Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

PUBLICATION NO. FHWA-HRT-23-019 APRIL 2023 

Developing Crash Modification Factors 

for Mini‐Roundabouts
FOREWORD

The research documented in this report was conducted as part of the Federal Highway 

Administration’s (FHWA) Evaluation of Low-Cost Safety Improvements Pooled Fund Study 

(ELCSI-PFS). FHWA established this PFS in 2005 to conduct research on the effectiveness of 

safety improvements identified by the National Cooperative Highway Research Program 

Report 500 guides as part of the implementation of the American Association of State Highway 

and Transportation Officials’ Strategic Highway Safety Plan. ELCSI-PFS studies provide a crash 

modification factor (CMF) and benefit–cost economic analysis for each targeted safety strategy 

identified as a priority by member States of the PFS.

This report documents the evaluated safety effectiveness of mini-roundabout (MR) installations 

at two-way stop-controlled (TWSC) and all-way stop-controlled (AWSC) locations. This study 

focused on MR safety effectiveness using data such as dimensions, number of lanes, median 

types and widths, and number of legs at various sites in Washington, Michigan, and Maryland. 

The analysis found a statistically significant crash reductions of 39 percent in multivehicle 

crashes at MRs converted from AWSC in all three States. 

These study results may be of interest to roadway safety professionals, State and local engineers, 

and planners responsible for the design and operation of facilities that may benefit from MR 

installations. 

Brian P. Cronin, P.E. 

Director, Office of Safety and Operations 

Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

(USDOT) in the interest of information exchange. The U.S. Government assumes no liability for 

the use of the information contained in this document. 

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement. 
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-23-019

2. Government Accession No. 3. Recipient’s Catalog No.

4. Title and Subtitle

Developing Crash Modification Factors for 

Mini-Roundabouts

5. Report Date

April 2023 

6. Performing Organization Code:

7. Author(s)

Raul Avelar (ORCID: 0000-0002-3962-1758), Eun Sug Park

(ORCID: 0000-0001-6224-7007), Boniphace Kutela (ORCID: 

0000-0002-5450-1623) 

8. Performing Organization Report No.

9. Performing Organization Name and Address

Texas A&M Transportation Institute

The Texas A&M University System

College Station, TX 77843

10. Work Unit No.

11. Contract or Grant No.

DTFH6116D00039L

12. Sponsoring Agency Name and Address

Office of Safety Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101

13. Type of Report and Period Covered

Final Report; May 2019–November 2022 

14. Sponsoring Agency Code

HRDS-20

15. Supplementary Notes

The Federal Highway Administration (FHWA) Office of Safety Research and Development managed this project 

under the Development of Crash Modification Factors program. The FHWA Office of Safety Research and 

Development Program Manager and Contracting Officer’s Representative was Roya Amjadi (HRDS-20; ORCID: 

0000-0001-7672-8485). 

16. Abstract

This study evaluated the safety effectiveness of mini-roundabout (MR) installations at two-way stop-controlled 

(TWSC) and all-way stop-controlled (AWSC) locations. Based on a longitudinal design including comparison 

sites, the database included three States: Washington, Michigan, and Maryland. Safety data were compiled for 

locations of known MR installations where the date of installation and prior intersection condition were known. 

Suitable comparison locations were included. The study included 15 MR locations from Washington, 6 from 

Michigan, and 6 from Maryland. Crash data from 2003 through 2019 were available from Washington, data from 

2013 through 2019 from Michigan, and data from 2015 through 2019 from Maryland. A fully Bayesian evaluation 

based on the Washington crash data estimated crash reductions for MR converted from TWSC ranging from 31 to 

42 percent for various crash types, which were statistically significant. The study found a statistically significant 

reduction of 39 percent in multivehicle crashes at MR converted from AWSC intersections from an additional 

analysis based on the complete database from all three States. This study also produced benefit–cost ratios of 2.88

and 2.87 for MR conversions from TWSC and AWSC, respectively, when only safety benefits were considered, 

whereas the ratio was 13.41 for AWSC intersections when operational benefits were also considered. These results 

indicate economic feasibility of MR installations.

17. Key Words

CMF, crash modification factor, mini-roundabout, 

crash severity, stop-controlled

18. Distribution Statement

No restrictions. This document is available to the public 

through the National Technical Information Service, 

Springfield, VA 22161.

http://www.ntis.gov

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

55 

22. Price

N/A

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized.
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iii

TABLE OF CONTENTS

EXECUTIVE SUMMARY .......................................................................................................... 1

CHAPTER 1. INTRODUCTION TO SAFETY EVALUATION OF 

MINI-ROUNDABOUTS .............................................................................................................. 3

Review of Literature ............................................................................................................... 3

Characteristics, Advantages, and Disadvantages of MRs ................................................... 3

Suitability of MRs ................................................................................................................... 4

Operational Evaluations of MRs ........................................................................................... 4

Safety Evaluations of MRs ..................................................................................................... 4

Cross-Sectional Studies ...................................................................................................... 5

Before–After Studies .......................................................................................................... 6

Chapter Summary .................................................................................................................. 8

CHAPTER 2. STUDY DESIGN AND METHODOLOGY ...................................................... 9

Study Design ............................................................................................................................ 9

Study Design: Interrupted Time Series Design with Comparison Groups ....................... 10

Database Design and Management ..................................................................................... 11

Data Management Extraction and Integration .................................................................. 12

AADT Imputation ............................................................................................................. 13

Data Balancing .................................................................................................................. 13

Data Elements and Sources .................................................................................................. 14

Crash Data ............................................................................................................................. 16

Traffic Data ........................................................................................................................... 16

Data Analysis Methods ......................................................................................................... 16

Modeling Framework for FB Analysis of Before–After Designs with Comparison 

Groups ............................................................................................................................... 16

Steps for Implementing FB Before–After Evaluations with Multiple Comparison 

Groups ............................................................................................................................... 17

Generalized Linear Regression Analysis with PS Weighting ........................................... 18

Chapter Summary ................................................................................................................ 20

CHAPTER 3. DATA COLLECTION AND INTEGRATION ............................................... 21

Crash and Traffic Volume Data Collection ........................................................................ 21

Anticipated Effect Size and Data Needs ........................................................................... 21

Treated and MR Sites........................................................................................................ 21

Characteristics of Selected MR Locations .......................................................................... 23

Chapter Summary ................................................................................................................ 26

CHAPTER 4. SAFETY-EFFECTIVENESS EVALUATIONS .............................................. 27

Washington rash Analysis .................................................................................................... 27

Consolidated Results............................................................................................................. 34

Panel Analysis on Multistate Data....................................................................................... 35

Chapter Summary ................................................................................................................ 37

CHAPTER 5. ECONOMIC ANALYSIS .................................................................................. 39

Benefits and Costs Estimates ............................................................................................... 39

Economic Effectiveness of MR Installation at TWSC ..................................................... 39
iv

Economic Effectiveness of MR Installation at AWSC ..................................................... 40

Chapter Summary ................................................................................................................ 40

CHAPTER 6. SUMMARY AND CONCLUSIONS................................................................. 41

ACKNOWLEDGMENTS .......................................................................................................... 43

REFERENCES ............................................................................................................................ 45
v 

LIST OF FIGURES

Figure 1. Map. Treated and comparison sites in Federal Way, WA (Google 2019). ................... 14

Figure 2. Equation. Conditional probability of y value, given explanatory variables and site 

characteristics. ..................................................................................................................... 19

Figure 3. Equation. Binomial-lognormal mixed-model parameterization. ................................... 20

