Conflict-Based Safety Performance Functions for Predicting Traffic Collisions by Type Emanuele Sacchi and Tarek Sayed be taken. This factor reduces the ability to evaluate the safety effects of a recently implemented countermeasure (2). Considerable recent research has focused on surrogate safety measures (3–6). A surrogate measure is taken to gain insight into a variable (e.g., collision frequency in road safety analysis) that is sometimes impractical or difficult to measure directly for the reasons mentioned. Surrogacy must meet two main conditions: the new indicator must be a measurable or observable event and must be physically linked to collision frequency through a causal relationship (7). As such, although the use of collision surrogates can offer several advantages for safety studies, the main challenge is to establish a functional relationship between collision frequency and surrogate measure. Methods that use observable noncrash traffic interaction events (sometimes referred to as near misses or traffic conflicts) have been growing in popularity as surrogate measures. Traffic conflicts are more easily measurable as they are much more frequent than crashes. The traffic conflict technique represents the most interesting application for the identification of hazardous situations involving potential risk of collision (8). The traffic conflict technique allows safety analysts to immediately observe and evaluate unsafe driving maneuvers at road locations and to investigate the relationship between such maneuvers and road characteristics. Research has shown how traffic conflicts data can be collected efficiently by field observers (9, 10), with simulation models (11), or through computer vision techniques (4, 5) to carry out a safety study.
In road safety analysis, safety performance functions (SPFs) are used to predict the average number of collisions per year at a road site. SPFs are a function of various amounts of exposure and, in some cases, sitespecific characteristics. Exposure is a measure of opportunities for collisions to occur. The circulating traffic volume is commonly adopted for this purpose. However, not all vehicles interact unsafely at a road site. Alternatively, traffic conflicts may provide a more appropriate exposure measure for collisions because they represent only unsafe interactions between vehicles. There has been some research on this topic, mainly based on aggregated data including all conflict types. In this study a stratified analysis was conducted by type of conflict. Hence, the main objectives of this research were to establish a relationship between predicted collisions and predicted conflicts by using an SPF with traffic conflicts as an exposure measure and to predict the number of specific types of conflicts and collisions at signalized intersections. The methodological framework used was a two-phase nested modeling process in which a Poisson–gamma SPF that uses traffic volume as exposure was used to predict conflicts, which were then used in another Poisson– gamma SPF to predict collisions. The proposed approach was applied to a data set of collision frequency and average hourly conflicts for 49 signalized intersections throughout British Columbia, Canada. The results demonstrate the proportional relationship between conflicts and collisions and the importance of carrying out stratified analyses when types of conflicts are combined.
The main focus of road safety research is the development of methods and techniques that can produce reliable estimates of the level of safety at various road facilities (segments and intersections). A large body of studies has focused on developing tools, that is, safety performance functions (SPFs), to predict road safety with collision frequency as the main safety measure (1). However, the development of SPFs requires prolonged observational periods because of the rarity and randomness of traffic collisions. Moreover, there are issues with the quality and availability of collision data in many jurisdictions: collision reports suffer from data entry errors, missing records, poor location information, and lack of accident severity levels. As well, the use of crash records for safety analysis is reactive, that is, many crashes must be collected before preventive action can
Conflict-Based SPFs Recently, SPFs for predicting the impact on road safety (given traffic volume and site-specific characteristics of a location) have been developed that use traffic conflict observations. In developing these conflict-based SPFs, researchers have argued that traffic conflicts are based on vehicle interactions and can be an appropriate predictor for collisions (12–14). Usually, exposure measures such as traffic volume are used as the main collision predictor. Exposure is generally defined as the number of traffic events in which there is a reasonable chain of events that could lead to a collision between road users (15). However, commonly used exposure measures such as the product of intersection volumes raised to a power are simplistic since not every vehicle entering the intersection is endangered by every other vehicle in the conflicting vehicular stream. Furthermore, aggregate measurements of traffic volume such as average annual daily traffic do not explicitly consider that not all vehicles are interacting unsafely. Development of conflict-based SPFs can offer several advantages. Since there are varying degrees of interactions for vehicles within a
Department of Civil Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, British Columbia V6T 1Z4, Canada. Corresponding author: E. Sacchi,
[email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 2583, Transportation Research Board, Washington, D.C., 2016, pp. 50–55. DOI: 10.3141/2583-07 50
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traffic stream, vehicles on a collision course (conflicting) should be more associated with a crash occurrence than an aggregate count of traffic volume. Hence, conflict-based SPFs can be used to predict the number of traffic conflicts occurring on an entity, and then the resulting expected conflict frequency can be used as a predictor for collision-based SPFs. Moreover, conflict-based SPFs can be useful for estimating the change in the expected conflict frequency caused by a change in an explanatory variable. That is, the conflict-based SPF can help transportation practitioners to better understand the effect of various contributing factors on the expected traffic conflict frequency.
