Accident Analysis and Prevention 74 (2014) 33–41

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A hazard-based duration model for analyzing crossing behavior of cyclists and electric bike riders at signalized intersections Xiaobao Yang a,b, *, Mei Huan a , Mohamed Abdel-Aty b , Yichuan Peng b , Ziyou Gao a a b

MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China Department of Civil, Environmental & Construction Engineering, University of Central Florida, Orlando, FL 32816, USA

A R T I C L E I N F O

A B S T R A C T

Article history: Received 6 August 2014 Received in revised form 2 October 2014 Accepted 9 October 2014 Available online xxx

This paper presents a hazard-based duration approach to investigate riders’ waiting times, violation hazards, associated risk factors, and their differences between cyclists and electric bike riders at signalized intersections. A total of 2322 two-wheeled riders approaching the intersections during red light periods were observed in Beijing, China. The data were classified into censored and uncensored data to distinguish between safe crossing and red-light running behavior. The results indicated that the red-light crossing behavior of most riders was dependent on waiting time. They were inclined to terminate waiting behavior and run against the traffic light with the increase of waiting duration. Over half of the observed riders cannot endure 49 s or longer. 25% of the riders can endure 97 s or longer. Rider type, gender, waiting position, conformity tendency and crossing traffic volume were identified to have significant effects on riders’ waiting times and violation hazards. Electric bike riders were found to be more sensitive to the external risk factors such as other riders’ crossing behavior and crossing traffic volume than cyclists. Moreover, unobserved heterogeneity was examined in the proposed models. The finding of this paper can explain when and why cyclists and electric bike riders run against the red light at intersections. The results of this paper are useful for traffic design and management agencies to implement strategies to enhance the safety of riders. ã 2014 Elsevier Ltd. All rights reserved.

Keywords: Cyclist Electric bike Red-light running Waiting time Hazard-based duration model Intersection

1. Introduction Cycling is one of the most popular modes of transportation in some Asian developing countries, such as Cambodia, India and China. Cycling still constitutes a substantial proportion among all travel modes in China. For example, regular bicycles (18.2%) and electric bikes (20.5%) were used for about 38.7% of trips in Shanghai in 2010 (City News in Shanghai, 2011). In developed countries, cycling is considered as a sustainable travel mode (Gatersleben and Appleton, 2007; Lawson et al., 2013). The advantages of cycling are energy efficient, healthy, quiet and compatible with the urban scale (Menghinia et al., 2010). Although bike is still a minority travel mode, the share rate of bicycle commuting has increased over the last decade in most developed countries (Chaurand and Delhomme, 2013). For example, the American Community Survey in 2008 showed that the City’s share of bike commuters had a full 48% increase from its

* Corresponding author at: MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China. Tel.: +86 10 5168 7070. E-mail address: [email protected] (X. Yang). http://dx.doi.org/10.1016/j.aap.2014.10.014 0001-4575/ ã 2014 Elsevier Ltd. All rights reserved.

2000 level of 0.61% to 0.90% in eight years (Los Angeles Department of City Planning, 2011). Two-thirds of all Australian households had two or more working bicycles in 2009 (Australian Bureau of Statistics, 2009). Electric bikes (e-bikes) are expanding rapidly in China in the recent ten years. Due to its labor-saving and speed, e-bike has quickly become as a popular mode of travel in many Chinese cities (Weinert et al., 2007). There were more than 160 million e-bikes in China in 2012 (Jinling Evening Newspaper, 2013). E-bikes are defined as electric two-wheelers with relatively low speeds and weights compared to motorcycles. Motorcycles are strictly restricted in urban areas of most large cities in China (Wu et al., 2012). In China, e-bikes are classified as non-motor vehicles and are given access to the bicycles’ infrastructure (Lin et al., 2008). Riders are considered as vulnerable road users, because they are unprotected in traffic crashes (ETSC, 1999). Cyclists often infringe on the traffic rules and have a higher likelihood of traffic collisions compared to pedestrians and drivers (Wegman et al., 2012). Two-wheeled riders involved in injuries and fatalities are overrepresented in traffic collisions. In 2010, 11,562 riders and their passengers of non-motorized vehicles died and 47,220 were severely injured, representing 17.7% of the total traffic deaths and 18.6% of injuries in Chinese road accidents (CRTASR, 2010). From