Figure 4. Map. MR locations in Washington (Google 2019). ...................................................... 22
vi 

LIST OF TABLES

Table 1. Data elements for MR evaluation. .................................................................................. 12

Table 2. Identified sites in Maryland. ........................................................................................... 23

Table 3. Traffic control type before MR installation. ................................................................... 23

Table 4. Traffic control type at comparison sites. ........................................................................ 23

Table 5. Other characteristics of treated and comparison sites. .................................................... 24

Table 6. Descriptive statistics—Washington data. ....................................................................... 24

Table 7. Descriptive statistics—Michigan data. ........................................................................... 25

Table 8. Descriptive statistics—Maryland data. ........................................................................... 25

Table 9. Crash descriptive statistics—Washington data (crashes per year). ................................ 26

Table 10. Crash descriptive statistics—Michigan data (crashes per year). .................................. 26

Table 11. Crash descriptive statistics—Maryland data (crashes per year). .................................. 26

Table 12. Number of MR sites and comparison sites in Washington for each 

implementation year. ........................................................................................................... 27

Table 13. Results for FB evaluation of total crashes for MR sites with TWSC as the before 

condition in Washington. .................................................................................................... 29

Table 14. MR CMF and uncertainty estimates for table 13. ......................................................... 29

Table 15. Results for FB evaluation of FI crashes for MR sites with TWSC as the before 

condition in Washington. .................................................................................................... 30

Table 16. MR CMF and uncertainty estimates for table 15. ......................................................... 30

Table 17. Results for FB evaluation of PDO crashes for MR sites with TWSC as the before 

condition in Washington. .................................................................................................... 31

Table 18. MR CMF and uncertainty estimates for table 17. ......................................................... 31

Table 19. Results for FB evaluation of MV_Total crashes for MR sites with TWSC as the 

before condition in Washington. ......................................................................................... 32

Table 20. MR CMF and uncertainty estimates for table 19. ......................................................... 32

Table 21. Results for FB evaluation of MV_FI crashes for MR sites with TWSC as the 

before condition in Washington. ......................................................................................... 33

Table 22. MR CMF and uncertainty estimates for table 21. ......................................................... 33

Table 23. Results for FB evaluation of MV_PDO crashes for MR sites with TWSC as the 

before condition in Washington. ......................................................................................... 34

Table 24. MR CMF and uncertainty estimates for table 23. ......................................................... 34

Table 25. CMFs for MR converted from TWSC for different crash types................................... 35

Table 26. Model estimates from panel multistate data by crash type. .......................................... 36

Table 27. CMFs for TWSC-to-MR conversion from panel multistate data. ................................ 37

Table 28. CMFs for AWSC-to-MR conversion from panel multistate data. ................................ 37
vii 

LIST OF ABBREVIATIONS

AADT annual average daily traffic

AWSC all-way stop-control (controlled) 

B/C benefit–cost

CMF crash modification factor

DCMF Development of Crash Modification Factors 

DOT department of transportation 

ELCSI-PFS Evaluation of Low-Cost Safety Improvements Pooled Fund Study 

FB fully Bayesian

FHWA Federal Highway Administration

FI fatal and injury 

GIS geographic information system 

GLM generalized linear model

GLMM generalized linear mixed model

HSIS Highway Safety Information System 

ITS-CG interrupted time series design and analysis with comparison groups 

KE kinetic energy

MCMC Markov chain Monte Carlo 

MR mini-roundabout 

NCHRP National Cooperative Highway Research Program 

OR odds ratio

PDO property damage only 

PIA personal injury accident 

PS propensity score 

PSL posted speed limit 

Std Dev standard deviation 

Std Err standard error 

TWSC two-way stop-control (controlled) 

vpd vehicles per day

1 

EXECUTIVE SUMMARY

The Federal Highway Administration’s (FHWA) Development of Crash Modification Factors 

(DCMF) Program was established in 2012 to address highway safety research needs and evaluate 

new and innovative safety strategies (improvements) by developing reliable quantitative 

estimates of their effectiveness in reducing crashes (FHWA 2022a). 

The ultimate goal of the FHWA DCMF Program “is to save lives by identifying new safety 

strategies that effectively reduce crashes and promote strategies for nationwide installation by 

providing measures of their safety effectiveness” (e.g., crash modification factors (CMFs) and 

benefit–cost (B/C) ratios) through research (FHWA 2022a). State departments of transportation 

(DOTs) and other transportation agencies need to have objective measures of the 

countermeasures’ safety effectiveness and B/C ratios before investing in new strategies for 

statewide safety improvements. 

Forty-one State DOTs are members of the Evaluation of Low-Cost Safety Improvements Pooled 

Fund Study (ELCSI-PFS) and provide technical feedback on high-priority research needs for 

safety improvements to the DCMF Program. These States implement new and unproven safety 

improvements to facilitate ELCSI-PFS evaluations and ELCSI-PFS functions under the DCMF. 

The ELCSI-PFS Technical Advisory Committee selected evaluating the safety effectiveness of 

mini-roundabouts (MRs) as one of ELCSI-PFS’ priorities. This report documents the evaluation 

of the safety effectiveness of MRs in the United States. 

More specifically, this study evaluated the safety effectiveness of MR installations at two-way 

stop-controlled and all-way stop-controlled locations. Databases were developed and analyzed 

representing three States: Washington, Michigan, and Maryland. Suitable comparison locations 

were included to control for covarying extraneous factors. Site features were collected for 

analysis, including dimensions, number of lanes, median types and widths, number of legs, and 

so on, before and after MR installation, as well as annual average daily traffic where available. 

The study included 15 MR locations from Washington, 6 from Michigan, and 6 from Maryland. 

Crash data from 2003 through 2019 were available from Washington, from 2013 through 2019 

from Michigan, and from 2015 through 2019 from Maryland. 

This research developed CMFs that indicated crash reductions in general, but some of the results 

were statistically insignificant. An additional, analysis of severe crash outcomes indicated a 

statistically significant reduction in risk of injury or death. B/C ratios were developed 

accordingly. Practitioners can use these results for decisionmaking in their project development 

and safety planning processes. 

3 

CHAPTER 1. INTRODUCTION TO SAFETY EVALUATION OF 

MINI-ROUNDABOUTS 

Mini-roundabouts (MRs) are small-diameter roundabouts (50- to 90-ft radii) with traversable 

islands (central island and splitter islands). MRs use less space than regular-sized roundabouts 

while offering most of the benefits. They are best suited for locations with slow operational 

speeds and where site constraints would preclude the use of larger roundabouts. As a particular 

type of roundabout, MRs are expected to improve traffic operations with a minimal impact on 

capacity—or even to increase capacity under certain conditions—and reduce frequency and 

severity of crashes, most likely by curbing right-angle crashes, typical at stop-controlled and 

signalized intersections.

While MRs are frequently used in European countries, their use is just emerging in the United 

States. A previous evaluation by the Federal Highway Administration (FHWA 2015) 

demonstrated that conversion from intersections controlled by all-way stop-controlled (AWSC) 

or two-way stop-controlled (TWSC) improved intersection operating efficiency and reduced 

congestion, and that a formal safety evaluation study based on actual crash data is challenging, 

partly due to the scarcity of locations and data. The limited number of crashes at MR sites with 

multiple years of crash data can provide significant challenges in developing crash modification 

factors (CMFs) for MRs. For assessing safety benefits of MRs, proper accounts for those 

different pretreatment conditions are needed. 

