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35 Framework for Safety Prediction and Data Needs This chapter presents the framework for roundabout safety prediction within this project. This framework defines can- didate safety performance functions (SPFs) and crash modi- fication factors or crash modification functions (CMFs) required for roundabout safety prediction. Also discussed are the required database attributes, study designs, and sample size requirements. Safety prediction for design applications, which is fundamental to the Highway Safety Manual [(HSM) AASHTO, 2010], is first presented, followed by safety prediction for other applications such as planning and network screening. 3.1 Candidate Safety Performance Functions for Design Applications Following is a discussion of candidate SPFs and CMFs for intersection design applications. These were identified based on the literature review findings and consideration of what crash prediction models could be most useful to practitioners. Three approaches to be pursued are discussed: (1) leg-level crash prediction, (2) intersection-level crash prediction using SPFs and CMFs, and (3) leg-level crash prediction using sur- rogate measures estimated from design features and related to crashes. 3.1.1 Leg-Level Crash Prediction One option considered for this project was to build on the leg-level SPFs developed and documented in NCHRP Report 572 (Rodegerdts et al., 2007). These SPFs would con- sider several crash types: â¢ Entering-circulating crashes, â¢ Exiting-circulating crashes, â¢ Approach crashes, â¢ Downstream crashes (evaluating the downstream effects of right-turn bypass lanes), and â¢ Other crashes (including pedestrian and bicycle crashes). A model for âother crashesâ would be calibrated so that total crashes at an intersection can be predicted using the leg-level models. The ability to account for total crashes is a requirement of the HSM predictive chapters. Any crash type for which a leg-level SPF is not developed would be included in the âotherâ category, as indicated above. Candidate SPFs would use annual average daily traffic (AADT) by basic movement (e.g., entering, circulating, exit- ing) for the exposure variables and would predict total crashes of all severities combined and, if feasible, separately for KABC and O [property damageâonly (PDO)] crashes on the KABCO scale. This could result in up to 15 SPF models depending on the feasibility of developing SPFs for specific severities. â¢ Entering-circulating crashes, total; â¢ Entering-circulating crashes, PDO; â¢ Entering-circulating crashes, KABC; â¢ Exit-circulating crashes, total; â¢ Exit-circulating crashes, PDO; â¢ Exit-circulating crashes, KABC; â¢ Approach crashes, total; â¢ Approach crashes, PDO; â¢ Approach crashes, KABC; â¢ Downstream crashes, total; â¢ Downstream crashes, KABC; â¢ Downstream crashes, PDO; â¢ Other crashes, total; â¢ Other crashes, PDO; and â¢ Other crashes, KABC. This approach would compare whether it is better to pre- dict total crashes directly from the SPF or by summing the predictions from the KABC and PDO SPFs. This comparison was proposed because of the inconsistent reporting of PDO crashes among jurisdictions. This inconsistency permeates the observed âPDOâ and âtotalâ crash frequency data. It adds an unknown amount of variation in data from multiple jurisdictions that makes it difficult to determine whether crash C H A P T E R 3
36 trends in a multijurisdiction database are due to differences in driver behavior or design practices (as may vary among jurisdictions) or due to differences in crash reporting thresh- olds and/or practices. For other combinations of severity (e.g., KAB) the prob- abilistic approach being taken in NCHRP Project 17-62, âImproved Prediction Models for Crash Types and Crash Severitiesâ and NCHRP Project 17-45, âEnhanced Safety Prediction Methodology and Analysis Tool for Freeways and Interchangesâ would be pursued. For this, a severity distribu- tion function (SDF) would be calibrated to separately predict K, A, B, and C crashes (or some combination) as a proportion of the KABC crash frequency. The SDF would be a function of the geometric and traffic control elements. It would predict the influence of each element on the proportion of K, A, B, and C crashes (or some combination). It would be calibrated using the same database assembled to develop the SPFs and CMFs and using the approach outlined in Section 2.4.3 in Chapter 2 Literature Review in which SDFs are developed based on probability models of injury severity estimated from data in individual crashes. Candidate CMFs for the leg-level SPFs are summarized in Table 3-1, indicating the crash types to which the CMFs would apply. CMFs Total Crashes Ent/Circ Ext/Circ App DwnStrm Entry width (ft) â width at the yield line Y Angle to next leg (deg) Y Inscribed circle diameter (ICD) (ft) Y Circulating width (ft) Y Approach half-width (ft) Y Lane Width (ft) â width 25 ft back from