1 A Bayesian Modeling Approach for Cyclist Injury Risk Analysis at Intersections and Corridors Jillian Strauss PhD Student Department of Civil Engineering and Applied Mechanics McGill University Macdonald Engineering Building Sherbrooke Street West, Montréal, QC HA K CANADA Phone: Luis F. Miranda-Moreno Assistant Professor Department of Civil Engineering and Applied Mechanics McGill University Macdonald Engineering Building Sherbrooke Street West, Montréal, QC HA K CANADA Phone: -- Patrick Morency Montreal Department of Public Health Montreal Health and Social Service Agency 0 Sherbrooke Street East, Montréal, QC HL M CANADA Phone: --00 ext.: Revised Version Re-Submission date: Thursday November th, 0 Word count *(),0
2 Strauss, Miranda-Moreno, Morency 0 0 ABSTRACT This study proposes a two-equation Bayesian modeling approach to simultaneously study cyclist injury occurrence and bicycle activity at signalized intersections as joint outcomes. This approach deals with the potential presence of endogeneity and unobserved heterogeneities and is used to identify contributing factors associated with both cyclist injuries and volumes. Its applicability in the identification of corridors at high-risk is also illustrated. An extensive inventory of a large sample of signalized intersections on the island of Montreal is used as the application environment. This inventory contains not only disaggregate vehicular traffic volumes and bicycle flows but also geometric design, traffic controls and built environment characteristics in the vicinity of the intersections. Among other results, this study identifies the importance of both bicycle and motor-vehicle flows on cyclist injury occurrence and further emphasizes the importance of turning motor-vehicle movements. It was also found that the presence of bus stops and total crosswalk width have a positive effect on cyclist injury occurrence whereas the presence of a raised median has a negative effect. The results also reveal that bicycle activity through intersections increases as employment, number of metro stations, land use mix, area of commercial land use type and length of bicycle facilities increase as well as in the presence of schools measured between 0 and 00 metres from the intersection. Also, intersections with three approaches are expected to have fewer cyclists than intersections with four approaches. Using Bayesian analysis, expected injuries and injury rates for each intersection are then used to build and rank corridors. We found that corridors with high bicycle volumes, located mainly in the central neighbourhoods of Montreal, have lower risk despite having a high number of cyclists riding along each day. This result may reflect a "safety in numbers" effect or identify safer geometric design and built environment. Despite these corridors having a lower individual risk, they are nevertheless associated with a greater number of injuries.
3 Strauss, Miranda-Moreno, Morency INTRODUCTION While cyclist numbers continue to rise and the benefits continue to be enjoyed, cycling in urban environments still comes with serious safety concerns, in particular at intersections. An intersection is a complex area where many interactions can occur between cyclists, motorvehicles and pedestrians. Over a five year period from to 00, over 000 cyclists were injured on the island of Montreal, about 0% of which occurred at intersections (). Cyclist injuries are not only frequent at signalized intersection but also with serious consequences. When a collision involves a motor-vehicle and a cyclist, 00 out of 000 require the hospitalization of the cyclist and 0 out of 000 result in a fatality. Whereas if a motor-vehicle is not involved, 0 out of 000 accidents require hospitalization and less than out of 000 results in a fatality (). 0% of cyclist fatalities are the result of a collision with a motor-vehicle (). Given the importance of this issue, cyclist injury occurrence at intersections is a topic that has started to receive the attention it deserves. Recent studies looking at different aspects of cyclist safety at intersections and bicycle facilities have been reported (,,,,,). Various studies have investigated the link between motor-vehicle and bicycle flows on crash frequency at intersections (,,) while very few have focused on analysing the safety effectiveness of bicycle facilities (). To date, little is known about the effect of traffic control, geometric design and built environment factors on cyclist injury risk (). Despite these important efforts, gaps in the current literature still exist. To our knowledge, no previous studies have tried to model cyclist injury risk and bicycle activity simultaneously. Observed geometric design and built environmental attributes as well as unobserved factors can be associated with both outcomes. For example, the implementation of an intersection treatment (e.g., bicycle lane, a change in geometry, vehicular traffic movements or behavioural changes) may be associated with an increase or decrease in bicycle volumes as well as in the historical number of injuries. Due to unobserved factors affecting both cyclist injuries and bicycle flows, there is need for a simultaneous model. This is often referred to as the endogenous problem. When identifying contributing risk factors or identifying corridors at high risk, this statistical issue should be taken into account. An appropriate method will also help to provide better estimates for identifying and ranking dangerous or problematic cycling corridors. This study has three main objectives, to: ) propose a two-equation simultaneous Bayesian model to study cyclist injury occurrence and bicycle activity while considering the endogeneity problem, ) identify geometric design, built environment and traffic control characteristics associated with injury occurrence and bicycle volumes and ) propose an approach for ranking bicycle corridors using different injury risk criteria. This paper is broken down into several sections. Section offers a literature review. Section describes the methodology followed the site selection and data in section. Section discusses the results and section presents the conclusions drawn from this study as well as the limitations and directions for future work.. LITERATURE REVIEW In recent years, cyclist safety studies examining the factors affecting crash occurrence (,,,,) and injury severity (0,,) have begun to emerge. Among the important crash occurrence studies, we can mention the work of Brüde and Larsson () who modeled cyclist injuries having occurred at junctions in 0 different municipalities in Sweden based on police report data from to. They obtained elasticities of % and.% for bicycle and motor-vehicle flows respectively on cyclist injury occurrence.
