply increase the probability of higher accident severity (OR = 13.11, 22.45, and 16.46; 17.66, 27.38, and 17.82). Similarly, in comparison with pedestrian-bus accident, when the other road users are motor vehicles, the risk of involving

in more severe accident get an observantly increase (OR = 22.35, 33.63, and 25.78). However, cyclist-bus accident only get a light decrease with accident severity to cluster 2 drivers (12%), and it is not found significantly related to bus accident severity to the other two clusters. And the occurrence of a bus fatal accident in rural area in comparison with in urban area increases the probability of more severe accident to all the three clusters (OR = 2.53, 3.68, and 2.88). Focusing on the manner of collision, in comparison with rearend collisions, head-on and sideswipe dramatically increase the likelihood of higher severe accidents (OR = 25.31, 33.88, and 36.24; 6.33, 10.28, and 8.65). Not with a motor vehicle collision decreases the probability of more severe accidents (OR = 0.23, 0.35, and 0.28), and the result is similar with the number of vehicle involved as we described in past paragraph. 5.3. Road characteristics The occurrence of a bus accident in an intersection only increases accident severity to cluster 2 drivers (OR = 1.28), and there are no significances to the other two clusters. Number of lanes and roadway profile have similar impact with section type, that is, they are only significant to cluster 2. Moreover, 2 and 3 or more lanes, and grade roadway are also positively associated with increased accident severity level (OR = 1.13 and 1.25; 1.12) when in comparison with 1 lane per direction, and level roadway, respectively. High speed limits are associated with aggravated fatal bus accident severity level. In comparison with speed limit fewer than 25 miles per hour, speed limits of 50–55 (OR = 1.33, 1.25, and 1.35), 60–65 (OR = 2.53, 5.26, and 2.66), and over 66 miles per hour (OR = 3.62, 17.61, and 5.33) increase the probability of more severe accidents. Furthermore, higher the speed limit, higher the probability. Fatal bus accidents which occur in curve roadway have less probability of higher severe accident to cluster 2 and cluster 3 drivers (28% and 25%) than in straight roadway. And when the road surface is snow or ice, with respect to dry roadway, the likelihood of being involved in more severe accidents increases sharply to all the three clusters of drivers (OR = 1.14, 2.54, and 1.39). Whereas when the surface is wet, only the drivers in cluster 2 have more possibility to get involved in level 2 and level 3 accidents (OR = 1.12), and this category is not found significantly related to the drivers in other clusters. Drivers in cluster 2 and cluster 3 are more likely to get involved in more severe accidents when there are no traffic controls (OR = 2.31 and 1.55) with the respect to device function controls. However, control or not have no on impact cluster 1 drivers. 5.4. Vehicle related variables School buses are less probability to get involved in more severe accidents with respect to other buses (OR = 0.88, 0.86, and 0.88). Regular buses and over 16 seats buses are more likely (OR = 1.18, 1.25, and 1.17; 1.21, 1.33, and 1.23) to get involved in level 2 and level 3 accidents when compare with van buses and 9–16 seats buses, respectively. Focusing on bus maneuver, in comparison with going straight, turning left and turning left lead to higher severe accidents to all the three clusters, moreover, turning right is riskier than turning left (OR = 7.87, 21.03, and 13.77; 5.53, 12.26, and 7.78). 5.5. Bus driver related variables In the data sample, about 60% of drivers are male. Relatively to the female drivers, male drivers not only have more accidents

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Table 3 Model estimation for drivers in different clusters. Variables The crash level Season

Day of week Time period

Number of vehicles involved

Land use Manner of collision

Section type Number of lanes per direction

Speed limit

Roadway alignment Roadway profile Roadway surface condition

Traffic control The vehicle level Bus service type Bus vehicle type Bus vehicle age

Bus seating capacity Bus maneuver

Other road users involved

The driver level Gender Age

License History of crashes History of convictions

Categories

Cluster 1 ERa (ORb )

Cluster 2 ERa (ORb )

Cluster 3 ERa (ORb )

Springc Summer Autumn Winter Weekdayc Weekend Morningc Afternoon Evening Night 1c 2 ≥3 Urban areac Rural area Rear-endc Head-on Sideswipe Not with a motor vehicle Non-junctionc Intersection 1c 2 ≥3 ≤25c 30–35 40–45 50–55 60–65 ≥66 Straightc Curve Levelc Grade Dryc Wet Snow or ice Device functioningc No controls