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lating traffic volume), the mixed-Poisson distribution family can be used in this regard. Let Zi denote the AHC at site i (i = 1, . . . , n). It is assumed that the AHC at n sites are independent and that Z i θi ∼ Poisson (θi )
(1)
θi = µ cf,i i ε cf,i
(2)
ln (µ cf,i ) = ln ( b0 ) + b1 ln (Vi ) + b2 X1i + . . . + b j Xji
(3)
where Research Statement There are quality, quantity, and statistical challenges associated with the reliance on collision data alone to evaluate road safety. Traffic conflicts may provide a more appropriate exposure measure for collisions as they represent only unsafe interactions among vehicles. Research has attempted to adopt and transfer the quantitative collision analysis methodologies to conflict-based analysis. This is a promising new stream of research as conflict-based SPFs represent a useful tool that can be used in a variety of road safety applications in the same way as collision-based SPFs (14). However, research on this topic has focused on aggregated data including all conflict types. El-Basyouny and Sayed, for instance, developed a conflictbased negative binomial SPF for all conflict types and showed that a significant proportional relationship exists between conflicts and collisions where the moderating effects of conflicts on collisions are nonlinear with decreasing rates (12). In this study a stratified analysis was conducted by types of conflicts. For the stratified analysis, the events were classified by the nature of the conflict for a better understanding of the relationship between crashes and near crashes for various types of conflicts. Each conflict type contains similarities in the sequence of events and potential contributing factors, whereas these similarities may be absent in an assessment across all types of conflicts. Therefore, the main objectives of this research were (a) to establish a relationship between predicted collisions and predicted conflicts and (b) to predict the number of specific types of conflicts and collisions (i.e., rear-end and left-turn) at urban and suburban intersection approaches with conflict- and collision-based SPFs. Similar to the work of El-Basyouny and Sayed (12), this study used a Poisson–gamma modeling framework to predict conflicts, which were then used in another Poisson–gamma SPF to predict collisions. The proposed approach was applied to a data set on collision frequency and average hourly conflicts (AHCs) for 49 signalized intersections throughout British Columbia, Canada. For the prediction, the Bayesian method was selected because it is a state-of-the-art technique for statistical analysis of road safety (16).