REVIEW OF LITERATURE

MRs are a simpler version of traditional roundabouts. They feature a single lane and smaller

diameters, ranging from 45 to 80 ft (Robinson et al. 2000). The key element of MRs is that their 

islands are traversable (central island and splitter islands). As a result, MRs use less space than 

regular-sized roundabouts, while still retaining most operational benefits and potentially safety as 

well. As a result, the cost of retrofitting an existing intersection with an MR is significantly lower 

than implementing traditional roundabouts (Jurewicz et al. 2013). 

While MRs are frequently used in European countries, only a few locations in the United States 

have had MRs for more than a decade, with wide MR use expanding just in the last decade. 

CHARACTERISTICS, ADVANTAGES, AND DISADVANTAGES OF MRs 

MRs offer a low-speed, low-noise intersection option that requires little regular maintenance

(Rodegerdts, Scarbrough, and Bansen 2010). As mentioned in the preceding section, the defining 

feature of a MR is a small and traversable central island, as well as traversable split islands that 

can accommodate large vehicles driving over them but are uncomfortable for small vehicles to 

mount (i.e., raised but traversable) (Zhang 2015; Adnan, Adem, and Osman 2014). One factor 

engineers should keep in mind when designing the central mini-island is that it should not cause 

problems for winter maintenance. With this issue in mind, stamped epoxy or concrete are the 

preferred materials used as the surface material for central islands (Walker and Pittam 1989). 

According to recent research, the major advantages of MRs are as follows: higher capacity than 

stop-control; better fit into existing intersection right of way; improved intersection operating 
4 

efficiency and safety; and low cost ($25,000 to $50,000 per intersection, assuming only 

pavement replacement under the central and splitter islands) (Chandler et al. 2013; Zhang 2015).

Given all their benefits, MRs have the same disadvantages as traditional roundabouts, which are 

mostly general issues pertaining to accommodating pedestrians and cyclists (Delbosc et al.

2017). Bodé and Maunsell (2006) recommend not placing MRs at intersections with known large 

pedestrian volumes. However, cyclists are considered “just as vulnerable” on roundabouts as on 

any other crossroad system. Additionally, MRs offer no protection for vulnerable users against 

drunk and reckless drivers because of the lack of nontraversable physical barriers compared with 

traditional roundabouts. 

Sawers (2009) presents an examination of successful and failed cases of MR applications in the 

United Kingdom, discussing geometric design, safety, and other aspects for potential 

applications in the United States. In his examination of conflict points, Sawers included statistics 

for crash types, pointing out a significant difference between three-legged and four-legged MRs: 

Clearly a larger proportion of right-angle crashes occur at four-legged locations. 

SUITABILITY OF MRs 

MRs have been used at urban junctions since their introduction in Europe in the early 1970s and 

produce some traffic calming effects (Kennedy, Hall, and Barnard 1998; Rodegerdts, 

Scarbrough, and Bansen 2010). They are suitable for intersections on two-lane or three-lane 

high-volume collector roads with comparable traffic volumes from major and minor approaches 

and with a total entering daily traffic volume value no more than approximately 15,000 vehicles, 

low truck volumes, and a posted speed limit (PSL) of 35 mph or less (Rodegerdts, Scarbrough, 

and Bansen 2010; Robinson et al. 2000; Kennedy, Hall, and Barnard 1998). As a particular type 

of roundabout, MRs are expected to improve traffic operations with a minimal impact on 

capacity and reduce the frequency and severity of crashes, most likely by curbing right-angle 

crashes, which are typical at stop-controlled and signalized intersections. 

OPERATIONAL EVALUATIONS OF MRs 

The literature shows a clear pattern of operational benefits of MRs. FHWA conducted a field and 

safety evaluation of five existing MRs and before-and-after operational evaluation of 15 MRs

(Georgia, Maryland, Michigan, Minnesota, New York, Washington, and Virginia) 

(FHWA 2015). This evaluation demonstrated that conversion from intersections controlled by 

AWSC or TWSC improved intersection operating efficiency and reduced congestion. 

A study in South Australia found a 62-percent drop in 85th percentile speeds through 

intersections with MRs (Zito and Taylor 1996). A study by Rodegerdts, Scarbrough, and Bansen 

(2010) found that MRs help reduce vehicle approach speeds. Delbosc et al. (2017) recorded 

driver and pedestrian behavior in 40 MRs and found that speed limit compliance increased after 

the installation.

SAFETY EVALUATIONS OF MRs 

MRs are expected to enhance safety for drivers and bicyclists by providing more time to make 

decisions, act, and react by reducing the number of directions a driver needs to monitor for 
5 

conflicting traffic. One can also argue that safety improves because of a reduced need to judge 

gaps accurately in fast traffic. Crosswalks are provided for bicyclist and pedestrians. These

benefits, combined with the lower impact angles due to the nature of MRs, should lead to lower 

impact kinetic energy (KE) in the event of a crash, resulting in “safer” crashes if they do occur 

(Candappa 2015). Candappa (2015) conducted a treatment control study that evaluated the 

behavior pattern and compliance of 533 vehicles. Results indicated that the KE generated by a 

typical crash at the control site was deemed higher than that generated at either treated site, thus 

implying that safety benefits of vulnerable road users (pedestrians and cyclists) exist at MRs.

Cross-Sectional Studies

A few cross-sectional studies can be found in the MR literature. Kennedy, Hall, and Barnard 

(1998) studied crash risk in the United Kingdom based on a national stratified sample of 200 

three-legged and 100 four-legged urban MRs on 30-mph single carriageway roads (311 sites, 

2,100 personal injury accidents (PIAs), 1986–1992) with an objective to develop relationships 

between crash frequency and traffic flow, road features, layout, geometry, land use, and other 

variables. Extensive data collection was conducted at these junctions, including 12-h vehicle and 

pedestrian counts and a geometric survey. Crash records were obtained for all reported PIAs 

occurring at the junctions from 1986 to 1992. The crashes were categorized based on 

frequencies, severities, and rates by type of central island and by region, crash group, road user 

involvement, and number of casualties per accident. Generalized linear modeling was used to 

quantify such relationships for different types of accidents. This study found that the average 

PIA frequency at four-legged sites was about 50 percent higher than at three-legged sites 

(0.92 PIAs per year). The study also found that the severity of crashes at MRs was reduced 

compared with two-way-stop junctions and signalized junctions. Reductions were found for 

pedestrian crashes as well—about half the number found at two-way-stop junctions and traffic 

signals. Bicycle and motorcycle crash involvement rates were found to be higher at MRs than 

those involving cars and light trucks. 

However, relative crash involvement rates for bicycles at MRs were higher than for

two-way-stop junctions (Kennedy, Hall, and Barnard 1998). Rates of motorcycle crashes 

remained the same for both types of intersections. The flush or mountable central island was 

found to pose higher risk of single vehicle crashes at four-legged MRs. The type of central island 

did not matter for the rest of the crash rates. The increasing proportion of two-wheelers increased 

the effect of crashes involving vehicles entering, circulating, and merging at three-legged MRs. 

Speed variables and deflection (vehicle path curvature) variables were not significant to crash 

rates. Researchers argued that appropriate angular displacement variables could be used in future 

studies to replace vehicle path curvature variables. Lastly, the research found that visibility 

affected a number of different crash groups, and that crashes increased with longer sight 

distances, with all other things being equal. 