4 Strauss, Miranda-Moreno, Morency At signalized intersections in Tokyo, Japan, Wang and Nihan () carried out a study to estimate cyclist injuries involving motor-vehicles and cyclists over a four-year period from to using police report data. Among their main findings, they identified that an increase in bicycle volume is associated with a lower collision risk with turning motor-vehicles whereas a higher number of turning lanes increases the risk of collision when vehicles are turning. Overall, these previous studies have identified that there is a non-linear relationship between both bicycle and motor-vehicle flows on cyclist injury occurrence. This relationship has been referred to as the "safety in numbers" effect with respect to bicycle flows (). As bicycle flows increase, so does the absolute number of cyclist injuries, however the individual risk faced by each cyclist declines. If the number of cyclists remains constant and there is an increase in motor-vehicle flow, this would cause an increase in cyclist injuries as well as in the risk per cyclist. In his recent paper, Elvik () summarizes some of the cyclist safety studies that have studied this non-linearity. Overall these studies have found that the frequency of bicycle accidents increases by 0% when bicycle flows increase by % to.% or when motor-vehicles increase by % to.%. In addition to modeling cyclist injury occurrence, it is also important to be able to identify hotspots and rank these sites. If there is a limited amount of funds available, this can be allocated to the most dangerous sites or distributed among all sites exceeding a desired safety threshold. This task requires good estimates in order to obtain accurate and comparable measures of the risk at each site. Several recent studies have defined and applied a Bayesian Hierarchical approach to identify hazardous locations (,,,,). Many applications of the multivariate Poisson hierarchical model with covariates and time-space random effects have been documented in the road safety literature. Among others, Tunaru (), Brijs et al. (), Song et al. (), Ma et al. (), Pei et al. (0) have analyzed accident datasets with different severity outcomes. For a literature review, refer to Lord and Mannering (). Bayesian models are very popular in road safety literature since posterior risk estimates can be easily computed. Risk estimates at different spatial levels can then be used to identify intersections, corridors or areas at high risk. Among the most popular posterior risk estimates is the posterior mean number of injuries, the posterior injury rate, the potential for injury reduction, the posterior distribution of ranks and the posterior probability that a site is the worst (,,). Despite this extensive literature, little effort has been done to map cyclist risk using Bayesian methods for the identification of dangerous corridors while also correcting for explanatory variables (traffic conditions, geometric design and traffic controls). Although these previous studies are useful, they suffer from several shortcomings. To date, cyclist safety studies are rare in North America and most have been carried out in European and Asian cities. While a few studies have been carried out in the United States and in Australia, these have mainly focused on cyclist injuries at the city or town level and did not focus on intersections (junctions) as the unit of study (). Efforts have recently been made to study this topic in a Canadian context (,). Also, most of these studies have used total cyclist and total motor-vehicle flows as a measure of risk exposure and have not considered more disaggregate measures to allow a complete observation of the impact of the different movements and have also not considered geometric design, built environment and traffic control characteristics related to the layout and location of the intersections. Furthermore, previous studies are based on old data and relatively small sample sizes. Most importantly, in the emerging literature, cyclist injury occurrence and bicycle activity have been modeled independently and very few studies, if any,
5 Strauss, Miranda-Moreno, Morency have accounted for endogenous effects which may arise since the relationship between cyclist injury occurrence, bicycle flows and facilities as well as other factors for which the direction of causality may be unknown or for which there are unobserved factors can cause endogeneity. When endogenous effects are present and left unaccounted for, this can lead to biased and incorrect parameter estimates, however, accounting for endogenous effects often requires more complex estimation procedures (). While the main focus of this paper is to model cyclist injuries, knowledge of the factors having a positive or negative effect on bicycle activity through intersections is required. Three recent studies in California as well as one even more recent study in Montreal have modeled bicycle activity based on certain geometric design and built environment factors, road and transit characteristics as well as socio-demographic attributes (,,,). These studies have applied both linear and log-linear regression models and found that: employment, presence of schools, metro stations, bus stops, land use mix, commercial retail properties, proximity to a major university, mean income, bus frequency, presence and proximity of bicycle facilities, road network connectivity as well as non-hilly terrain have a positive effect on bicycle activity, whereas average street length and the presence of parking entrances/exits have a negative effect on bicycle activity. This research tries to address some of the above mentioned research gaps by developing a methodology that includes the combination of different sources of data and the use of disaggregate motor-vehicle flows and addresses