Methodology This section describes the methodological framework used to estimate the relationship between predicted conflicts and predicted collisions (12). First, the number of potential conflicts related to the number of vehicles arriving within a small time interval at a road site can be modeled as a Poisson process. Assuming that traffic conflict data are of nonnegative, discrete, and rare events (compared with the circu-
µcf,i = estimate of predicted AHCs, cf = conflicts, Vi = exposure parameter such as the square root of the product of conflicting volumes, Xj = explanatory variables added to the model, (b1, . . . , bj) = vector of unknown coefficients, and εcf,i = random error term to model possible overdispersion in traffic conflict count. Moreover, when ε cf,i ∼ gamma ( a, b )
(4)
the model is called Poisson–gamma with mean and variance defined as E(ε) = a • b and var(ε) = a • b2. When a = κ and b = 1/κ, the Poisson– gamma model is equivalent to the traditional negative binomial error structure for collision-based SPFs where the overdispersion parameter κ conflicts ∼ gamma (1, 1)
(5)
indicates the variability around the estimated mean. In the same way, let Yi denote the number of accidents at site i. It is assumed that accidents at n sites are independent and that Yi ∼ Poisson ( λ i )
(6)
To address overdispersion for unobserved and unmeasured heterogeneity, it is assumed that λ i = µ cl,i i ε cl,i
(7)
, 1 κ ε cl,i ∼ gamma collisions κ collisions
(8)
where cl = collisions and κcollisions is the inverse dispersion parameter and the predicted number of accidents µi can be given by a collision prediction model based on traffic conflicts: ln (µ cl,i ) = ln (c0 ) + c1 ln (θi )
(9)
where c0 and c1 are the model parameters. The parameter θi can be expressed as expected AHC and obtained from a traffic conflict prediction model (Equation 3). The Poisson–gamma hierarchy leads to the negative binomial model, under which the mean and variance of Yi is given by E (Yi ) = µ i
(10)
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var (Yi ) = µ i +
Transportation Research Record 2583
µ i2 κ
(11)
The negative binomial (Poisson–gamma) model is the preferred distribution for modeling collision data since the model account for the discrete, rare, nonnegative, and random characteristics of crash events while addressing the overdispersion that commonly exists in collision data. Traffic Conflict Prediction Model According to Equation 3, the expected AHC frequency, E(AHC), for a specific site can be calculated as E ( AHC) = b0 i PEV b1
Then, the posterior distributions were sampled with Markov chain Monte Carlo techniques so that it was possible to obtain approximate quantities of the posterior mean and variance of the mean. The WinBUGS code, which was used as the modeling platform, produces draws from the posterior distribution of the parameters. In this study, the posterior mean and standard deviation of the parameters were computed with 40,000 iterations of two independent Markov chains for each of the parameters in the models. Chains were thinned with a factor of 10, and the first 10,000 iterations in each chain were discarded as burn-in runs. The convergence was monitored by reaching ratios of the Monte Carlo errors relative to the standard deviations for each parameter smaller than 5% through use of the Brooks–Gelman–Rubin diagnostic statistics of WinBUGS (19) and with visual approaches such as observation of trace plots.
(12) Data Description
with PEV = AHV1 i AHV2
(13)
where PEV is the geometric mean of the product of entering volumes, that is, AHV1 (the major volume) and AHV2 (the minor volume), and bi are model coefficients to be estimated. Collision Prediction Model Based on Traffic Conflicts Traffic conflicts are based on vehicle interactions; they can provide a more appropriate predictor for collisions than traffic volumes because not every vehicle entering the intersection is endangered by every other vehicle in the conflicting vehicular stream. For this reason, once AHC is known for a specific intersection, it is possible to estimate the expected collision frequency for that site, E(Y), as E (Y ) = c0 i AHCc1
(14)
where the collision prediction model represents a functional relationship between predicted traffic conflicts and predicted number of collisions (12). Bayesian Estimation of Model Parameters In classical (frequentist) inference, the parameters of the regression model are fixed quantities that are obtained, for instance, by maximizing the likelihood function (17). The formulation of Bayesian models has the additional feature of requiring the formulation of a set of prior distributions for any unknown parameter. A prior distribution summarizes any knowledge about the parameters that may be available before any data are observed. Then a posterior distribution is estimated with sampling techniques. The specification of a set of prior distributions for a problem usually involves hyperparameters (i.e., parameters of the prior distribution). In this study, prior distributions for the whole set of parameters (e.g., bj and cj) were assumed as noninformative to reflect the lack of precise knowledge of their value. In detail, following the work of El-Basyouny and Sayed (18), the regression parameters were chosen as diffused normal distributions, with zero mean and large variance, that is, normal(0, 103), and as gamma(1, 1) for the shape parameter.