In their 1989 cross-sectional study, Walker and Pittam (1989) stated that PIAs within 20 m of 

MRs occurred at an average frequency of 0.61 PIA per junction per year for three-legged sites 

and 0.88 PIA per junction per year for four-legged sites. The corresponding crash rates per 

100 million vehicle inflows were 10 and 17, respectively. Crash severity (the percentage of fatal 

and serious crashes) was between 16 and 18 percent for the MRs. These results are similar to the 

severities of other urban junctions (small roundabouts: 18 percent; traffic signals: 20 percent) but 
6 

are less than 27 percent for urban conventional roundabouts. The average crash frequencies and 

rates for MRs were similar to those for rural T-junctions (0.5 PIA per junction per year and 

17 PIAs per 100 million vehicles) but were considerably lower than those for other types of 

roundabouts and for traffic signals. This result might be explained in terms of the likely 

similarity in the aggregate traffic flows and the balance of flows within the junctions between 

MRs and rural T-junctions, and the dissimilarity of these flows between MRs and the other 

junctions (Walker and Pittam 1989). 

Before–After Studies

The majority of research efforts assessing MRs use a before–after design. These works are 

mostly based in European countries, particularly in the United Kingdom, and span over several 

decades.

Green (1977) evaluated safety change in a before–after design in 1977. Results indicated a 

significant reduction of between 28 and 37 percent for all injury crashes and 46 percent reduction 

in fatal and serious injury crashes when TWSC intersections were converted to small 

roundabouts or MRs. This study evaluated 150 junctions that were converted to MRs. 

Considered separately, 132 of these junctions were previously governed by 30 or 40 mph speed 

limits with TWSC, traffic signals, or roundabouts. The average lengths of the before and after 

periods were 3.4 and 2.5 yr, respectively.

Another safety study was conducted at 20 MRs in greater London by Lalani (1975). This study 

showed that vehicle crashes within 50 m of the MR declined 29.5 percent, and pedestrian crashes 

within 50 m declined 37.5 percent. Total injury crashes declined 30.3 percent after construction 

of a MR, which was statistically significant at the 90-percent confidence level (Waddell and

Albertson 2005). The injury crash data in this study were limited to the period from January 

1970 to May 1975. Lalani (1975) did not provide information on crashes at each site but gave the 

total number of crashes during the before and after periods for different categories of roundabout 

sites.

Ibrahim and Metcalfe (1993) studied the effect of replacing TWSC intersections by MRs and 

installing new MRs at six groups of sites (each collected and analyzed in separate studies) by 

observing rates of crashes during the before and after periods and using two Bayesian methods. 

The first method assumed a constant treatment effect on all six groups and involved combining 

studies chronologically. The second method allowed for variation of treatment effect between 

groups and is based on a Bayesian hierarchical framework. They concluded that a policy of 

replacing TWSC intersections by MRs is likely (chances of 90 percent) to lead to a reduction in 

crashes of at least 13 percent (1.3 standard deviations (Std Devs) below the pessimistic mean), 

and the best estimate of the benefit was a reduction in crashes of between 23 and 28 percent. 

However, there was evidence that some groups of sites benefitted more than others. Except for 

one study, all the analyzed studies reported a reduction in crash rate after MRs were installed at a 

group of sites. 

Another before–after study on a single MR at the Village of Dimondale (Dimondale, MI), 

conducted by Waddell and Albertson (2005) considered all crashes that occurred within 300 ft of 

the intersection. Five crashes were reported in the 3 yr both before and after the installation 
7 

period, with only a $733 reduction in the cost of crashes (due only to a shift in injury classes). 

The authors could not claim any significant benefits to the conversion of the TWSC intersection 

to a MR (Waddell and Albertson 2005). 

In another study based in the United Kingdom, MRs were found to improve the safety at 

three-legged intersections. Reportedly, crash rate reductions of approximately 30 percent were 

found compared with signalized intersections (Bodé and Maunsell 2006). The estimated rate is 

similar to that of priority T-junctions. The severity of crashes (percentage of fatal and serious 

crashes to all injury crashes) at three-legged MR sites was found to be lower than at three-legged

signaled junctions and considerably lower than at 30-mph T-junctions, which can be attributed to 

the operational effect of the design (i.e., reduced speeds). 

A study by Brilon (2011) in Germany found a 29-percent reduction in crash rate following a 

conversion of 13 unsignalized intersections to MRs. Only personal injury crashes and 

damage-only crashes were included in the study to calculate the crash rate and crash cost rates, 

since only data for these types of crashes were available. The before–after study reported a 

reduction in crash rate (crashes per motor vehicle) from 0.79 to 0.56, and the crash cost rate 

(euros per 1,000 vehicles) was reduced from 9.47 to 3.91. Based on this study, MRs were 

recommended at urban areas with a PSL of less than 50 km/h and maximum number of vehicles 

20,000 per day. However, the authors did not recommend the use of MRs outside urban areas. 

Delbosc et al. (2017) analyzed crash records 3 yr before and after the installation of 40 MRs in 

Australia, along with a case study of two adjacent MRs installed in 2016. The crash comparison 

clearly suggested a crash reduction associated with the MR installation. Crashes were reduced by 

78.9 percent, with the number of serious crashes reduced from six to zero. The “cross traffic” 

and “right far” crashes virtually disappeared after the installation of MRs. The change was also 

found to have an increased yielding rate to pedestrians, which might have resulted in a decreased 

number of crashes. Additionally, driver behavior was recorded through a questionnaire survey 

(32 respondents, 16 pedestrians, and 16 residents) to assess community acceptance. The MRs

were shown to improve the perception of safety by offering a safer driving and walking 

experience at the intersection than before the installation. Based on the results, the authors 

recommended MRs at locations with significant bus or heavy vehicle traffic, or in grid-based 

local road networks. However, authors argue that MRs might not be appropriate in areas with 

high cyclist movements on local roads. 

Finally, a recent evaluation in the United States has indicated decreases in total crashes and fatal 

and injury (FI) crashes (CMFs of 0.83 and 0.41, respectively) for MR conversions from TWSC 

or one-way stop-controlled intersections (Pulugurtha, Mishra, and Mathew 2021). However, this 

study also reported a statistically significant increase in property damage only (PDO) crashes for 

these types of conversions (CMF of 1.09). Moreover, this study indicated large crash increases 

when AWSC intersections were converted to MRs. The corresponding CMFs increases for total, 

FI, and PDO crashes are 3.25, 1.74, and 3.84, respectively.
8 

CHAPTER SUMMARY

Past safety evaluations of MRs clearly suggest that safety benefits are present. Most safety 

evaluations of MRs based on crash data have been performed abroad, especially in Europe. 

Results are consistent over several decades and from multiple countries, suggesting that the 

treatment offers benefits independent of the country in which it is applied. Highlights from the 

literature review findings are given as follows. 

Some studies have found that MRs provide an increased perception of safety among users. 

Regarding operational benefits, several observations have been documented: a drop in 

85th percentile speeds; a reduction in the number of conflict points; and more time to make 

decisions, act, and react, thus, reducing the number of directions a driver needs monitor for 

conflicting traffic and reducing the need for drivers to judge gaps accurately in fast traffic (Zito 

and Taylor 1996; Sawers 2009; Rodegerdts, Scarbrough, and Bansen 2010). 

Studies have found that replacing TWSC intersections with MRs is linked to crash reductions by 

at least 13 percent and up to 79 percent (Ibrahim and Metcalfe 1993; Delbosc et al. 2017). The 

best estimate of the benefit range provided by Ibrahim and Metcalfe (1993) is between 23 and 

28 percent and has been confirmed by later works. For example, a similar estimate was obtained 

from a study in Germany that found a 29-percent reduction in crash rate by converting 

13 unsignalized intersections to MRs (Brilon 2011). Similarly, MRs in the United Kingdom were 

found to be linked to improved safety at three-legged intersections with reported crash rate 

reductions of approximately 30 percent compared with signalized intersections (Bodé and 

Maunsell 2006). 