the possibility that cyclist injury occurrence and bicycle activity are correlated.. METHODOLOGY A two-equation simultaneous Bayesian framework is proposed to study cyclist injury occurrence and bicycle activity (also referred to as volumes or flows) as joint outcomes. In the model, cyclist injuries are a function of bicycle flows, motor-vehicle flows, geometric design, traffic controls and built environment characteristics as well as some unmeasured factors (unobserved sitespecific characteristics, cyclist behaviour, etc.). Bicycle flows can be a function of the built environment, geometric design variables, weather conditions and other observed and unobserved variables. In our previous work, Miranda-Moreno et al. () and Strauss and Miranda-Moreno (,), these two outcomes were studied independently. However, unobserved factors may be affecting both outcomes and potentially generating an endogeneity problem. The two outcomes can be represented as shown in Equation : Y i = f (t i, Z i, V i, x i, i ) () Z i = f (V i, w i, i ) Where: Y i = Number of cyclist injuries observed at a given intersection i (i=,..n intersections) during a period of time t i. Z i = Average annual daily bicycle flow at the same intersection calculated based on eight-hour counts which have been expanded. V i = Motor-vehicle traffic flow at the same intersection, disaggregated into left turn, right turn and through movements entering the intersection in all approaches. x i = Vector of variables including geometric design and built environment characteristics (population density, presence of metro (subway) or bus stops, bicycle facilities in the vicinity of the intersection, etc.) as well as traffic controls (left turn signals, road and crosswalk widths, presence of median, pedestrian/bicycle half or full phase, etc.).
6 Strauss, Miranda-Moreno, Morency w i = Vector of variables including mainly built environment characteristics (population density, presence of metro or bus stops, bicycle facilities in the vicinity of the intersection, etc.) as well as some geometric design and traffic controls. Note that w i and x i can contain the same or different variables. t i = Time period of observation. This varies across intersections since for intersections with bicycle facilities, we are only interested in modeling the accidents having occurred after its installation. and = Correlated error terms representing unobserved factors influencing both injuries and flows. For example, at a particular intersection, the risk perception of cyclists or adverse weather conditions might affect both the probability of injury and bicycle flows. Also, unobserved built environments or designs (e.g., red-light violations) can affect both, bicycle volumes and risky behaviours simultaneously. This study hypothesizes that there is correlation between the error terms due to unobserved factors (endogeneity). To model these two outcomes simultaneously, a bivariate mixed Poisson model with correlated Lognormal error terms is proposed. This model is formulated as: Yi ~ Poisson(t i ) Zi iz ~ Poisson( iz) With V Z exp( x... x ) iz i i exp( 0 0 w ~ N M (0, ), i i i... k w ik k where, N M () stands for the bivariate Normal distribution with mean vector 0 and covariance matrix T. In addition,,,, are model regression parameters that are assumed to follow a non-informative or informative Gaussian (Normal) distribution. Non-informative priors have a mean equal to 0 and a very large variance is assumed on each of the regression parameters, e.g. ~N(0,000). Informative priors can be assumed for some parameters with prior knowledge. j Also, the regression parameters are mutually independent. For comparison purposes, only the posterior mean of iy and the injury rates per million cyclists are computed at each intersection. The first criterion,, is perhaps the most popular in safety literature and is generally defined as shown in Equation : iz ik ) = E [ y ] p( y ) d () i 0 In addition to using posterior expectation of injury frequency, another interesting risk indicator can be formulated as the rates of injury frequency denoted here by R and defined as shown in Equation (): 0 R ti Zi () As defined previously, Z i represents the average annual bicycle flows crossing the intersection. The units of injury rate (or risk) is in millions of injuries per unit of time. Based on the injury rate values computed for all intersections with available data, corridors (with a minimum of five intersections with data and intersections no more than three kilometres apart) were constructed. These corridors built from the intersection data can be ranked allowing i
7 Strauss, Miranda-Moreno, Morency 0 resources to properly be allocated where they are most needed. To rank corridors using injury rates, one can use Equation, n c R Y R / nc i k () where n c stands for the number of intersections in the corridor.. SITE SELECTION AND DATA. Site Selection The island of Montreal, Quebec, Canada is used as the application environment. signalized intersections were selected since they meet the following four criteria: ) recent cyclist and motor-vehicle counts are available, ) counts were carried out during the cycling season, between April st and November 0 th when seasonal bicycle facilities are open, ) data regarding a large variety of geometric design and built environment characteristics have been collected and ) the completion dates are available for bicycle facilities starting, ending or passing through the intersections. Figure shows a map of the island of Montreal and the intersections studied. This figure identifies that most of the intersections are located in the central neighbourhoods of the island and clearly identifies that some areas of the island are either over or under-represented. 0 FIGURE Study intersections and average observed injury rates.