yield lane Z Z Central island diameter (ft) Z Entering vehicle speed Z Z Posted speed on approach to the roundabout Z Z Circulating vehicle speedA Z Intersection sight distance Z Z Combination of entering, circulating, and exiting lanes Z Z Presence of right-turn bypass lane O Radius of right-turn bypass horizontal curve (ft) O Radius of exiting vehicle path adjacent to right-turn bypass (ft) O Distance from circulating roadway to gore point of merge with right-turn bypass (ft) O Lane Width (ft) â width at gore point of merge with right-turn bypass (ft) O Number of luminaires within 200 ft of the roundabout O O O O Presence and type of lane use markings O O O Notes: Ent/Circ = Crashes between entering and circulating vehicles. Ext/Circ = Crashes between exiting and circulating vehicles. App = Crashes occurring on the vehicle approach to a roundabout. DwnStrm = Crashes occurring downstream of the roundabout shortly after a vehicle has exited the roundabout. Y = Included in preferred model from NCHRP Report 572 (Rodegerdts et al., 2007) for total crashes. Z = Literature review revealed attribute found to inÂluence crashes at roundabouts. O = Concept based on design decisions practitioners encounter. A Circulating vehicle speed to be able to calculate the variation in vehicle speed as the difference between entering vehicle speed and circulating vehicle speed. Table 3-1. Candidate CMFs at approach level (models to inform design decisions).
37 Candidate SPFs would be attempted for various feasible combinations of numbers of entering, circulating, and exiting lanes. The latter are the exit lanes adjacent to the entry lanes (i.e., separated by the splitter island). In this context, the exit lanes do not include the right-turn bypass lane if it is present. The safety effect of a right-turn bypass lane would ideally be captured with a CMF, as indicated in Table 3-1. 3.1.2 Intersection-Level Crash Prediction Models for Design Applications Intersection-level predictive models for design applica- tion were also considered for development in this project. This model form would predict the crash frequency for the overall roundabout (i.e., roundabout-related crashes on all approaches and the circulating roadway) and include CMFs that reflect changes in geometric design attributes of the roundabout. This form is consistent with that of the inter- section safety prediction models in Part C of the HSM (i.e., they predict crash frequency for the overall intersection, as opposed to a specific intersection leg or approach). The main advantage of the intersection-level model used to inform design decisions are related to the level of effort on the part of practitioners using the model. The intersection- level model does not require practitioners who wish to apply the model to â¢ Obtain crash reports (in addition to crash data); â¢ Assign crashes to specific roundabout approaches based on the crash reports; and â¢ Reassign the crash types conventionally used at intersections (e.g., rear-end, sideswipe) to a crash typology unique to roundabouts (e.g., entering-circulating). The primary disadvantage of the intersection-level model used to inform design decisions is that it may not be as accu- rate in its estimate of the safety effect of an isolated geometric change to one roundabout approach when compared to the leg-level crash prediction models. Another potential risk is that this option, an intersection-level crash prediction model that captures the effects of geometric attributes potentially unique to different intersection approaches, is not reflected in published literature related to roundabout crash prediction. It has been used successfully in research for nonroundabout intersections, most recently as part of NCHRP 17-45. 22.214.171.124 Proposed Framework The intersection-level models to inform design decisions could include separate predictive models developed for the following combinations of basic roundabout configurations and crash severity. These configurations represent the majority of roundabout installations in the United States. The sample size of sites with more than four legs or more than two circu- lating lanes is too small to be useful for model development. â¢ One circulating lane, 3 legs, total; â¢ One circulating lane, 3 legs, KABC; â¢ One circulating lane, 3 legs, PDO; â¢ One circulating lane, 4 legs, total; â¢ One circulating lane, 4 legs, KABC; â¢ One circulating lane, 4 legs, PDO; â¢ Two circulating lanes, 3 legs, total; â¢ Two circulating lanes, 3 legs, KABC; â¢ Two circulating lanes, 3 legs, PDO; â¢ Two circulating lanes, 4 legs, total; â¢ Two circulating lanes, 4 legs, KABC; and â¢ Two circulating lanes, 4 legs, PDO. One SPF would be developed for each of the predictive models listed above. Similar to what is proposed in Sec- tion 3.1.1, models for predicting total crashes of all severi- ties would be developed and compared to an alternative approach in which the estimates from the appropriate PDO and KABC