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X. Yang et al. / Accident Analysis and Prevention 74 (2014) 33–41

6432 cyclist collisions in Victoria, Australia between 2004 and 2008, 33.9% resulted in severe injury of the cyclist (Boufous et al., 2012). About 2100 cyclists were killed in road accidents in 2010, representing 7.2% of all traffic fatalities recorded in the 24 EU countries (ETSC, 2012). A cycle network is only as good as its weakest features and these are often the junctions (ETSC, 1999). In North Carolina, USA, 50.2% of bicycle–motor vehicle accidents occurred at intersections (Kim et al., 2007). Riders’ red-light infringement is a type of highly dangerous behavior occurring at intersections. Due to the weakness of safety awareness and enforcement, red-light infringement behavior is rather prevalent, and represents a substantial safety problem at Chinese urban intersections (Wu et al., 2012). So far, many scholars have studied the red-light crossing behavior at intersections. Most focused on pedestrian red-light violation behavior. Some useful reviews of the existing research on pedestrian street-crossing behavior can be found in Papadimitriou et al. (2009). However, only a few studies have been conducted on the red-light running behavior of cyclists, much less to electric two-wheelers. Johnson et al. (2011) used video cameras to investigate the violation rate and risk factors of cyclists’ red-light infringement at urban intersections in Melbourne, Australia. The results showed cyclists turning left were more likely to infringe on the red light compared to cyclists running straight through the intersection. Furthermore, Johnson et al. (2013) investigated various risk factors of cyclists’ red-light crossing behavior in Australia by conducting a survey on the internet. The results indicated that male, young, and cyclists with no crash experience had a larger likelihood of violating traffic lights. Their findings suggested that some cyclists were motivated to infringe by their safety perception and that infrastructure factors had significant effects on the red-light running behavior. Wu et al. (2012) used logistic model to study behavior characteristics and associated factors of red-light running for two-wheeled riders in China. The results indicated that gender, age and conformity behavior had significant effects on the cyclist’ violation, and classified the red-light crossing behavior to three types: obey the rules (44%), risk-taking (31%), opportunistic (25%). However, logistic models cannot be used to investigate riders’ waiting endurance times and violation hazards (i.e., instantaneous failure rate or conditional failure rate). Zhang and Wu (2013) used two video cameras to investigate the effect of sunshields on red-light infringement behavior of cyclists and e-bikers in the city of Hangzhou, China. Their results suggested that sunshields installed at intersections can reduce red-light infringement rates of cyclists and e-bikers on both sunny and cloudy days. Till now, however, no studies addressed the waiting times of two-wheeled riders. The waiting process is crucial to riders in the street-crossing behavior. Once riders terminate their waiting processes during the red light period, they would infringe on the traffic signal and put themselves in danger. The waiting process can be regarded as a continuous-time state which is affected by internal and external factors. Special attention should be given to riders’ waiting durations and violation hazards. In this study, hazard-based duration approach was proposed to investigate riders’ red-light running behavior. This approach can be used to describe the duration of a certain state and how various factors affect the duration. What is more, it can take into account censored data, which improves the accuracy to measurement. Duration models have been widely applied in biometrics, social science, and industrial engineering fields to determine causality in duration data. In the transportation field, they have been used to study many time-related events including travel activity, traffic accident duration, and automobile ownership (Bhat, 2000;