An Australian study found that MRs provide similar benefits as traditional roundabouts 

(Jurewicz et al. 2013). One United States-based study, however, found no change in crash 

numbers after MR installation, whereas another indicated large increases for AWSC conversions 

to MRs (Waddell and Albertson 2005; Pulugurtha, Mishra, and Mathew 2021). 
9 

CHAPTER 2. STUDY DESIGN AND METHODOLOGY 

The study design for this evaluation needed to account for multiple features and overcome the 

particular challenges anticipated from a safety evaluation of MRs, as described in chapter 1. A

proper study design can significantly maximize the chances of obtaining meaningful, quality 

results. Generally speaking, safety studies rely on observational data because randomization is 

not possible, and true experiments, such as randomized control group experiments where injury 

or death is a potential outcome, are not feasible or ethical. This study is no exception. However, 

a good observational study should be consistent with key elements of control group experiments 

to the extent possible. Building a dataset that represents both treated and nontreated sites is one 

such key element, as well as an account of key confounding variables. This study followed a 

quasi-experimental design by using a nonequivalent comparison group or a control series design

(Campbell and Stanley 1966; Campbell and Ross 1968). However, in the case of evaluating the 

safety potential of MR installations, the researchers deemed obtaining a large before–after 

dataset representing multiple jurisdictions to be the biggest challenge after reviewing potential 

data sources. The selection of jurisdictions was driven mostly by the potential to produce a 

dataset large enough for a robust safety analysis. However, due to the effort needed for 

developing a before–after study, the number of jurisdictions that can be included was limited by 

budget and schedule. 

A safety evaluation in the face of limited study locations could benefit from incorporating 

existing knowledge about safety performance of roundabout and stop-controlled intersections 

into the evaluation. This strategy was considered because of its potential to produce more precise

CMF estimates. However, this approach’s validity greatly depends on the transferability of that 

knowledge of roundabout safety in general to MR designs. Although potential differences in 

safety performance are expected, this approach takes advantage of any similarities between MRs 

and other roundabout types. The National Cooperative Highway Research Program (NCHRP) 

Report 572 offers various functional forms of roundabout intersection designs where the only 

independent variable is annual average daily traffic (AADT) and where the crashes increase with 

additional legs (three to five) and additional circulatory lanes (one to four) (Rodegerdts et al. 

2007). On the other hand, functional forms from various jurisdictions already in possession of 

crash prediction models for AWSC and TWSC intersections (e.g., studies by Gates et al. 2018

and Walker et al. 2020) could be potentially incorporated. These crash prediction models and 

their parameter estimates imply probability distributions of crashes for the before–after 

conditions that can be incorporated as inputs in the analysis that would produce MR CMFs. The 

Bayesian framework—described in more detail in the Data Analysis Methods section—offers a 

way of incorporating past results while producing new updated information (i.e., CMFs in this 

case) by integrating new data with information from past research. 

STUDY DESIGN

Longitudinal study designs (e.g., before–after) are preferred when developing CMFs because of 

their ability to effectively account for site-to-site variability and biases due to omitted variables. 

Such a design can be strengthened if a reference group or a comparison group is available that 

can control for covarying extraneous variables. 
10 

This study intended to establish the safety effectiveness of MRs using TWSC or AWSC

intersections as the basis of comparison. The design of the evaluation is a before–after design

with a comparison group; thus, having the dates of conversion to MR at the study locations was 

relevant for data collection. However, the small number of MR facilities in the United States was

a limiting factor, combined with the fact that most of these installations are relatively recent. As 

a result, the research team decided to include MR installations and safety data in the study, with 

special emphasis on the jurisdictional location. The need to identify a robust set of baseline 

condition sites (TWSC or AWSC intersections) with comparable features to the MR sites in the 

study was clear in the early stages of the study. The research team identified MR 

implementations in multiple States and requested data for the before and after periods when 

available. 

Another FHWA guidance was to consider the possibility of incorporating operational 

assessments into the evaluation, such as metrics that can be obtained from external vendors. In 

response to this guidance, the research team investigated the feasibility of obtaining operational 

and safety data for the main analysis but ultimately could not secure a sufficently large 

operational dataset to pair with the safety data. However, later in this reseach, the researchers 

derived rough operational benefits of MR installations from past studies to estimate B/C ratios.

The unit of analysis for the study was determined as an intersection-year, given that the analysis 

will explicitly model the conversions to MR. The safety performance evaluations included the 

following general data types: 

• Location (such as city and State) of each intersection. 

• Years that the intersection type (MR, TWSC, or AWSC) design has been in place.

• Geometric characteristics of the intersection (such as number of legs, number of lanes, 

lane widths, channelization, advanced signage, pedestrian and bike facilities, island 

radius, median types, and so on). 

• Sufficient number of crashes for the period of analysis. 

• Crash types and severities. 

• Date and time of crashes. 

• Traffic volume data (AADTs for both major and minor approaches). 

Study Design: Interrupted Time Series Design with Comparison Groups 

The research team implemented an interrupted time series design and analysis with comparison 

groups (ITS-CG) to cope with the small number of treatment (MR) sites. 

ITS-CG is a quasi-experimental method that can minimize the threat of confounding (Campbell 

and Stanley 1966; Campbell and Ross 1968). An interrupted time series design and an ITS-CG

are study designs often used in social science to determine the impact of an intervention. As 

stated in the report from Campbell and Ross (1968), “In the Interrupted Time-Series, the ‘causal’ 

variable is examined as an event or change occurring at a single time, specified independently of 

inspection of the data.” Here the causal variable (intervention) is a deployment of an MR. These 

study designs require crashes to be aggregated monthly or yearly at each site. ITS-CG has been 

applied to before–after data to evaluate the impact of the intervention treatment on the crash 

frequency (Wagenaar and Maybee 1986; Wagenaar 1986). Comparison groups are added to 
11 

control for extraneous variables and strengthen the study design. In ITS-CG, a treatment group is 

also compared to the comparison group that had not undergone the treatment but was selected to 

be as similar as possible to the treatment group to better isolate the effect of the treatment. 

The next section of the report describes the database preparation for the evaluation. 

DATABASE DESIGN AND MANAGEMENT

Locations of interest included sites that have MR installations, with entering volumes in excess 

of 800 vehicles per hour, and potentially low speed applications. Those characteristics are most 

likely found in arterials, minor arterials, and collector roads, which will be the focus of this 

evaluation. The key data element would be locations with MRs, preferably with known dates of 

installation, and the type of traffic control present before the MR installation. In addition to MR 

locations, a suite of appropriate locations was needed to form a comparison group. The purpose 

of a comparison group is to provide a reference of the natural fluctuations in safety for MR

viable but untreated sites, so that any changes in safety found for the treated locations can be 

assessed against the normally expected changes had no MR been installed. 

To develop the intended CMFs for MRs, explicit consideration of different factors was needed, 

including land use, traffic control device before the MR installation, speed limit, and traffic 

volume, among other factors. Table 1 shows a list of data elements necessary for this evaluation. 
12 

Table 1. Data elements for MR evaluation. 

Category Elements

Crash 

characteristics

• State, county, city, and milepost (measure). 

• Latitude and longitude. 

• Date (weekday, month, year). 

• Time (nighttime, daytime). 

• Crash contributing factor (fixed object, speed). 

• Crash type (single vehicle, multivehicle). 

• Crash severity (fatal, severe injury). 

• Driver impairment and distraction. 

• Vehicle type (passenger, truck). 

MR characteristics

• Traffic control device before and after MR installation. 

• MR diameter. 