– −0.02 (0.98) 0.22 (1.25) 0.14 (1.15) – 0.25 (1.28) – –d 0.60 (1.83) 0.51 (1.67) – 2.57 (13.11) 2.87 (17.66) – 0.93 (2.53) – 3.23 (25.31) 1.85 (6.33) −1.47 (0.23) – –d – –d –d – –d –d 0.29 (1.33) 0.93 (2.53) 1.29 (3.62) – –d – –d – –d 0.13 (1.14) – –d

– −0.05 (0.95) 0.39 (1.48) 0.28 (1.32) – 0.51 (1.67) – –d 1.24 (3.45) 0.98 (2.66) – 3.11 (22.45) 3.31 (27.38) – 1.30 (3.68) – 3.52 (33.88) 2.53 (10.28) −1.05 (0.35) – 0.25 (1.28) – 0.12 (1.13) 0.22 (1.25) – –d –d 0.22 (1.25) 1.66 (5.26) 2.87 (17.61) – −0.33 (0.72) – 0.11 (1.12) – 0.11 (1.12) 0.93 (2.54) – 0.84 (2.31)

– −0.03 (0.97) 0.26 (1.30) 0.19 (1.21) – 0.36 (1.43) – –d 0.79 (2.21) 0.60 (1.83) – 2.80 (16.46) 2.88 (17.82) – 1.06 (2.88) – 3.59 (36.24) 2.16 (8.65) −1.27 (0.28) – –d – –d –d – –d –d 0.30 (1.35) 0.98 (2.66) 1.67 (5.33) – −0.29 (0.75) – –d – –d 0.33 (1.39) – 0.44 (1.55)

School bus Other busc Van-based busc Regular bus ≤5yearsc 6–10 years ≥11 years 9–16 seatsc >16 seats Going straightc Turning left Turning right Pedestrianc Cyclist Motor vehicle

−0.13 (0.88) – – 0.17 (1.18) – –d –d – 0.19 (1.21) – 1.17 (5.53) 2.06 (7.87) – –d 3.11 (22.35)

−0.15 (0.86) – – 0.22 (1.25) – –d –d – 0.29 (1.33) – 2.51 (12.26) 3.05 (21.03) – −0.13 (0.88) 3.52 (33.63)

−0.13 (0.88) – – 0.16 (1.17) – –d –d – 0.21 (1.23) – 2.05 (7.78) 2.62 (13.77) – –d 3.25 (25.78)

Male Femalec ≤25 26–35 36–45c 46–55 56–65 ≥66 Valid = yese Crashes = yesf Suspensions = yesg Speeding = yesg Other convictions = yesg

0.12 (1.13) – –d –d – 0.11 (1.12) 0.33 (1.39) 0.57 (1.76) −0.13 (0.88) −0.13 (0.88) −0.19 (0.83) −0.16 (0.85) −0.24 (0.79)

0.14 (1.15) – 1.00 (2.73) 0.68 (1.98) – –d 0.60 (1.83) 0.91 (2.49) −0.07 (0.93) 0.12 (1.13) 0.12 (1.13) 0.14 (1.15) 0.17 (1.19)

0.06 (1.06) – 0.22 (1.25) 0.16 (1.17) – 0.14 (1.15) 0.39 (1.47) 0.71 (2.03) −0.12 (0.89) –d –d –d –d

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Table 3 (Continued ) Variables

Categories

Cluster 1 ERa (ORb )

Cluster 2 ERa (ORb )

Cluster 3 ERa (ORb )

Behavior

Drowsy = yesh Ill, blackout = yesh Alcohol/drugs = yesh Careless = yesh Speeding = yesh Distracted = yesh Belt = yesi

0.07 (1.07) –d 1.06 (2.89) 0.39 (1.48) 0.55 (1.73) 0.19 (1.21) −0.29 (0.75) 0.7520 2.7636 425 −369.572 −300.783

0.10 (1.11) 0.21 (1.23) 1.33 (3.78) 0.41 (1.51) 0.72 (2.06) 0.27 (1.31) −0.25 (0.78) −1.4322 −0.0736 302 −285.694 −233.597