8 Strauss, Miranda-Moreno, Morency 0 0. Intersection Inventory In order to achieve the objectives identified in this research, specific data is required. This data comes from an intersection inventory that combines several different sources such as: a) bicycle and motor-vehicle counts recently collected by the Montreal Department of Transportation, b) cyclist injury data provided by the Montreal Department of Public Health (Urgences-santé), c) geometric design and traffic control data that was collected by our McGill team as well as d) built environment data from Statistics Canada, DMTI Spatial Inc., STM (Société de transport de Montréal) and AMT (Agence métropolitaine de transport). The count, injury, geometric design, traffic control and built environment data is described below and some summary statistics are provided in Table. TABLE Summary Statistics Standard Variable Mean Deviation Min Max Cyclist injury count (observed) Period of observation (years).. Bicycle flows.... Motor-vehicle right turn flows.. 0 Motor-vehicle left turn flows.. 0 Motor-vehicle through flows Presence of bus stops Total crosswalk width (sum for all approaches)....0 Presence of raised median Pedestrian signal (with or without countdown) Total number of lanes (sum for all approaches) m Employment ('000)* m Presence of schools* m Metro (subway) stations* m Land use mix* m Area of commercial land use ('000)* m Length of bicycle facilities*.. 0. Presence of three approaches * These variables were measured within either a 0, 0, 00 or 00 metre radius around the intersections a. Manual Count Data In 00, the Montreal Department of Transportation manually collected both bicycle and motorvehicle counts. These counts were carried out during three periods of the day, morning peak (:00a.m. to :00a.m.), lunch period (:00a.m. to :00p.m.) and evening peak (:0p.m. to :0p.m.), providing a total of eight hours of flow data. This dataset was filtered to only include the months for which Montreal's bicycle facilities are open, from April st to November 0th. The city of Montreal has also provided bicycle count data collected from automatic bicycle counters, loop detectors, located in specific areas along five bicycle facilities running alongside specific streets in Montreal's central neighbourhoods. Using this automatic bicycle count data, expansion factors for hour, day and month were developed. As identified in the literature, bicycle flows are affected by weather (,0). By combining the automatic bicycle count data with the weather conditions present during each hour of counts, weather models specific to Montreal have been developed (0). These weather models along with the expansion factors can then be applied to convert the eight hours of bicycle counts
9 Strauss, Miranda-Moreno, Morency into average annual daily values (). The eight hours of motor-vehicle flows have also been expanded using expansion factors provided by the city. Therefore it is the annual average daily bicycle and motor-vehicle flow values that are used as inputs in the analysis. b. Bicycle Injury Data This study uses cyclist injury count data having occurred at the intersections of interest over a six-year study period from 00 to 00. Accidents are considered as having occurred at an intersection if they are within metres of the centre point of the intersection. This study uses ambulance data instead of police report data since this data has less under-reporting and misallocation problems (). Although ambulance data may be biased towards more severe injuries, in Montreal, this source of data identified more cyclist injuries than police reports. From 00 to 00, the ambulance data reported on average,0 injuries per year whereas the police report data only reported injuries per year. Figure shows all intersections, represented by each dot, and the average observed injury rates, represented by the size of the dot. This figure identifies that overall, the intersections located in the central neighbourhoods of the Island have witnessed a greater number of cyclist injuries. Bicycle injury data is provided at the level of the individual and not at the level of the crash. If a crash should involve two cyclists, this would actually be considered as two separate injuries, however this situation arises in a very small percentage of the cases reported in this dataset. Some intersections have bicycle facilities, either bicycle lanes or cycle tracks, that were installed during the six-year study period for which we have injury data. In this case, we are only interested in accidents having occurred after the facility was completed and therefore the number of years with injury data, based on the completion date of the facilities, is considered. This is accounted for in the cyclist injury model as defined by t i in Equation. c. Geometric Design and Traffic Control Data An important data collection campaign was undertaken at McGill University during summer and fall of 00 and 0. Our team collected a rich inventory at almost 0% of signalized intersections in Montreal which includes a wide variety of geometric design and traffic control characteristics such as: number of approaches, number of lanes, type of traffic signals, pedestrian/cyclist phasing, left turn lanes and phasing, presence and width of medians, presence and type of bicycle facilities, crosswalk width and so on. Students visited each intersection in groups of two with specific data collection sheets and an odometer. All data was collected on paper and later input into identical looking sheets on the computer. d. Built Environment Characteristics Built environment characteristics such as land use, urban form and bicycle facility characteristics have been provided by different sources: Statistics Canada, DMTI Spatial Inc., STM and AMT. This data includes population, employment, income, land use, presence of metro (subway) stations, bus stops, street typology, other demographics and road and transit characteristics. These variables were extracted for four different buffer dimensions: 0 metres, 0 metres, 00 metres and 00 metres to evaluate the impact of these variables at different distances from the intersection. Although bicycle activity may be better predicted using larger buffer sizes, caution must be taken when selecting variables for the model since the proportion of correlated variables is very likely to increase with increasing buffer sizes which has been witnessed with the current buffer dimensions.