• Alignment (curves, angle of intersection). 

• Speed limit. 

• Signage. 

• Number of lanes. 

• Pavement markings. 

• Lane width. 

Approach roads 

characteristics

• Area type (rural, urban). 

• Number of lanes. 

• Lane width. 

• Median width and type. 

• Alignment (curves, angle of intersection). 

• Signs and signals. 

• Shoulders. 

Traffic operations • Traffic volume for facility. 

• Daily hourly volume profile for these locations. 

Data Management Extraction and Integration 

The data management stage of the process involved collecting and revising data, supplementing 

the data where appropriate, concatenating variables across multiple sources, and preparing the 

data for statistical analyses. In response to actual data availability, the research team refined the 

final datasets through a data integration process explained in this section. The research team used 

geographic information systems (EsriTM 2019) software to prepare, filter, and combine data from 

multiple sources and geolocations (typically in shapefile format). GIS tools allow the 

manipulation, combination, and display of data for different types of attributes, including 

crashes, road infrastructure, traffic volume, census tract, land use, and other types. The starting 

point of this process is the locations with known MR installations. The research team then 

located nearby sites that could potentially become comparison sites. This potential was judged by 

the roadway character (rural/urban), surrounding land use (residential/commercial/industrial), 

facility type (major or minor arterial/collector), number of lanes in the main road, and relative 

proximity to each MR site. After reviewing all candidate sites, the research team selected a set of 
13 

three comparison sites per MR site, and geometry variables were collected for each study 

location (both MR and comparison). Geolocated crash data and traffic volumes were obtained 

where available and linked to the geolocation of each study site using GIS tools. In instances for 

which the data obtained were not geolocated, the research team did the corresponding linkage 

using other languages and appropriate tools, such as Sequential Query Language queries on 

Access and R-statistical language (The R Foundation 2021), or additional manual extraction 

(mostly for traffic volume data), such as spreadsheets or other tabular data. 

AADT Imputation

The research team found challenges in obtaining AADT data for all sites and all periods in the 

study, especially for those located in lower functional classes. Needing to cover almost two 

decades (due to different dates of installation), the research team often performed AADT data 

extraction using AADT maps and GIS layers available from various sources online to obtain the 

needed AADT figures. Inevitably, multiple periods of analysis were unavailable, prompting the 

research team to apply imputation methods to estimate the missing values where that was 

feasible from a trend (i.e., for sites with more than 1 yr of AADT available, or for locations 

where other nearby locations had sufficient AADT data available). 

Using imputed values instead of measured ones always carries an inherent risk. However, the 

alternative is to drop the sites and periods without measures of exposure, which would further 

reduce an already limited dataset. Even published AADTs are not always necessarily derived 

from actual counts and are often estimated, especially for lower functional classes. A common 

practice is to perform actual counts at a subset of locations to produce their AADTs, whereas 

AADTs for a sizable proportion of sites are estimated using the counts from similar sites. 

Because of the inherent inaccuracy of AADTs, the research team ascertained that the benefit of 

implementing imputation—avoiding the need to drop study locations—outweighed the 

uncertainty of using imputation, which could be comparable to the uncertainty already given in 

AADT values. Although using imputation was not expected to add significantly to the existing 

uncertainty of the AADTs, the research team recognized that the extent of that uncertainty and its 

shift due to imputation was unknown. 

Data Balancing 

Although other States were initially considered for this evaluation, the research team ultimately 

gathered safety data from Washington, Michigan, and Maryland. The research team collected 

three comparison sites for each treated site; ratios of 3:1 or 4:1 for comparison and treated sites 

have been recommended to maximize statistical power (Linden and Samuels 2013). The 

selection of comparison sites required consideration of several factors and approaches to 

establish the degree of similarity between treated sites and comparison sites. 

Given the relatively small size of the samples in each study State, the research team deemed a 

propensity score (PS) analysis might not be robust enough to select comparison sites with similar 

characteristics as the treated sites because regression models might not have enough data to 

identify a set of covariates to balance. For this reason, the researchers selected the comparison 

sites using a systematic approach based on the roadway geometric and land use data available 

during data collection. Locations with the same number of legs, adjacent land use, and functional 
14 

class, and in the same city or jurisdiction, were preferred when sites were selected for the 

comparison group, as illustrated in figure 1 for one location in Washington using publicly 

available satellite imagery (Google 2019). 

Original map © 2019 Google® EarthTM. Modified by FHWA (see Acknowledgments).

Figure 1. Map. Treated and comparison sites in Federal Way, WA (Google 2019). 

Although the research team considers proximity between treated and comparison sites to be 

desirable, too much proximity is a potential issue because the safety performance of both sites 

could be mutually influential (e.g., between two adjacent intersections). Therefore, the research 

team used a threshold of 0.5 mi to include additional rules of inclusion. In case a comparison site 

was closer than 0.5 mi, either it should not be on the same roadway as the treated site, or there 

should be another intersection in between the two sites. 

DATA ELEMENTS AND SOURCES 

The research team obtained detailed information for about 120 MRs from different sources. The 

identified MRs were located in 30 States, including Washington, Arizona, Oregon, Pennsylvania, 

Rhode Island, Texas, and Vermont. Most of these States, however, were found to have only one 

MR each. 
15 

In the initial stages, the MR information obtained from various sources included the following: 

• Location (e.g., city, State) of each improvement deployment. 

• Year(s) of installation. 

• The traffic control device before the MR installation. 

• Number of legs. 

• Intersection name and coordinates. 

While the research team collected the geometric and signage characteristics directly, traffic and 

crash data were procured either directly from online resources or through communications with 

the corresponding State DOTs.

In contrast, the research team used various criteria and tools to identify and collect detailed 

information related to the comparison sites, once a subset of treated sites was reduced to a 

manageable number of sites and States.

Although the research team received detailed information of MRs from 30 States, due to the 

incremental effort required for data collection in multiple States, the research team estimated that 

the budget and schedule would allow using up to 4 States with at least 6 MRs each. The research 

team narrowed down the search to nearly 60 MRs in 6 States. Nineteen MRs were identified in 

Washington, six in Michigan, six in Maryland, and six in North Carolina, which were the States 

of most interest from a sample-size standpoint. At FHWA’s request, other locations were 

considered (i.e., Georgia, Minnesota, and Missouri), but ultimately many of these States were 

discarded due to either determining they were traditional roundabouts, a small number of MR 

locations identified, the small number of available periods after the installation date (i.e., 

Minnesota), and/or the increased complexity of managing data collection for an increasing 

number of States. The final database consisted of three States: Washington, Michigan, and 

Maryland. 

MR installment years range from 2006 to 2019 across the three States selected for this study. 

Most of the potential sites were converted from either TWSC at four-legged or three-legged

intersections. In contrast, a few sites were converted from AWSC intersections. The research 

team evaluated the location (land uses) of potential sites, which include residential, commercial, 

and mixed land uses. 

The research team also found out about a number of recent or planned installations across the 

country (e.g., in the cities of Elizabethtown, KY; Takoma Park, MD; and McLean, VA) that 

would be useful in the economic analysis. 

Since the research team selected three similar comparison sites for each MR location, the 

research team defined evaluation groups consisting of the subsets of data from each MR location 

and its three comparison sites. 
16 

CRASH DATA

The research team collected crash data from various sources. The data include online sources 

such as an online data repository for Maryland (Maryland.gov 2022), and various 

jurisdiction-specific sites for Washington and Michigan (King County 2022; Michigan DOT 

2022), including GIS layers with traffic and crashes, as well as direct contact to the respective 

DOTs. After collecting crash data, the team used ArcGIS® (Esri 2019) tools to obtain crashes 

that occurred on the MRs and control sites. A buffer of 250 ft and intersection-related fields were 

used to extract crashes that occurred at or near the sites of interest.