0.11 (1.12) 0.10 (1.11) 1.21 (3.34) 0.31 (1.36) 0.63 (1.88) 0.23 (1.26) −0.25 (0.78) 0.6523 1.9483 653 −664.520 −598.461

Restraint system Intercept 2 Intercept 3 Number of observations Log-likelihood with constants only Log-likelihood at convergence a b c d e f g h i

Estimate result. Odds ratio. Base category. Not significant at the 0.05 level. Based on license not valid. Based on no history of crashes. Based on no history of convictions. Based on no charged offense. Based on no belt used.

but also are more likely to get involved in higher severe accidents. More specifically, male drivers relate to increased accident severity by 13%, 15%, and 6% to all the three clusters. In comparison with drivers in 36–45 years old, results show that accident severity increases with both young and elder drivers. Less than 25 and 26–35 years old drivers have similar impact on accident severity in cluster 2 and cluster 3; that is, younger ones are more likely to get involved in higher severe accidents (OR = 2.73 and 1.25; 1.98 and 1.17). 46–55 years old drivers in cluster 1 and cluster 3 have higher possibilities to get involved in level 2 and level 3 accidents (OR = 1.12 and 1.15). The elder drivers with the age of 56–65 years and over 66 years see significantly sharp rise of more severe accidents in all the clusters (OR = 1.39, 1.83, and 1.47; 1.76, 2.49, and 2.03). Similarly with common sense, the results show that using valid licenses and proper safety belts can reduce the probability of level 2 and level 3 accidents to all clusters. And notably, the decrease ratios in the three clusters are almost the same (OR = 0.88, 0.93, and 0.89; 0.75, 0.78, and 0.78). Histories of crashes and convictions have different impact on the three clusters. In cluster 1, driver with history of crashes or convictions has remarkable low possibility of involving in more severe accidents. However, the driver in cluster 2 who has history of driving violations is more easily to get involved in level 2 and level 3 accidents. Driving while being drowsy has an adverse effect on accident severity to all the three clusters (OR = 1.07, 1.11, and 1.12). And similarly, driving under the influence of alcohol or drugs, careless driving, speeding and distracted driving are also associated with increased casualties (OR = 2.89, 3.78, and 3.34; 1.48, 1.51, and 1.36; 1.73, 2.06, and 1.88; 1.21, 1.31, and 1.26). Ill or blackout is only found significant to cluster 2 and cluster 3 drivers, and it also has a detrimental effect on accident severity (OR = 1.21, 1.31, and 1.26). 6. Discussion and conclusion Results show that different types of drivers have different behaviors when facing the same risk factors. Firstly, some risk factors associated with complex traffic and environmental conditions only have influence on cluster 2 drivers, such as section type, number of lanes per direction, road profile, wet road surface, and cyclist–bus accident. The results indicate that drivers in cluster 2 are more likely to get involved in more severe accidents in

these conditions, in other word, they cannot handle with complicated conditions well. Secondly, several risk factors are not found significantly related to cluster 1 drivers though they are significant to the other two clusters; for instance, curve roadway, traffic controls, and ill driving. It may indicate that cluster 1 drivers perform better when facing with complex traffic conditions. Thirdly, when considering with the categories which are significantly linked to all the three clusters, the odd ratios in cluster 2 are almost the highest, then cluster 3 and cluster 1. Besides, taking the frequency of more severe accidents into consideration, cluster 2 drivers have the highest ratios to get involved in level 2 and level 3 accidents (30.3% and 18.4%); cluster 3 drivers are in the middle (12.8% and 8.5%); and cluster 1 drivers have the lowest rates (4.2% and 0.5%). These results may indicate that drivers in cluster 1 are “the safest ones”, that is, they are unlikely to get involved in more severe accidents. In contrast, cluster 2 drivers are “the riskiest ones”, and cluster 3 drivers are in the middle. As we noted above, cluster 1 drivers are “middle-aged drivers with history of driving violations”, cluster 2 drivers are “young and elderly drivers with history of driving violations”, and the cluster 3 ones are “drivers without history of driving violations”. It can be seen that the mainly differences among the three clusters are age and history of driving violations. The results in Table 3 and previous research give the answer of why these characters make drivers more or less likely to get involved in more severe accidents. Firstly, young age have significant impact on accident severity. Table 3 shows that young drivers are risky to get involved in more severe accidents. The results are similar with previous research, that is, young bus drivers are more likely to get involved in higher severe accidents (Lambert-Bélanger et al., 2012; Choi et al., 2011; Salmon et al., 2011). It may primarily due to young drivers their own physiological characteristics (e.g., an underdeveloped brain) (Steinberg, 2008), underdeveloped hazard perception skills (Lee et al., 2008) and underestimation of risks (Weinstein, 1980). Besides, they have less driving experiences (Ryan et al., 1998), and are more likely to get involved in high-risk behaviors, such as abusing drug and alcohol (Scott-Parker et al., 2013), speeding (Hasselberg and Laflamme, 2009), and driving violations and errors (Lucidi et al., 2010). Secondly, elder drivers also increase the risk of higher accident severity. The result is similar to previous studies, drivers over the age of 65 have a higher rate of motor vehicle collisions per mile driven than middle-aged drivers (Li et al., 2003; Meuleners et al.,