models would be added to obtain an estimate of the total average crash frequency for a given roundabout. For other combinations of severity (e.g., KAB), the probabilistic approach being taken in NCHRP 17-62 and NCHRP 17-45 would be pursued as outlined in Section 3.1.1. The distribution of each crash type (e.g., rear-end crashes, sideswipe, single- vehicle) would be developed from the database assembled to develop the SPFs and CMFs; this approach is consistent with current approaches in the HSM. Roundabout sites that include a combination of one and two circulating lanes within a single roundabout were included in this project. These hybrid roundabouts, those including two circulating lanes for any portion of the roundabout, are categorized as two circulating lanes. A variable is included to account for whether the two circulating lanes reduce to one circulating lane for any portion of the roundabout. One set of CMFs, from Table 3-2, would be developed for each of the predictive models. This procedure would help the analyst estimate the average crash frequency at the intersection level and consider the effects of different geometric features. 126.96.36.199 CMF Development The geometric features that underlie several of the CMFs in Table 3-2 are anticipated to correlate. This correlation will make it difficult to separate the individual safety effect of each geometric feature without careful site selection. Specifically, sites would need to be identified for which there is a range of variable values and for which the correlation is identified and accounted for within the CMF development. Achieving this
38 objective in site selection will measurably increase the time needed for data collection because of the limited number of roundabouts in the United States. For example, speed will be correlated with most geometric variables. As a result, isolating the effect of speed will require identifying sites that collectively have a range of speeds but little (or no) variation in geometric variables. Thus, careful site selection to quantify the influence of a change in speed may require the preliminary screening of several hundred roundabouts to find the subset of round- abouts with the desired attributes. Given the likely correlation among CMF variables and the time and effort necessary to carefully select sites, potential CMFs (i.e., attributes) and data collection efforts will need to be prioritized. Some of the geometric elements associated with the CMFs in Table 3-2 describe the design of the approach (e.g., entry width). The CMFs associated with each of these elements would be developed to reflect changes to element size (or presence) on one or more approaches at an intersection level. In this manner, the analyst would be able to evaluate changes to one or more approaches on the average crash frequency for the overall roundabout (i.e., at the intersection level). One method for developing this type of intersection-level CMF to describe leg-level geometrics is to compute a weighted average of the leg-level CMFs, where the weight used is the proportion of AADT on the individual approach. As noted above, this approach to CMF development was used in NCHRP 17-45 for developing an intersection-level CMF that reflects the addition of a turn bay to one or more approaches. More-sophisticated methods for developing these types of intersection-level CMFs would be explored during model development, and the approach providing the most accurate estimates of intersection-level average crash frequency would be recommended. 3.1.3 Surrogate-Based Models Vehicle speed through a roundabout is a promising sur- rogate model. There are two methods available for predicting CMFs Total Crashes Entry width (ft) â width at yield line Y Angle to next leg going in counterclockwise direction (deg) Y Inscribed circle diameter (ft) Y Circulating width (ft) Y Approach half-width (ft) Y Lane width (ft) â width 25 ft back from yield line Z Central island diameter (ft) Z Use of ishhook lane coniguration pavement markings on multilane approaches O Posted speed on approach to the roundabout Z Intersection sight distance Z Combination of entering, circulating, and exiting lanes Z Presence of right-turn bypass lane on exit O Radius of right-turn bypass horizontal curve (ft) O Radius of exiting vehicle path adjacent to right-turn bypass (ft) O Distance from circulating roadway to gore point of merge with right-turn bypass (ft) O Lane width (ft) â width at gore point of merge with right-turn bypass (ft) O Number of luminaires within 200 ft of the roundabout O Presence and type of lane use markings O NOTES: Y = Included in preferred model from NCHRP Report 572 (Rodegerdts et al., 2007) for total crashes. Z = Literature review revealed attribute found to inluence crashes at roundabouts; from nonâU.S.-based studies. O = Concept based on design decisions practitioners encounter. Table 3-2. Candidate CMFs at intersection level (models to inform design decisions).