For each location, the research team obtained 17 yr of crash data (2003–2019) for Washington, 

7 yr of crash data (2013–2019) for Michigan, and 5 yr of crash data (2015–2019) for Maryland. 

Additionally, the research team compiled safety and exposure data and the geometry, for each 

period of analysis. 

TRAFFIC DATA

Traffic data are key to explaining changes in crash frequencies and should be accounted for in 

the safety evaluation of MRs. The research team procured the AADT at treated and control 

locations for at least 3 yr before and 3 yr after the MR installation. Since some of the MRs had 

very early installation dates, and because their location was at low classification roadways, the 

research team could not obtain the AADT for all the periods at the sites under evaluation. Thus, 

the performed model-based imputation of AADT was at the locations for which sufficient data 

were available, either from other periods or from other nearby locations with similar 

characteristics, such as land use and road class. 

DATA ANALYSIS METHODS

The empirical analyses in this study were conducted using the statistical methods appropriate to 

the characteristics of the assembled datasets. The research team used Fully Bayesian (FB) 

analyses and generalized linear mixed-model (GLMM) variants (binomial mixed) to obtain the 

safety-effectiveness estimates of interest, given the ITS-CG design. 

Modeling Framework for FB Analysis of Before–After Designs with Comparison Groups

The FB analysis of safety effectiveness of MR in this study builds on the basic modeling 

framework from previous research, utilizing an ITS-CG design as a study design (Park, Park, and 

Lomax 2010; Park, Carlson, and Pike 2019). The research team employed Poisson-gamma 

mixture models to model crash counts. Poisson-gamma mixture models are equivalent to 

negative binomial distributions for observed crash frequencies. The modeling framework of 

Poisson-gamma mixture models for a FB before–after evaluation with comparison groups is 

presented as follows. 

Let yit denote an observation at site i (i=1, ..., I) during time (year) t (t=1, ..., T). That is, yit is the 

number of crashes that occurred in year t at site i. Let K be the number of covariates and 

Xit=(1, X1it, ..., XKit) be a (K+1)-dimensional vector of covariates. 
17 

Let β=(β0, β1, ..., βK)′ denote the (K+1)-dimensional column vector of the regression coefficients 

for the crash count. Let υit denote a vector of yearly random effects corresponding to site i and 

year t, explaining extra-Poisson variability. Suppose that conditional on υit and β∈RK+1, the 

crash count at site i in year t, yit, follows a Poisson distribution with mean μit, where the 

parameter μit is itself parameterized as the product of υit and the exponential of the product of Xit

and β. 

The yit values are independent, given the μit values. υit follows the gamma distribution with 

parameters η and 1/η. 

The marginal distribution of yit is given as a negative binomial distribution with mean λit and 

variance λit[1+λit/η], where λit=μit/υit. The Poisson-gamma mixture model allows for intrasite 

correlation among crash counts from the same site as well as overdispersion. 

Let the elements of the covariate vector Xit include indicator variables for treatment and time, an 

indicator variable for t>t0, an interaction term between treatment and time, an interaction term 

between treatment and the indicator for t>t0, and variables for intersection characteristics.

Then this model can be viewed as a change-point model, which assumes that, at the time of 

implementation, there is a possible change in the level with respect to time at treatment sites that 

might be attributable to the implementation of the countermeasure. Specifically, the coefficient 

for the interaction between the treatment indicator and the indicator for t>t0 represents a possible 

“jump” or “drop” effect of the countermeasure on crashes at the treatment site. The comparison 

group also has the imaginary before and after periods defined the same as those for the matching 

treatment group, although no treatment is applied to sites in the comparison group. For each 

group and period, the model can be rewritten in terms of mean crash count versus time. 

An FB analysis of the model as described requires the (second-level) prior distributions for the 

parameters, β0, β1, β2,..., βK as well as η, to be chosen. Estimation of model parameters is 

performed using Markov chain Monte Carlo (MCMC) methods (Gilks et al. 1996). 

We assume a normal prior distribution for β, with parameters mk and σ2

k and a gamma prior 

distribution for η with parameters c0 and d0. 

Once the posterior samples for model parameters and the true average crash frequencies (μit) for 

the treatment and comparison groups per period are obtained, the following steps can be 

followed to estimate the index (θ) of safety effectiveness (CMF) of MR.

Steps for Implementing FB Before–After Evaluations with Multiple Comparison Groups

The steps for implementation are as follows:

1. Specify the hyperparameter values, (c0, C0, r0, R0) for prior distribution of model 

parameters.

2. Obtain the draws of model parameters and the expected annual crash frequency for each 

site (i) and year (t) by MCMC.
18 

3. Obtain posterior distributions of crash frequencies during the before period for the 

treatment group (μTB), during the after period for the treatment group (μTA), during the 

before period for the comparison group (μCB), and during the after period for the 

comparison group (μCA) by taking an average of the expected crash frequencies over the 

appropriate years and the sites.

4. Obtain a posterior distribution of the ratios of the expected crash frequencies before and 

after periods for the comparison group (comparison ratio) for the gth comparison group 

by the ratio Rc(g)=μCA(g)/μCB(g). 

5. Step 5. Obtain a posterior distribution of the predicted frequencies that would have 

occurred without treatment in the after period for the gth treatment group as: 

π(g)=μTB(g)RC(g). 

6. Step 6. Obtain a posterior distribution of the index of effectiveness (of the 

countermeasure) for the crashes as the ratio of the sum of all μTA(g) to the sum of all π(g). 

7. Step 7. Obtain the point estimates for βk and θ as the sample means of corresponding 

posterior distributions. 

8. Step 8. Obtain the uncertainty estimates for βk and θ as the sample Std Dev of 

corresponding posterior distributions. 

9. Step 9. Construct the 95 percent (or 90 percent) credible intervals of βk and θ using the 

2.5th (or 5th) percentiles and the 97.5th (or 95th) percentiles of the corresponding 

posterior distributions. If the credible interval contains the value 1, then no significant 

effect has been observed. The credible interval placed below 1 (i.e., the upper limit of the 

interval is less than 1) implies that the countermeasure has a significant positive effect 

(i.e., a reduction in crashes) on safety. The credible interval placed above 1 (i.e., the 

lower limit of the interval is greater than 1) implies that the countermeasure has a 

significant negative effect (i.e., an increase in crashes) on safety.

The FB approach addresses the regression-to-the-mean problem by focusing on estimation of the 

expected number of crashes for both before and after periods without directly using the observed

crash count in the comparison. In the FB approach, the uncertainty in model parameters is 

incorporated into the final CMF estimate.