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2006) and when injured in a collision, they are more likely to die or sustain serious injury (Bedard et al., 2002; Savolainen et al., 2011). The reason of this phenomenon may be complex; previous studies show that the drivers’ physique (Salva et al., 2014) decrease with age, and as well as their endurance (Molnar and Eby, 2008), getting information ability (Owsley et al., 2011), visual field (Huisingh et al., 2015), and hearing (Green et al., 2013). In addition, the increasing of average reaction time when facing with complicated traffic situation (Keskinen et al., 1998; Savolainen et al., 2011) may also contribute to higher severity. Thirdly, histories of crashes and convictions have different influences on the drivers in different clusters. The variables are significant in cluster 1 and cluster 2 while unapparent in cluster 3. Besides, the variables decrease the likelihood of more severe accidents to cluster 1 middle-aged drivers. It may indicate that the middle-aged drivers are ‘once bitten, twice shy’, in other word, the histories of driving violations may have some educational and warning impact on them. The results are in line with some previous studies, researchers found that previous not-at-fault crashes and suspensions are associated with alleviative accident severity (Chandraratna et al., 2006) and convictions are associated with a 35% reduction in the relative risk of a crash to middle-aged drivers (Redelmeier et al., 2003). Differently with cluster 1, drivers in cluster 2 are mainly young (22.6%) and elder (70.4%); and the variables to them are associated with aggravated accident severity. These results are also similar with some previous research; Knight (2004) figured out that the young male drivers who have previous crash, suspension, speeding, or DWI violation are more likely to get involved into fatal accidents (OR = 1.5, 1.6, 1.5, and 1.5); Blows et al. (2005) also found that young drivers (less than 25 years) who have traffic convictions in past 12 months are between two and four times more likely to have severe injuries or fatal accidents while driving the same time period, moreover, the probability has significant positive correlation with the amount of previous traffic convictions. Focusing on older drivers (over 56 years old), Daigneault et al. (2002) discovered that elder drivers with previous convictions or accidents have an increase risk to have subsequent accidents, and elder the driver, higher the risk. And the last, risky behaviors are also significantly associated with accident severity. Though only a small percent of bus drivers involved in accidents are charged with bad driving behaviors, their impact of aggravating accident severity are far from being ignored. Previous research have the same conclusion with these results (Beyth-Marom et al., 1993; Cooper et al., 2000; Klauer et al., 2014; Marlatt and Donovan, 2005; Sternas, 2014). Notably, the percentages of the bus drivers involved in accidents with risky behaviors are diverse in different clusters, cluster 2 has the highest percent and following is cluster 3 and the least is cluster 1. From the differences among the three clusters, we infer that the reason of different types of drivers charged by different probabilities of risky driving behaviors may be the comprehensive influences of age, gender, history of traffic violations and other factors. The conclusions are in line with some previous research; Roman et al. (2015) figured out male drivers and younger age are more easily getting involved with higher levels of aberrant behavior; Atchley et al. (2012) also found that young drivers are more likely charged by distracted driving despite consistent results showing they know the risk of driving distracted. Weng and Meng (2012) concluded that effects of environment (i.e., bad weather, road and light conditions), vehicle and driver characteristics (i.e., age and gender) have various impact on different types of drivers, and in their results, middle-aged drivers behave better than young-aged and elder drivers. However, there still remains some unclearly details, such as the mechanism of action of these behaviors, and more research should to be done to figure out the underlying factors affecting risky driving behaviors. And research is also needed regarding the measures aimed