39 speed through a roundabout. One is presented in NCHRP Report 672 (Rodegerdts et al., 2010) as the Fastest Path method. The second method, developed by Chen et al. (2013), created geometric-based models for predicting average vehicle speeds and then used these estimates to develop SPFs for roundabout approaches using a larger database of sites without in-field speed measurements. This project compared the two speed prediction methods, and the most reliable and accurate one was used along with AADT to estimate more robust models for crashes of all types and severities combined. Chen et al. (2013) contains preliminary results from a similar approach. 3.2 Candidate Safety Performance Functions for Planning and Network Screening This project built on the intersection-level SPFs developed and documented in NCHRP Report 572 (Rodegerdts et al., 2007). These SPFs take into account the number of approaches, number of circulating lanes, and total entering AADT to predict the number of crashes at a roundabout. Additional variables were considered, including the posted speed on the approaches (i.e., less than 45 mph and greater than or equal to 45 mph) and rural versus urban/suburban setting. Recognizing that these intersection-level models were intended for activities such as planning and network screening, these models did not include detailed design-related variables and would include total entering AADT as the exposure variable. Models were developed for all crash types, and severities combined for the following groups: â¢ Urban/Suburban: â Single-lane and â Multilane. â¢ Rural: â Single-lane and â Multilane. For crashes of all types combined, models were estimated for predicting crashes by severity. For KAB and KABC crashes on the KABCO scale, SPFs were developed directly and compared. This approach was compared to that outlined in Section 2.4.3 in the Chapter 2 literature review in which SDFs were developed based on probability models of injury sever- ity estimated from data in individual crashes. Intersection-level CMFs included number of approaches (i.e., 3, 4, or more than 4 approaches); number of circulating lanes (for multilane model onlyâtwo lanes circulating or more than two lanes circulating); a variable to capture if one or more approaches have a posted speed greater than or equal to 45 mph (i.e., high-speed approach); and a variable to capture if the intersection is a ramp terminal intersection. The approach to estimating these CMFs was through cross-sectional mod- els because a significant number of roundabouts could not be found where these variables were changed in isolation (i.e., without the confounding influence of other concurrent changes), and the site was a roundabout both before and after the change. 3.3 Assessing Driver Learning Curve Impacts of a driver learning curve at newly constructed roundabouts were assessed using only data for those round- abouts where data from the time of construction were avail- able and by re-evaluating the intersection-level models to include the time from the roundabout being open to traffic as an explanatory variable. The models were explored on a yearly basis. Indicator variables were used to quantify the change in safety from one time period to the next. The presence of a driver learning curve was exhibited by a trend in the indicator variable coefficients. The challenge for such a model is that by making the units of observation short, the data exhibit a pre- ponderance of zeros (i.e., periods of time where no crashes occurred and/or would be expected to occur). Therefore, model convergence can be difficult. However, using a unit of observation that is too long may mask any driver learning curve effects. 3.4 Predicting Pedestrian and Bicycle Crashes Developing SPFs specific to predicting vehicleâpedestrian and vehicleâbicycle crashes is difficult because reported pedestrian and bicycle crashes were rare events and therefore limited within the crash data, thus increasing the sample sizes required to develop the SPFs. For example, based on research findings from NCHRP Report 572 (Rodegerdts et al., 2007), the frequency of pedestrianâvehicle crashes at roundabouts is on average 0.02 crashes per year per roundabout. Depending on how guidance regarding required sample sizes is inter- preted and used from Srinivasan and Bauer (2013), 3,000 to 15,000 sites would be needed to develop an SPF that estimates pedestrianâvehicle crashes. Such a sample size is not possible given the existing number of roundabouts currently in the United States is approximately 3,000 to 4,000 sites, and many of those are too new to have any significant history. SPFs specific to predicting pedestrian and bicycle crashes are also challenging to predict because pedestrian and bicycle volumes are not consistently collected on most roadway networks. Collecting this exposure data can be time and cost intensive. Pedestrian and bicycle volume data were not readily available for use in this project. This, combined with the rarity of pedestrian and bicycle crashes noted previously, prompted