10 Strauss, Miranda-Moreno, Morency 0. RESULTS a. Factors Associated with Cyclist Injury Risk After model formulation, Gibbs sampling is used for posterior inference. This is implemented by using the open-source software OpenBUGS (Bayesian inference using Gibbs sampling). In order to obtain parameter estimates (posterior means, standard deviations and confidence intervals of regression parameters) and the DIC (Deviance Information Criterion) value, 0,000 updates are burned and then, 0,000 additional samples are drawn. For model specification, correlation among geometric design, built environment and traffic control variables was first tested using STATA software to avoid high co-linearity (value greater than 0.). Also, a standard Negative 0 Binomial regression model was fitted to each of the outcomes to pre-select potential variables for the Bayesian model. These models were also used as reference for comparison purposes. The best regression outcomes, selected based on the best DIC values and significance of all variables, are presented in Table. It is important to mention that only variables significant to the % level were retained in the final models and are shown in Table. TABLE Results Standard Coefficient Cyclist Injury Model Deviation Credible Interval Elasticity* Ln bicycle flows Ln motor-vehicle right turn flows Ln motor-vehicle left turn flows Presence of bus stops Total crosswalk width Presence of raised median Constant Bicycle Activity Model 00m Employment ('000) m Presence of schools m Metro (subway) stations m Land use mix m Length of bicycle facilities m Area of commercial land use ('000) Presence of three approaches Constant DIC Covariance. *Elasticities are expressed in terms of a 0% change in the independent variable or a 0 to change in the case of a dummy variable 0
11 Strauss, Miranda-Moreno, Morency Consistent with the literature, cyclist injury results reveal the importance of both bicycle and motor-vehicle flows on cyclist injury occurrence. Injury occurrence is expected to increase by over % with a 0% increase in bicycle flows. In terms of motor-vehicle flows, both left and right turn movements have significant effects on cyclist injuries whereas through moving vehicles do not and therefore have been omitted from the final results. The results identify that right turn flows have a greater impact, over left turn flows, on cyclist injury occurrence. A 0% increase in right turn and left turn motor-vehicle flows is expected to cause a.% and a.% increase in cyclist injury occurrence respectively. Overall in terms of exposure, bicycle flows are three to four times more important than any other movement at signalized intersections. These results highlight the importance of upgrading and improving intersections with high bicycle volumes in Montreal. This work suggests that particular attention be placed on right turns which should either be reduced or treated with specific countermeasures at intersections. Such countermeasures include the reduction of turning radii to force slower motor-vehicle right turns or to provide an exclusive bicycle and pedestrian signal phase. Bicycle boxes can also be used to provide a safe place for cyclists, who wish to go straight or turn left, to wait for the signal to change to green. While completely restricting either left or right turns is a common practice in Montreal, it can simply move the problem to neighbouring intersections and can have negative impacts on network connectivity, travel times and delays. This countermeasure may however by justifiable at intersections with very high cyclist and/or pedestrian flows. The results related to the effect of intersection attributes on cyclist injury occurrence make intuitive sense. The presence of bus stops located at the intersection increase cyclist injury occurrence by 0%. When buses are present there is constant stopping and starting of traffic as well as manoeuvring done by both motor-vehicles and cyclists to bypass the bus, negatively affecting cyclist safety. Also, a 0% increase in the total crosswalk width at an intersection would cause a % increase in injuries. In other words, as the distance that cyclists need to cross increases so does the likelihood of them being involved in a crash. Retrofitting strategies such as curb and sidewalk extensions at intersections reduce road and therefore crossing widths. The presence of a raised median at the intersection reduces injury occurrence by over 0%. Raised medians can provide a refuge for cyclists who may have run out of time to safely cross the intersection. b. Factors Associated with Bicycle Activity A variety of built environment characteristics were tested to see their effect on bicycle activity. Employment, presence of schools, metro stations, land use mix, length of bicycle facilities and area of commercial spaces were found to have a significant and positive effect on bicycle activity. The presence of schools within 00 metres of an intersection increases bicycle activity through that intersection by %. The effect of metro stations can be interpreted as having a direct effect on bicycle activity through mode transfers during a given trip (which might be marginal). An indirect link can also be observed since in general, neighbourhoods that use transit also tend to walk and cycle more and therefore these central neighbourhoods may have a high bicycle mode share. Also, intersections with three approaches are expected to have fewer cyclists than intersections with four approaches. These results highlight the importance of the indirect link between built environment and bicycle safety. Changes in the built environment in the vicinity of an intersection can dramatically affect bicycle activity. For instance, the construction of a new school or bicycle