Chang and Yeh, 2007; Chung, 2010; Hensher and Mannering, 1994; Hojati et al., 2013; Van den Berg et al., 2012). In recent years, several scholars have applied hazard-based duration approach to investigate pedestrian crossing behavior at signalized intersections. Hamed (2001) used parametric hazard models to analyze pedestrians’ waiting times at signalized intersections in Jordan. The results revealed that pedestrians’ expected waiting time influenced the number of attempts needed to successfully cross the street. Tiwari et al. (2007) applied the non-parametric Kaplan–Meier method to study pedestrians’ violation behavior at signalized intersections in India. The results showed pedestrians would not like to wait for a long time to cross the street. Pedestrians would become impatient and violate the traffic signal as pedestrians’ waiting times increase. Wang et al. (2011), and Guo et al. (2011, 2012) used proportional hazards models to investigate pedestrian red-light infringement behavior and the associated risk factors at unban intersections in Beijing. The results showed that human factors and the external environment had significant effects on pedestrians’ street-crossing behavior. However, they did not investigate the duration of waiting times of two-wheeled riders. Besides, unobserved heterogeneity was not considered in the existing research about pedestrian waiting times. The first aim of this study is to provide an effective and practical methodology for investigating riders’ waiting times, violation hazards and associated risk factors. The second aim is to explore the differences in waiting times, violation hazards, and the effects of associated factors between cyclists and e-bikers. The finding of this paper can explain when and why cyclists and e-bikers infringe on the traffic signal at intersections. The results might help to provide solutions to enhance the safety of two-wheeled riders, which is a major issue in some developing countries in general and China in particular. 2. Model The variable of interest in duration analysis is the length of time that elapsed from the beginning of an event until its end (Nam and Mannering, 2000). In this study, the length of time is the waiting duration of a rider who arrives at the intersection during the red light period. The waiting time for each rider was taken as the difference between the arrival time when he/she arrives at the intersection and the departure time when he/she begins to cross the intersection. The waiting time can be classified into uncensored data and censored data. It is defined as uncensored data if the rider terminates the waiting duration to cross the intersection during the red light period. Otherwise, it is considered as censored data as long as the rider terminates the waiting duration to cross the intersection during the green light period. The maximum of waiting endurance is unknown for the censored data, because the real waiting endurance may be longer than the waiting time which is terminated by the presence of the green light (Guo et al., 2011). This waiting duration is a continuous random variable T with a cumulative distribution function F(t). F(t) is also known as the failure function and gives the probability that a rider has the red-light running behavior before some specified waiting time t. Conversely, the survival function, S(t), is defined as the probability that a rider waits longer than some specific time t. SðtÞ ¼ PrðT > tÞ ¼ 1  PrðT  tÞ ¼ 1  FðtÞ

(1)

The survival function is known as the endurance probability or survivor probability. The hazard function h(t) of duration time T gives the conditional failure rate. This is defined as the probability of failure during a

X. Yang et al. / Accident Analysis and Prevention 74 (2014) 33–41

very small time interval, assuming that the event has lasted to the beginning of the interval. In our study, it is the probability that a rider runs against the red light in a very short interval [t, t + Dt], given that he/she has waited to time t. hðtÞ ¼ lim

Dt!0

Prðt  T < t þ DtjT  tÞ dlnSðtÞ ¼ dt Dt

(2)

The nonparametric Kaplan–Meier (KM) estimator is the most widely used method for estimating survivor functions (Lee and Wang, 2003). In this study, it can be used to measure the waiting endurance time until the occurrence of riders’ red-light running behavior. In addition, riders’ waiting duration is influenced by various factors. A primary purpose of this study is to accommodate the effects of the explanatory variables. The effect of these variables can be accounted for by two alternative methods: fully parametric hazards and semi-parametric lifetime models (Van den Berg et al., 2012). Both methods can be used to study the waiting duration of riders. A parametric approach involves extensions of existing parametric failure time models such as exponential, Weibull and log-logistics models by means of re-parameterizations to include covariates. On the other hand, a semi-parametric approach is distribution free and involves less stringent assumptions on the underlying distribution of failure time (Balakrishnan and Rao, 2004). The fully parametric hazard model is powerful if the underlying survival distribution is known. However, the exact form of the distribution is usually unknown and it could be hard to find an appropriate model in many practical situations. According to Li (2013), the distribution of pedestrians’ intended waiting times during red light phases at intersections is U-shaped. Therefore, in such cases, the use of parametric methods is somewhat limited. Using a semi-parametric method is an ideal choice because the resulting estimates are consistent and the loss of efficiency may not be substantial even when a particular parametric form is appropriate (Bhat, 2000). The Cox proportional hazards model is the most commonly used semi-parametric model in which exp(bX) is used as the function form of the covariate influence. However, the traditional Cox proportional hazards model is based on an assumption of homogeneity of the survival distribution across individuals. If this is not the case (i.e., heterogeneity is present), the coefficient estimates will be inconsistent and the interpretation of the results will probably be incorrect (Meyer, 1990; Nam and Mannering, 2000). In addition, a key assumption in the Cox model is that the observed duration times are independent. However, in practice, duration times may be observed from related individuals. For example, some riders arrived at the intersection in the same signal phase in groups in this study. They were not independent because each rider in a group shared the same situational factors. Expanding proportional hazards model to include an unobserved random effect, called a frailty, allows for modeling association between individual duration times within a group. Specifically, suppose there are m groups with ni individuals in the ith group; Xij is the observable covariate vector for the jth individual in the ith group. Let ni be the unobservable covariates for the i th group and u be its regression coefficient. The hazard function of the jth individual in the ith group is hij ðtÞ ¼ h0 ðtÞexpðbX ij þ uni Þ; i ¼ 1; . . . ; m; j ¼ 1; . . . ; ni