40 the need for an alternative to predicting pedestrian and bicycle crashes at roundabouts. The findings from reviewing the pedestrian and bicycle crashes in the database are discussed in Chapter 6, Section 6.4. 3.5 Study Designs for CMFs Two study designs are typically used to estimate CMFs. One design is a retrospective beforeâafter study of round- abouts. In this approach, a set of locations must have had the same before condition, experienced the same change, and have a sufficient after period to provide ample data for the analysis. This requirement could not be met in this project (see Section 2.1.3 of the Chapter 2 literature review). There- fore, the focus became the less desirable, but more feasible study design: the estimation of CMFs from the coefficients of cross-sectional regression models. The issues with this type of study, such as colinearity and omitted variable bias, are well known in the research community and are summarized in resources such as Hauer (2010). These issues were over- come through careful site selection, inclusion of variables often missing from agency infrastructure databases, and cor- roboration with intuition and knowledge from international research. A recent paper by Wu et al. (2014), which has shown that this design can be viable, was a key resource. 3.6 Database Requirements for Developing SPFs and CMFs Developing the anticipated SPFs and CMFs required assembling a database with linked roadway inventory, traffic volume, and crash data. Specific desired variables are organized below into basic categories: roadway inventory data; speed data; traffic volume data; and crash data. 3.6.1 Roadway Inventory Data â¢ Intersectionwide data attributes: â Area type = urban/suburban versus rural environment. â Opening date. â Number of circulating lanes. â Number of approaches. â Inscribed circle diameter (ft). This data attribute could vary per approach for non-circular roundabouts (e.g., oblong shaped roundabouts). â Central island diameter (ft). â Ramp terminal intersection (âyesâ or ânoâ per site). â¢ Approach-specific data attributes: â Number of entering lanes per approach. â Number of exiting lanes per approach. â Entry width (ft), measured at yield line. â Angle to next leg going in the counterclockwise direc- tion (deg). â Approach half-width (ft). â Circulating width (ft). â Lane width (ft), measured 25 ft back from the yield line. â Intersection sight distance. â Presence of right-turn bypass lane: î® Radius of right-turn bypass horizontal curve (ft), î® Radius of exiting vehicle path adjacent to right-turn bypass (ft), î® Distance from circulating roadway to gore point of merge with right-turn bypass (ft), and î® Lane width (ft), measured at gore point of merge with right-turn bypass. â Number of luminaires within 200 ft of the roundabout. â Presence and type of lane use markings. 3.6.2 Speed Data â¢ Entering vehicle speed (mph), â¢ Posted speed on approach (mph), and â¢ Circulating vehicle speed (mph). Where not available from direct measurement or observa- tion (e.g., posted speed limit), speeds were estimated using the speed prediction models in NCHRP Report 672 (Rodegerdts et al., 2010) and Chen et al. (2013). 3.6.3 Traffic Volume Data â¢ AADT on major and minor street approaches. â¢ Estimates of AADT by the following movements: â Entering, â Exiting, and â Circulating. 3.6.4 Crash Data â¢ At least 3 years of crash data per site; and â¢ Crash data and/or crash reports including the following attributes: â Crash type: î® Traditional intersection crash types (e.g., rear-end, sideswipe) and î® Roundabout-specific crash types (e.g., entering- circulating); â Location relative to the roundabout; and â Severity on the KABCO severity scale. The development of the crash counts by crash type required access to the police reports for individual crashes to be able to explore and compare the alternative crash prediction model- ing approaches described in Section 2.1.1 and Section 2.1.2.