12 Strauss, Miranda-Moreno, Morency 0 0 facility will generate more bicycle traffic. This means that without the appropriate interventions implemented simultaneously with changes in the built environment, the number of cyclist injuries is expected to go up. Most importantly, the covariance term between the injury and activity models was found to be significant. This demonstrates the importance of taking endogeneity into account. Although not presented due to a lack of space, the results of the two-equation simultaneous model can be compared with the univariate model results. Comparing the results reveals that there are both some important and minor differences in the magnitudes of the estimated parameters. One of the advantages of the joint cyclist injury and bicycle activity model is that the potential impact of built environment changes on injuries can be estimated. To illustrate this, for example, a 0% increase in employment within 00 metres of an intersection would result in an increase of.% in bicycle flows which represents an increase of.% (0.0 x 0.) in cyclist injuries at that intersection. c. Cyclist Injury Risk along Corridors Using the posterior distribution of bicycle injuries, the posterior expected number of injuries and injury rates, as defined in Equation, were determined for all intersections. The individual risk for intersections belonging to the same corridor were then summed up and divided by the number of intersection in the corridor. Using these risk indicators, the corridors were then ranked from most to least dangerous. Figure shows these corridors with the thicker lines representing the corridors with the greatest risk for cyclists. The rates are also shown through the use of colours ranging from green for safer to red for more dangerous intersections. Boulevard Lacordaire running North-South between the Trans-Canada Highway and Boulevard Henri-Bourassa East in Saint Leonard, is identified as having the greatest risk for cyclists as can be seen in Figure as well as in Table. Note that the worst corridors in terms of the injury rates, rank quite low in the observed and expected number of accidents. This result is not surprising given the low bicycle volumes. This highlights the importance of taking into account cyclist volumes as well as the importance of the definition of the ranking criteria. FIGURE Injury rates along corridors.
13 Strauss, Miranda-Moreno, Morency 0 0 The first part of Table lists the top 0 out of corridors in terms of risk (rates) and how they rank in terms of both the observed and expected number of accidents as well as the average annual daily bicycle flows. Overall Table shows that corridors ranking high in terms of injury rates generally rank low in terms of injury frequency but rank even lower in terms of the number of cyclists riding along them. As Table shows, only one intersection ranked in the top 0 in terms of injury rate falls within the top 0 in terms of the expected number of injuries. On the other hand, corridors which are characterized as having a low risk for cyclists generally rank high or somewhere in the middle in terms of accidents but rank very high in terms of cyclist numbers, therefore providing a low risk to each individual cyclist. It is also worth mentioning that some of these corridors have either a bicycle path or cycle track along certain sections. Most importantly, the corridors in the top 0 ranking do not have any bicycle facility along them except for Rue Jean Talon Est, Avenue de L'Eglise and Boulevard Thimens which each have a cycle track along a small section of the corridor. The second part of Table shows the 0 worst corridors in terms of the posterior expected number of injuries. One can observe that several corridors are partially served by a bicycle facility. Boulevard de Maisonneuve, which has a physically separated cycle track running along most of its length, ranks th in terms of risk, th and th in terms of observed and expected number of accidents respectively, while ranking st in terms of the number of cyclists. For corridors with cycle tracks (thirteen corridors) and bicycle paths (eight corridors), the average rank is and 0 respectively in terms of risk. The ranking of the corridors revealed that corridors with high flows (exposure) in the central neighbourhoods have lower individual risk. This result may reflect the presence of a "safety in numbers" effect or identify that cyclists are riding in high numbers where safe designs have been implemented. It is also important to recognize that corridors with high bicycle flows also have a greater chance of ranking high since increasing bicycle flows also increases the absolute number of cyclist injuries.