Hazard-based duration models have been widely cited in the literature. For detailed discussion of duration models see Bhat (2000); Lee and Wang (2003); Balakrishnan and Rao (2004). In this study, likelihood ratio statistics are used to calculate the goodness-of-fit of the model. This statistic has been used in many previous studies to assess model fit and thus is used here (see for instance Nam and Mannering, 2000; Nam and Mannering, 2000). All statistical analyses were performed using STATA (version 12, StataCorp LP, Texas, USA). 3. Data Field observations with video recordings were used in this study. They have been widely used to investigate the red-light crossing behavior at urban intersections (Hamed, 2001; Tiwari et al., 2007; Guo et al., 2012; Johnson et al., 2011; Wu et al., 2012; Lipovac et al., 2013; Zhang and Wu, 2013). 3.1. Test sites A cross-sectional observational study was conducted at six signalized intersections in Beijing, China. Three criteria were used to choose the intersection sites. Firstly, each site should have similar geometric and traffic characteristics. Secondly, the chosen sites should be typical representations of signalized intersections in urban arterial streets. Thirdly, there should be a considerably high volume of cycling traffic. Before the final list of intersections was selected, eleven signalized intersections were observed and tested. Six typical intersections in Haidian District, Beijing were selected as the observational sites after the pilot. These chosen intersections are four-legged and have separate left-turn phases. All the sites are on the main thoroughfares in the center of the city. They have no refuge islands which can be used as a safe refuge by pedestrians and riders. 3.2. Data collection Data of riders’ crossing behavior were collected at these intersections by placing a video camera at each zebra crossing. Fig. 1 gives a photograph at Z–Z (Zhichun Rd.–Zhongguancun East Rd., observed direction: north–south) intersection to illustrate the crossing behavior of riders. The cameras were hid behind the intersection stop line so that it would not be visible. The data collection was conducted on weekdays during the daytime (i.e., 7:00 a.m.–6:30 p.m.) in good weather conditions. There were no traffic wardens employed by the police force to assist in regulating traffic order during the video recording.

(3)

Across groups, the frailties are assumed to be gamma-distributed latent random effects that affect the hazard multiplicatively. The heterogeneity can be readily handled in duration models using gamma distribution. Again, the frailty model reduces to standard Cox model when u = 0.

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Fig. 1. Photograph of riders’ crossing at Z–Z intersection.

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X. Yang et al. / Accident Analysis and Prevention 74 (2014) 33–41 Table 2 Red-light infringement rates by each subcategory.