The sample of intersections used for this study was part of the Insurance Corporation of British Columbia (ICBC) road improvement program, which is a partnership between ICBC and various road authorities in British Columbia for investing in road safety improvements to reduce the frequency and severity of collisions and thereby reduce insurance claim costs. The partnership often starts with an engineering study of a problematic location that is nominated by the road authority, with some input from local ICBC staff. The engineering study typically identifies (a) the causal factors of the safety problem at the site and (b) the road improvement strategies (countermeasures). Traffic conflict analysis is usually used in the safety analysis. The data set used was obtained from two sources. The AHC data were collected in 1996 through conflict surveys conducted by ICBC in partnership with British Columbia municipalities and the British Columbia Ministry of Transportation and Highways (3, 12). The data on collision frequency were provided by the Ministry of Transportation and Highways for a 3-year period (1995 to 1997). Table 1 describes the data on collision frequency, AHCs, average hourly volumes, and area type (urban or suburban) for 49 signalized intersections throughout British Columbia. Thirteen of these signalized intersections are in urban areas where congestion is a typical cause for traffic conflicts; the remaining 36 intersections are in suburban areas where speeding and intersection inconspicuity are typical causes for traffic conflicts. For each study intersection, traffic conflicts were observed for 2 days, 8 h per day. Typically, two trained observers were stationed at strategic intersection observation locations. The British Columbia traffic conflict observation manual was used to train the observers to recognize traffic conflicts that typically occur at intersections and to provide them with step-by-step instructions for conducting the survey and recording traffic conflicts through time–proximity measures. The hours of observation were distributed as follows: morning period, 07:00 to 10:00; noon period, 11:00 to 13:00; and afternoon period, 15:00 to 18:00. The time to collision (TTC) was used in this analysis to define a traffic conflict. TTC is defined as “the time that remains until a collision between two vehicles would have occurred if the collision course and speed difference are maintained” (20). The main advantage of TTC is its ability to capture the severity of an interaction in an objective and quantitative way. Typically, the severity of a traffic conflict is based on the TTC value, lower values indicating a more serious conflict. In this study, only traffic conflicts with a TTC of 1.5 s or less were used. Reliability tests
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TABLE 1 Statistical Summary of Data Set Variable
Symbol
Collision frequency (3 years) Average hourly conflicts Average hourly volume—minor
Y AHC AHV1
Average hourly volume—major Area type (1 = urban, 0 = suburban)
AHV2 AREA
Minimum
Maximum
Mean
Standard Deviation
0.00 0.00
69.00 11.38
27.78 4.33
18.19 3.08
90.00 625.00 0.00
2,843.50 3,496.67 1.00
1,105.81 1,946.10 na
624.05 774.23 na
Note: na = not applicable.
of the observation method gave 77% accuracy with a 95% level of confidence and 85% accuracy for assessing the correct TTC. Figure 1 shows the distribution of observed conflicts and collisions by type for the 49 signalized intersections under investigation. The most frequently observed conflict types were left-turn conflicts (39%) and rear-end conflicts (35%). At signalized intersections, left-turn conflicts include left-turn crossing and left-turn opposing conflicts and are those that occur when a vehicle makes a left turn, placing a second vehicle, going in another direction, in danger of a head-on or right-angle collision. Rear-end conflicts occur when the first vehicle slows or changes direction and places a following vehicle in danger of a rear-end collision. The remaining conflicts (26%) identified were grouped as “others.” These proportions are comparable to the those recorded for observed collisions: collisions caused by left-turn maneuvers were 29% of the total, and rear-end collisions were 37%. Other collisions recorded were 34% of the total, including single-vehicle crashes. Modeling Results This section presents the results of the two-phase nested safety performance modeling. Models were estimated for various collision and conflict types (i.e., left-turn and rear-end conflicts) and for total collisions and conflicts. In addition to the intercept and exposure, a dummy variable, AREA (1 = urban, 0 = suburban), was added to the traffic conflict prediction model with a functional form as E ( AHC) = b0 i PEV b1 i exp ( b2 i AREA )
(15)
Others 26% Left Turn 39%
Rear End 35%
Regarding the collision prediction model based on traffic conflicts, the baseline model functional form was used, that is, E (Y ) = c0 i AHCc1
(16)
All-Conflict–All-Collision SPF The results of fitting the two-phase model for all conflicts and all collisions are reported in Table 2. For the part of the model related to the prediction of traffic conflict, the estimate of b1 was found to be positive and highly significant (i.e., the 5% and 95% confidence levels lie between 0.531 and 1.187), indicating that the predicted conflicts increase with traffic volume. Further, the mean estimate of b1 is less than one and suggests that the moderating effects of the exposure on conflicts are nonlinear with decreasing rates. For b2, the estimate was also positive and highly significant, demonstrating that conflicts are more likely in urban rather than suburban areas. For similar conditions in terms of exposure, the predicted conflicts in urban areas are almost twice (e0.618 = 1.85) those in suburban areas. For the part of model related to collision prediction from traffic conflicts, c1 was equal to 0.874, which indicates a 0.8% increase in predicted collisions for each 1% increase in predicted conflicts. This result confirmed the proportional relationship between conflicts and collisions where the moderating effects of conflicts on collisions are nonlinear with decreasing rates. Finally, in both cases the shape parameters, κ, were found to be highly significant, demonstrating the presence of extra-Poisson variation and thereby justifying the use of the Poisson–gamma model.