14 Strauss, Miranda-Moreno, Morency TABLE Ranking of Corridors Ranking based on posterior injury rates Average across corridors Ranking of corridors Bicycle Facility % % Corridor Observed Expected Observed Expected Risk AADC* Risk AADC* Cycle Bicycle injuries** injuries** injuries injuries track path Lacordaire de la Verendrye Notre-Dame Dickson Langelier Henri-Bourassa Est Cavendish Marcel-Laurin Viau Newman Maurice-Duplessis Jean-Talon Est Cote-Vertu Dollard Industriel Henri-Bourassa Ouest de l'eglise Papineau Thimens Cote-Saint-Luc Ranking based on posterior injury frequency Average across corridors Ranking of corridors Bicycle Facility % % Corridor Observed Expected Observed Expected Risk AADC* Risk AADC* Cycle Bicycle injuries** injuries** injuries injuries track path Atwater Jeanne-Mance Viger Saint-Laurent Ontario Saint-Denis Rene-Levesque Parc de Maisonneuve Amherst Sherbrooke Lorimier University Papineau Hotel-de-Ville Montagne Pins Sainte-Catherine Saint-Antoine Frontenac * AADC stands for average annual daily cyclists ** computed based on the average of the intersections per year and averaged over the corridor
15 Strauss, Miranda-Moreno, Morency CONCLUSIONS AND FUTURE WORK This study focused on almost 0 intersections on the island of Montreal providing a wide range of traffic and bicycle exposure as well as injury counts. This paper proposes a simultaneous Bayesian modeling framework to investigate geometric design, built environmental and traffic control factors associated with both cyclist injuries and volumes. The applicability of this framework for the identification of high-risk corridors is also illustrated. Among other results, it was found that cyclist injury occurrence is sensitive to changes in both bicycle and motor-vehicle flows. This is in accordance with past studies. Cyclist volumes however have the greatest effect and injury occurrence is expected to increase by over % with a 0% increase in bicycle flows. In terms of motor-vehicle flows, right turning vehicles were found to have the greatest effect whereas the effect of through moving motor-vehicle was found to be insignificant. Several geometric design and built environmental factors are associated with cyclist safety. For instance, cyclist injuries are expected to increase at intersections where there is at least one bus stop and with increasing crosswalk width. The presence of a raised median on the other hand, is expected to reduce crashes. This study also demonstrates the important indirect effects of built environment on cyclist safety. Changes in the built environment are expected to cause direct changes in bicycle volumes and therefore indirect changes in the number of cyclist injuries at intersections. These results highlight the importance of improving safety standards when modifications are made to the built environment. Bicycle flows through intersections or along corridors are sensitive to changes in the built environment, such as the construction of a new school, metro station, bicycle facility, etc. Due to changes in bicycle flows after the installation of a new bicycle facility for example, the number of injuries is likely to increase without appropriate countermeasures. Also, as hypothesized, correlation between the error terms due to unobserved factors was found to be significant therefore confirming the presence of endogeneity. According to the corridor risk analysis, corridors ranking high in terms of injury rates, in general, rank low in terms of injury frequency. In other words, corridors with high bicycle volumes located mainly in the central neighbourhoods of Montreal have lower risk despite having a high number of cyclists riding along each day. Since there are more cyclists, these corridors have a greater chance of ranking high therefore demonstrating the "safety in numbers" effect. Again, this effect can be offset by injury occurrence since more cyclists means more expected injuries. Safety in numbers should be used as a criterion to propose and justify interventions. As part of future work, a larger sample of intersections will be used to investigate the impacts of geometric design and built environment characteristics on cyclist injury occurrence. An inventory of non-signalized intersections is currently in the process of being collected and similar studies can be tested. Even more importantly, for this inventory, cyclist movements are recorded, in -minute intervals, and not simply along which approach they are crossing. This will allow us to look more closely and disaggregately at the motor-vehicle and cyclist movements which are conflicting. Also, bicycle injury data coming from police reports will be used to validate these results. We are also preparing a before-after study to evaluate the effectiveness of bicycle facilities (cycle tracks) in Montreal. Finally, cyclist injuries occurring along road segments will be included in addition to the intersection data as used here in order to thoroughly study corridors in Montreal.
16 Strauss, Miranda-Moreno, Morency ACKNOWLEDGMENTS We acknowledge the financial support provided by the "Programme de recherche en sécurité routière" financed by FQRNT-MTQ-FRSQ. We would like to thank the Montreal Department of Public Health (Urgences-santé) for collecting and validating the injury data and for their collaboration as well as the city of Montreal for providing motor-vehicle and bicycle flow data. All remaining errors and the views expressed in this research are, however, solely ours.