3.3. Videotape coding All road users who entered the intersection were recorded on video, but only the two-wheeled riders who approached the intersections during red light phases and traveled through the intersections were coded (Wu et al., 2012). Right-turners were excluded because they were not subject to the traffic light according to Chinese road traffic rules, while left-turners were also omitted on account of the limited field of view of the cameras (Zhang and Wu, 2013). Videotape data was monitored by research assistants in the laboratory. Two data files in a pre-designed format were made for each site, one for riders and the other for motor vehicles which may conflict with riders. The data file for riders was used to record riders’ personal characteristics and movement information. The variables about personal characteristics included rider type, gender, and age group (Zhang and Wu, 2013). The variables about movement information included the arrival time, the departure time, the state of the traffic signal at each time, the waiting position, and the number of other riders crossing upon departure. In addition, the data file for motor vehicles was used to record environmental factors related to motor traffic, including signal timing, motor vehicle volume during the red light cycle for riders, and intersection site. Finally, two data files were matched according to the arrival time of each rider and the signal cycle which contained his/her arrival time. The main variables and their definitions are listed in Table 1. 4. Results 4.1. Descriptive statistics A total of 2322 valid samples were recorded and presented in Table 2. The overall proportion of riders’ red-light running behavior was 61.1% and varied from 46.4% to 72.1% across sites. Cyclists were less likely to cross against the red light than e-bikers (55% vs. 67%). The red-light running rate of female riders was lower than male riders (52% vs. 64%). In addition, young cyclists had lower rates of red-light infringement than middle-aged and old cyclists (48% vs. 57% and 66%, respectively). On the other hand, young and middle-aged e-bikers were found to have higher rates of red-light running than old e-bikers (68% and 68% vs. 51%). Finally, riders waiting at the appropriate position had considerably lower proportion of red-light violation than riders who did not stop at the appropriate position (30% vs. 68%). 4.2. Estimated results of the nonparametric method Fig. 2 shows the estimates of riders’ waiting endurance times for three different calculation methods: (1) only using uncensored

Rider type

Gender Male Female – Age group Young (50) – Waiting position Appropriate Inappropriate Overall

Overall

Cyclists

E-bike riders

58%a (449/778)b 50% (184/366)

69% (687/998) 55% (99/180)

64% (1136/1776) 52% (283/546)

48% (177/371) 57% (330/582) 66% (126/191)

68% (222/326) 68% (523/771) 51% (41/81)

57% (399/697) 63% (853/1353) 61% (167/272)

25% (56/223) 63% (577/921) 55% (633/1144)

37% (69/188) 72% (717/990) 67% (786/1178)

30% (125/411) 68% (1294/1911) 61% (1419/2322)

a

Red-light running proportion of the observed samples in this subcategory. The numerator is the number of the violation samples, the denominator is the number of the observed samples. b

data, (2) taking censored data as uncensored data and using both, and (3) considering censored data properly based on the nonparametric method and using both. The results indicated that cases 1 and 2 would underestimate the waiting endurance times of two-wheeled riders. Fig. 2 also shows that the endurance probability estimated by nonparametric method (case 3, a solid line) represents the probability that riders complied with the traffic signal when they crossed the intersection. The endurance probability can be divided into two parts according to the gradient. First, a rapid fall in the first 1 s indicated that a number of two-wheeled riders (21% of sample size) would cross against the red light with negligible waiting time. Next, the endurance probability decreased gradually with the increasing waiting duration. In addition, the median of the distribution was 49 s, which indicated that over half of the observed riders cannot endure 49 s or longer. The 25% quantile of the distribution was 97 s, which indicated that approximately 25% of the observed riders can endure 97 s or longer. The sample hazard calculated by the nonparametric method is shown in Fig. 3. The hazard is non-monotonic. Similarly to the endurance probability, the hazard can be divided into two parts roughly. Firstly, a high violation hazard in the first 1 s reflected parts of two-wheeled riders hurried to cross the intersection without any waiting. Then, there was a general increasing trend over time after the first 1 s. This indicates that the hazard of terminating the waiting duration would increase over the time elapsed, and so is the trend of violation for the waiting riders. In addition, for the waiting riders, the hazard curve indicated one spike at 80 s and corresponding hazard rate changed obviously. Firstly, the hazard fell to a relatively low level and fluctuated in a

Table 1 Definitions of variables coded. Variables Personal characteristics Rider type Gender Age group – Movement information Event time Traffic light status Waiting position No. of riders crossing upon departure – Environmental factors Motor vehicle volume Intersection site

Descriptions Regular bicycle rider: 0, electric bike rider: 1 Female: 0, male: 1 Estimated age group: elderly (>50): 0, middle-aged (30–50):1, young (