Others 34%
Left Turn 29%
Rear End 37% (a)
(b)
FIGURE 1 Distribution of observations by type: (a) conflicts and (b) collisions.
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TABLE 2 Parameter Estimates for All-Conflict–Collision SPF
TABLE 4 Parameter Estimates for Rear-End Conflict–Collision SPF
Parameter
Mean
Standard Deviation
5% CL
95% CL
ln(b0) b1 b2 κconflict ln(c0) c1 κcollision
−3.033 0.857 0.618 7.428 −0.992 0.874 4.831
0.542 0.198 0.195 1.985 0.585 0.158 1.220
−3.922 0.531 0.301 4.615 −1.991 0.626 3.027
−2.109 1.187 0.939 11.150 −0.024 1.144 7.263
Parameter
Mean
ln(b0) b1 b2 κconflict ln(c0) c1 κcollision
−3.858 1.913 0.526 5.052 −0.508 0.562 4.145
Standard Deviation
5% CL
95% CL
0.737 0.387 0.291 1.741 0.557 0.123 1.159
−5.000 1.299 0.048 2.592 −1.466 0.378 2.586
−2.605 2.575 1.006 8.217 0.397 0.782 6.316
Note: CL = confidence level.
Left-Turn Conflict or Collision SPF The results of fitting the two-phase safety performance model for left-turn conflicts and collisions only are shown in Table 3. In this case, the coefficient related to traffic volume (b1) was less than 1 and equal to 0.773, which means that the traffic conflict count increased less rapidly than traffic volume. However, the frequency of collisions was found to increase more rapidly than the volume of exposure if the number of potential conflicts is used as an indicator of exposure to risk. This result is showed by coefficient c1, which was estimated as equal to 1.164. For the confidence intervals of the whole set of estimates, the sign of the coefficients was significant at both the 5% and the 95% confidence level (i.e., the ranges did not include a value with a sign different from the mean, apart from the log-intercept value, which always provides a positive value for b0 and c0).
the frequency of collisions is likely to decline as a function of the volume of exposure if the potential number of conflicts is used as an indicator of exposure to risk. This result is confirmed by the mean value of c1, which was estimated to be equal to 0.562 and is lower than that for the all conflict–collision model (i.e., c1 = 0.874). Looking at the confidence intervals of the whole set of estimates, the sign of the coefficients was significant at both the 5% and 95% confidence level (i.e., the ranges did not include a value with sign different from the mean, apart from the log-intercept value which provides always a positive value for b0 and c0). Overall, the model parameters in Tables 3 and 4 show that the actual relationship between crashes and near crashes for various types of conflicts can get lost when the assessment is carried out across all types. Therefore, stratified analysis is needed when left-turn conflicts and rear-end conflicts at intersections are combined, such as in this study.