41 This requirement is twofold. First, the crash types discussed in Section 2.2.1 (e.g., entering-circulating) are not included on police crash report forms, and reliably identifying crash types using electronically coded data is challenging. Similarly, to reliably assign a crash to a specific approach, the crash report would need to be consulted. 3.7 Sample Size Requirements There is no formal statistical method for determining the required sample sizes for the cross-sectional regression analysis studies that was used to estimate CMFs. For multi- variable regression models, the number of locations and crashes required will depend on a number of factors includ- ing the following: â¢ Average crash frequencies at the sites, â¢ The number of variables desired in the model, â¢ The level of statistical significance desired in the model, and â¢ The amount of variation in each variable of interest between locations. Determining if the sample size is adequate can be done only once the model output is available. If the variables of interest are not statistically significant, then more data may be required. For this reason, the determination of required sample size was an iterative process, although through expe- rience and familiarity with specific databases an initial edu- cated guess may be possible. Useful SPFs and CMFs were obtained with a sample for NCHRP Report 572 (Rodegerdts et al., 2007) that was much smaller than what appeared feasible for this project. In NCHRP Report 572, 90 roundabouts sites were used to develop intersection-level crash prediction models applicable to planning applications, and a subset of 39 of those round- abouts were used to develop leg-level crash prediction models applicable to informing design decisions. As discussed in Section 3.6, this project collected data for 530 roundabouts for intersection-level crash prediction models, with a subset of 150 roundabouts used for the approach-level crash predic- tion models. As data were collected, preliminary models provided the updated sample size, and sample size requirements were re-evaluated; less promising SPFs were dropped to focus resources on more promising SPFs. Although there are nearly 3,000 roundabouts in the United States, the sample from this project was restricted by the following: â¢ Traffic volume and/or design information are not available; â¢ Few or no years of crash data are available (the research team proposed to seek 3 years of data for each roundabout in the sample, given the low crash frequencies at roundabouts); â¢ Practical and theoretical issues where data for only one or two roundabouts are available in jurisdiction (the research team proposes a minimum of five roundabouts per jurisdictionâcity, county, state); and â¢ Timeliness and responsiveness of agencies. The minimum of five roundabouts per jurisdiction (city, county, state) note above was selected based on the level of effort and time required to coordinate obtaining traffic volume and crash data from agencies for specific intersections. 3.8 References and Bibliography American Association of State Highway and Transportation Officials (AASHTO). 2010. Highway Safety Manual, 1st edition. AASHTO, Washington, D.C. Chen, Y., B. Persaud, E. Sacchi, and M. Bassani. 2013. Investigation of Models for Relating Roundabout Safety to Predicted Speed. Accident Analysis & Prevention, Vol. 50, pp. 196â203. Hauer, E. 2010. Effect and Regression in Road Safety: A Case Study. Accident Analysis & Prevention, Vol. 42, Issue 4, July, pp. 1128â1135. Rodegerdts, L., M. Blogg, E. Wemple, E. Myers, M. Kyte, M. Dixon, G. List, A. Flannery, R. Troutbeck, W. Brilon, N. Wu, B. Persaud, C. Lyon, D. Harkey, and D. Carter. 2007. NCHRP Report 572: Round- abouts in the United States. Transportation Research Board of the National Academies, Washington, D.C. Rodegerdts, L., J. Bansen, C. Tielser, J. Knudsen, E. Myers, M. Johnson, M. Moule, B. Persaud, C. Lyon, S. Hallmark, H. Isebrands, R. B. Crown, B. Guichet, A. OâBrien. 2010. NCHRP Report 672: Round- abouts: An Informational Guide, Second Edition. Transportation Research Board of the National Academies, Washington, D.C. Srinivasan, R. and K. Bauer. 2013. Safety Performance Function Develop- ment Guide: Developing Jurisdiction-Specific SPFs. FHWA-SA-14-005. Federal Highway Administration, Washington, D.C. Wu, L., D. Lord, and Y. Zou. 2014. Validation of CMFs Derived from Cross Sectional Studies Using Regression Models. Paper submitted for the 94th Annual Meeting of the Transportation Research Board, Washington, D.C.