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at reduce the ratios of risky behaviors: (a) use of advanced driver information system (ADIS); (b) more severe punishment toward risky behaviors; (c) establishment of drivers’ self-inspection programs; (d) use of speeding alarm or other equipment for preventing speeding. All the four portions above show why drivers in different clusters have different possibilities to get involved in more severe accidents. In some extent, the results can be used to define which kind of drivers is the safest, and which kind of drivers should be taken more measures to reduce their possibilities to get involved in more severe accidents. Furthermore, it could be used to identify drivers as a pre-intervention screening measure. Considering the risk factors which significantly associated with accident severity to all the three clusters, some conclusions can be confirmed. Model results show that autumn and winter increase the severity levels of bus accidents in comparison to spring. The results are in line with some previous research; for instance, Zhang et al. (2000) found that July-September and October-December raise the possibility of more severe accidents by 29% and 11% in comparison with January–March; Mehmandar et al. (2014) analyzed of crash data in Iran and found that the mortality rate was 82.8% in wintertime, 60.2% in autumn, and in 35.8% in summertime, which is the lowest rate. Results show that driving at evening and night also increase the severity of accidents sharply. These results agree with the results procured for other road accidents in general. For instance, Akerstedt et al. (2001) found that the highest total accident risk was seen at 04:00 h (OR = 5.7), with an OR of 11.4 for fatal accidents at the same point; Innamaa et al. (2014) found that during the night and evening the accident risk seems to have increased risk per hour. Research is needed regarding the impact of policy implications that are possibly beneficial for improving bus safety: (a) determine the reasonable final bus hour; (b) ascertain rational illumination intensity; (c) consider the rationality of driver substitution. Model results indicate that high speed limit has adverse effect on accident severity. This result is agreed with previous research (Brewster et al., 2015; Chung et al., 2014; Montella et al., 2011). However, research is needed to identify the speed differences between general traffic and bus in order to ascertain rational speed limits. The GPS data and in-vehicle data records may take into use to figure out accident-prone area, then take more measures to prevent accidents. School bus seems safer than the other bus. The result is similar with previous research; Yang et al. (2009) investigated that school buses experience low crash rates, and the majority of crashes do not lead to injury; Kaplan and Prato (2012) found that school buses are associated with lower accident severity with respect to other buses, with 19.8–37.8% decrease in the likelihood of being involved in light or severe injury accidents. These results may be related to both higher federal motor vehicle safety standards for school bus and lower driving speed. Though school bus is a relatively safe transport mode, more improvement is still needed. For instance, education for drivers of other vehicles in school zones, particularly young drivers, may be helpful in reducing school bus crashes. Results show that turning left or right are more dangerous in comparison with going straight. The results are similar with other motor vehicles (Dawson et al., 2013; McDonald et al., 2014; Peesapati et al., 2013), indicating that turning left or right have the same adverse influence in accident severity to no matter car drivers, truck drivers or bus drivers. It is probably due to visual blind and the loss of perception of the surrounding situation when the drivers turn left or right. Research is needed regarding the effectiveness of policy measures to decrease the risk; for example, retraining drivers, and establishing special lanes and multiphase for turning. The results of current research indicate that more studies and measures should to be done to improve the bus safety, and the

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following research directions are proposed: (a) bus safety improvement in developing countries, (b) a more scientific accident severity classification, especially the fatal accidents, (c) the pre-intervention in hiring bus drivers and the retraining to the drivers, and (d) the use of facility and equipment which can improve bus safety. Acknowledgments This work was financially supported by the Grant from the National High Technology Research and Development Program of China (863 Program, No. 2014AA110304). The contents of this paper reflect the views of the authors, who are responsible for the facts and the views of the authors, who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the School of Transportation Science and Engineering, the Harbin Institute of Technology. References ˜ J., 2013. 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