Rear-End Conflict or Collision SPF
Conclusions
Table 4 illustrates the results of fitting the two-phase nested model for rear-end conflicts and collisions only. The resulting magnitude of coefficient b1 (traffic volume) was found with a value of approximately 1.9, which means that the conflict count increases more rapidly than traffic volume. This finding is similar to what has been recently hypothesized by Elvik et al. (21), who stated that it is reasonable that the number of conflicts involving lane changes or braking at intersections increase more rapidly than traffic volume. Then,
In this research, conflict and collision SPFs were successfully developed with Bayesian statistical techniques. The proposed two-phase nested model was applied to a data set corresponding to 49 signalized intersections in British Columbia. In the first phase, a Poisson–gamma model was used to predict conflicts, which were then used in the second phase in another Poisson–gamma SPF to predict collisions. The Bayesian method was selected to estimate the SPF parameters because it is a state-of-the-art technique for road safety statistical analysis. Models were estimated for various collision and conflict types (i.e., left-turn and rear-end conflicts) and for all collisions and conflicts. The results for all conflicts and collisions indicated that the predicted AHCs increase with traffic volume, suggesting that the moderating effects of the exposure on conflicts are nonlinear with decreasing rates. For the part of the model related to collision prediction from traffic conflicts, a 0.8% increase in predicted collisions for each 1% increase in predicted conflicts was estimated. This result confirmed the proportional relationship between conflicts and collisions where the moderating effects of conflicts on collisions are nonlinear with decreasing rates. For left-turn conflicts and collisions only, the traffic conflict prediction model showed that left-turn conflicts increase less rapidly than traffic volume. However, the frequency of left-turn collisions was found to increase more rapidly than the potential number of left-turn conflicts. However, the count of rear-end conflicts increases more
TABLE 3 Parameter Estimates for Left-Turn Conflict–Collision SPF Parameter
Mean
ln(b0) b1 b2 κconflict ln(c0) c1 κcollision
−2.993 0.773 0.524 4.797 −0.352 1.164 2.675
Standard Deviation
5% CL
95% CL
0.651 0.266 0.263 1.630 0.757 0.295 0.868
−4.080 0.346 0.109 2.682 −1.598 0.723 1.472
−1.925 1.227 0.960 7.815 0.908 1.681 4.355
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rapidly than traffic volume, but the frequency of collisions is likely to decline as a function of the volume of exposure if the potential number of conflicts is used as an indicator of exposure to risk. These findings highlight the importance of carrying out stratified analyses when various types of conflicts are combined. Further research should expand the analysis to other conflict types to generalize the results achieved. Moreover, in this study, conflicts were collected through conflict surveys and field observers. However, because of recent advances in computer vision techniques (4, 5), the automatic extraction of conflicts from video streams is becoming particularly useful for addressing the major limitation associated with collecting conflict data through field observers. Hence, it is hoped that a similar study can be replicated in the future with this new method for collecting conflicts. References 1. Highway Safety Manual. AASHTO, Washington, D.C., 2010. 2. Sacchi, E., and T. Sayed. A Comparison of Collision-Based and ConflictBased Safety Evaluations: The Case of Right-Turn Smart Channels. Accident Analysis and Prevention, Vol. 59, 2013, pp. 260–266. 3. Sayed, T., and S. Zein. Traffic Conflict Standards for Intersections. Transportation Planning and Technology, Vol. 22, No. 4, 1999, pp. 309–323. 4. Saunier, N., and T. Sayed. Automated Analysis of Road Safety with Video Data. In Transportation Research Record: Journal of the Transportation Research Board, No. 2019, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 57–64. 5. Sayed, T., M. Zaki, and J. Autey. Automated Safety Diagnosis of VehicleBicycle Interactions Using Computer Vision Analysis. Safety Science, Vol. 59, 2013, pp. 163–172. 6. Chen, Y., B. Persaud, E. Sacchi, and M. Bassani. Investigation of Models for Relating Roundabout Safety to Predicted Speed. Accident Analysis and Prevention, Vol. 50, 2013, pp. 196–203. 7. Tarko, A., G. Davis, N. Saunier, T. Sayed, and S. Washington. Surrogate Measures of Safety. White paper. Subcommittee on Surrogate Measures of Safety, Transportation Research Board, Washington, D.C., 2009. 8. Hydén, C. The Development of a Method for Traffic Safety Evaluation: The Swedish Traffic Conflicts Technique. Bulletin 70. Institute för Trafikteknik, LTH, Lund, Sweden, 1987.
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