17 Strauss, Miranda-Moreno REFERENCES. Vélo Québec. L État du vélo au Québec en Rodgers, G. B. Bicyclist Deaths and Fatality Risk Patterns. Accident Analysis and Prevention, Vol. (),, pp. -.. Brüde, U. and J. Larsson. Models for Predicting Accidents at Junctions Where Pedestrians and Cyclists are involved. How Well Do They Fit? Accident Analysis and Prevention, Vol.,, pp Jacobsen, P.L. Safety in Numbers: More Walkers and Bicyclists, Safer Walking and Cycling, Injury Prevention Vol., 00, pp Wang, Y. and N.L. Nihan. Estimating the Risk of Collisions Between Bicycles and Motorvehicles at Signalized Intersections. Accident Analysis and Prevention, Vol., 00, pp. -.. Elvik, R. The Non-Linearity of Risk and the Promotion of Environmentally Sustainable Transport. Accident Analysis and Prevention, Vol., 00, pp. -.. Miranda-Moreno, L.F. and J. Strauss. Disaggregate Exposure Measures and Injury Frequency Models of Cyclist Safety at Signalized Intersections. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C., 0, pp. -.. Lusk, A.C., P.G. Furth, P. Morency, L.F. Miranda-Moreno, W.C. Willett and J.T. Dennerlein. Risk of Injury for Bicycling on Cycle Tracks versus in the Street. Injury Prevention, 0, doi:0./ip Strauss, J and L.F. Miranda-Moreno. Effect of Intersection Designs on Cyclist Injury Risk. Proceedings of the nd Canadian Multidisciplinary Road Safety Conference, Banff, Alberta, Kim, J.K., S. Kim, G.F. Ulfarsson and L.A. Porrello. Bicyclist Injury Severities in Bicycle- Motor Vehicle Accidents. Accident Analysis and Prevention, Vol., 00, pp. -.. Eluru, N., C.R. Bhat, D.A. Hensher. A Mixed Generalized Ordered Response Model For Examining Pedestrian and Cyclist Injury Severity Level in Traffic Crashes. Accident Analysis and Prevention, Vol. 0, 00, pp Zahabi, S.A.H, J. Strauss, K. Manaugh and L.F. Miranda-Moreno. Estimating Potential Effect of Speed Limits, Built Environment, and Other Factors on Severity of Pedestrian and Cyclist Injuries in Crashes. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C., 0, pp. 0.. Van den Bossche, F., G. Wets and E. Lesaffre. A Bayesian Hierarchical Approach to Model the Rank of Hazardous Intersections for Bicyclists using the Gibbs Sampler. Transportation Research Board rd Annual Meeting, Washington D.C., USA Tunaru, R. Hierarchical Bayesian Models for Multiple Count Data. Austrian Journal of Statistics, Vol., No. &, 00, pp. -.. Miaou, S.-P. and J.J. Song. Bayesian Ranking of Sites for Engineering Safety Improvements: Decision Parameter, Treatability Concept, Statistical Criterion, and Spatial Dependence. Accident Analysis and Prevention, Vol., 00, pp Schluter, P.J., J.J. Deely and A.J. Nicholson. Ranking and Selecting Motor Vehicle Accident Sites by using a Hierarchical Bayesian Model. The Statistician, Vol., No.,, pp. -.
18 Strauss, Miranda-Moreno. Brijs, T., D. Karlis, F. Van de Bossche and G. Wets. A Bayesian Model for Ranking Hazardous Road Sites. Journal of the Royal Statistical Society, Vol. 0, No., 00, pp Song, J.J., M. Ghosh, S. Miaou and B. Mallick. Bayesian Multivariate Spatial Models for Roadway Traffic Crash Mapping. Journal of Multivariate Analysis, Vol., 00, pp. -.. Ma, J. K.M. Kochelman and P. Damien. A Multivariate Poisson-Lognormal Regression Model for Prediction of Crash Counts by Severity, using Bayesian Methods. Accident Analysis and Prevention, Vol. 0, 00, pp Pei, X. S.C. Wong and N.N. Sze. A Joint-Probability Approach to Crash Prediction Models. Accident Analysis and Prevention, Vol., 0, pp Lord, D. and F. Mannering. The Statistical Analysis of Crash-Frequency Data: A Review and Assessment of Methodological Alternatives. Transportation Research Part A: Policy and Practice, Vol., No., 00, pp. -0. Miranda-Moreno, L.F. Statistical Models and Methods for Identifying Hazardous Locations for Safety Improvements. PhD thesis, 00, University of Waterloo.. Keshk, O.M.G. Simultaneous Equation Models: What are they and how are they estimated. 00. Retrieved March, 0.. Haynes, M. and S. Andrzejewski. GIS Based Bicycle & Pedestrian Demand Forecasting Techniques. Travel Model Improvement Program Webinar. Available online April, 00.. Griswold, J.B., A. Medury and R.J. Schneider. Pilot Models for Estimating Bicycle Intersection Volumes. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C., 0, pp. -.. Jones, M., S. Ryan, J. Donlon, L. Ledbetter, D.R. Ragland, and L. Arnold. Seamless Travel:Measuring Bicycle and Pedestrian Activity in San Diego County and its Relationship to Land Use,Transportation, Safety, and Facility Type. Caltrans Task Order. California Department of Transportation, 00.. Strauss, J. and L.F. Miranda-Moreno. Spatial Modeling of Bicycle Activity at Signalized Intersections. Journal of Transport and Land Use Research, In press, 0.. World Road Association (PIARC) Technical Committee on Road Safety. Road Safety Manual. Route Market, France, 00. pp... Nankervis, M. The Effect of Weather and Climate on Bicycle Commuting. Transportation Research Part A: Policy and Practice, Vol.,, pp Miranda-Moreno, L.F. and T. Nosal. Weather or Not to Cycle: Temporal Trends and Impact of Weather on Cycling in an Urban Environment. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C., 0, pp. -.. Langley, J.D., N. Dow, S. Stephenson and K. Kypri. Missing Cyclists. Injury Prevention, Vol., 00, pp. -.