Generalized Linear Regression Analysis with PS Weighting

To increase statistical power, the research team performed some analyses using generalized 

linear regression models to aggregate locations from the three States, as well as to include 

locations for which the longitudinal data did not include the date of change to MR, locations that 

otherwise needed to be discarded in the ITS-CG analyses. While allowing the estimation to 

include such locations, generalized linear model (GLM)-based analysis also allowed for accounts 

of yearly trends, and changes in yearly trends by type of location (MR and comparison), 

grouping at two different levels (by evaluation group and by specific location within evaluation 

group), as well as other influential factors. The analyses were consistent with predictive methods 

described in the Highway Safety Manual (American Association of State Highway and 

Transportation Officials (AASHTO) 2010). The models included an error term that describes the 

variability between the mean response and the observations. 
19 

In the context of safety statistical modeling, the effect of a countermeasure is generally estimated 

by comparing the expected crash frequency or crash probability at treated sites to the expected 

crash frequency or probability when the treatment is absent. In the current evaluation, the data 

structure permits the focus on these contrasts to consider before and after periods for each MR 

conversion, while controlling for the corresponding change at the set of three comparison sites 

within the evaluation group. Although this approach can account for regression to the mean, this 

type of comparison could still be fraught with safety changes in other safety-influential 

covariates if not properly accounted for properly. For example, if sites with the countermeasure 

carry more traffic than those without the countermeasure, then the sites with the countermeasure 

would tend to experience more crashes merely because of their increased exposure to crash risk, 

despite the presence of the countermeasure. This effect should be explicitly controlled for in the 

analysis before estimation of the effect of the countermeasure under study. Similar to the FB 

approach, using GLMs allows for an account of such potential key differences explicitly in the 

set of parameter estimates while developing CMFs from a subset of parameters. 

PS weighting was used in the GLM analysis balancing for representation on the overlap 

distribution of sites, as defined by Li, Morgan, and Zaslavsky (2018). Under this framework, 

weights are developed based on a PS analysis of the data, so that the contrasts reflect a

population of sites approximately equally likely to be in either the treated or comparison groups. 

Binomial Mixed Models for Estimating Severity CMFs Through Severe Crash Risk 

The research team used binomial mixed models on data with two levels of aggregation 

(i.e., evaluation group, and study site), to assess the change in safety linked to the MR 

conversion at the treated sites. In this instance, the distribution of a response variable Y

indicating the number of successful observations (i.e., fatal crashes) from a binomial set of trials

(i.e., number of crashes in each period for that location in the study) can be modeled as a 

function of independent variables X and appropriate adjustments for the two nested grouping 

levels as a binomial variable (figure 2). 

Figure 2. Equation. Conditional probability of y value, given explanatory variables and site 

characteristics.

Where: 

P = probability of Y taking value yi, given the ith realization of a vector of explanatory 

variables X and MR_CO_ID (defined as the identification number for the site study) and 

evaluation group (Eval_Group) random effects. 

Y = count of observed successes, given n trials.

yi = a particular value in the domain of random count variable Y. 

MR_CO_Idi = random effect for the ith MR_CO_ID in the dataset. 

Eval_Groupj = random effect for the jth Eval_Group in the dataset.

ni = reference number of trials for which Y is observed. 

p = probability of a crash. 

k = multiplicative random function of MR_CO_ID and Eval_Group capturing binomial 

overdispersion in the data through crossed-random-effects variability. 
20 

For a crash corridor i, the logit of pi can be expressed as in figure 3. 

Figure 3. Equation. Binomial-lognormal mixed-model parameterization. 

Where: 

ɡ(pi) = logit function of pi. 

pi = probability of crash at ith MR_CO_ID. 

X = vector of independent variables (including key variable in evaluation and other 

safety-influential covariates). 

β = vector of regression coefficients.

The mixed-effects model approach allows an explicit account for possible correlations between 

multiple realizations of the outcome variable at a common MR_CO_ID and at nearby locations 

within a given Eval_Group. From each model, the research team estimated rate parameters, 

which were used to estimate the odds ratios (ORs) (when combined with the different levels of 

the independent variables). An OR is a direct estimate of a CMF and is expressed as the expected 

increase or decrease in crash risk of one level of treatment (MR intersection) relative to a base

level (TWSC or AWSC). An OR greater than 1.0 indicates that the change in that condition 

increases risk, and a ratio less than 1.0 indicates a decrease in risk.

CHAPTER SUMMARY

This chapter describes the study design, database structure, statistical methodologies, analysis 

methods, and tools that the research team used in performing the safety evaluations in this study. 

The chapter discusses the methodological features associated with the evaluations and the critical 

steps to develop a database suitable for statistical analysis. 

Finally, this chapter outlines statistical analysis methods to assess the safety effectiveness of MR 

installations (FB analysis of before–after designs with comparison groups) and contrasts in crash 

risk between MR and either TWSC or AWSC (via binomial mixed-effects regression models, as 

specified in figure 2 and figure 3) to support developing the CMFs of interest. 
21 

CHAPTER 3. DATA COLLECTION AND INTEGRATION

The research team identified several data sources to meet the needs of the MR safety evaluations 

in this study. As described in chapter 2, the research team focused on balancing the sites from 

treated and comparison locations, and, when selecting the latter, obtaining data from additional 

comparison locations to substitute less suitable locations for the comparison group when 

necessary. 

CRASH AND TRAFFIC VOLUME DATA COLLECTION

The research team obtained crash data from Washington, Michigan, and Maryland. Washington 

crash data covered 17 yr (2003–2019), Michigan crash data covered 7 yr (2013–2019), and

Maryland crash data covered 5 yr (2015–2019). The team further determined that MRs were 

installed in Washington between 2006 and 2019, in Michigan between 2015 and 2018, and in 

Maryland between 2000 and 2013. The research team ideally intended to use at least 3 yr before 

and after installation, but this number was not feasible for all locations and States, given the 

ranges of data representation. However, the methods of analysis described in chapter 2 can be 

adapted to have before and after periods of different lengths. 

Anticipated Effect Size and Data Needs

From the literature review, various international studies have quantified the safety benefit of 

MRs compared with TWSC intersections. Crash reduction effect estimates range from 25 to 

37 percent (Brilon 2011; Green 1977; Ibrahim and Metcalfe 1993; Bodé and Maunsell 2006). 

The study by Ibrahim and Metcalfe (1993) found a benefit had a sample of 88 MRs. Given the 

preliminary exploration of the available data in the United States, the research team considered 

that such a large sample size may not be available for this study. However, the team anticipated 

that a smaller sample might yield meaningful results, given the relatively large safety effect 

expected of at least 25 percent and up to 37 percent of crash reductions from those studies, as 

well as the use of statistical methods capable of handling small sample sizes.

Treated and MR Sites

For some study locations, satellite and street-level imagery did not offer sufficient detail to 

determine the geometric features of interest, especially in the periods before MR conversions. 

Additionally, due to limited availability of AADT data at locations from lower functional 

classes, the research team had to use imputation based on AADT history of similar locations, as 

explained in chapter 2. After a few locations without AADT data were removed from the study, 

the final number of MRs in the evaluation was 27, representing three States: Washington, 

Michigan, and Maryland. 

The research team determined that a substantial number of candidates for this study were located 

in Washington. A screening of data in March 2020 revealed 19 sites that could be potentially 

used. These sites include 11 MRs that were converted from either TWSC or STOP on minor 

roadways and 1 converted from AWSC, leaving 7 sites with an unknown before condition. 
22 

A map with these locations is shown in figure 4. Additionally, the research team confirmed that 

Highway Safety Information System (HSIS) data dictionaries indicated no intersection file 

available for Washington (HSIS 2022). For those reasons, the research team contacted the 

Washington DOT directly to request crash data.

Original map © 2019 Google® EarthTM. Modified by FHWA (see Acknowledgments).

Figure 4. Map. MR locations in Washington (Google 2019). 

Initially, the research team searched data availability in the HSIS (2022) database from 

Washington and found safety data available up to 2018 but not at locations out of the 

State-maintained highway system. 

The research team was able to collect information for six sites in four different cities in 

Maryland, leaving seven sites with an unknown before condition (table 2). Among the sites 

obtained, two were converted from TWSC, one from a STOP on a minor roadway, and three 

from AWSC.
23 

Table 2. Identified sites in Maryland. 

City Location 

Year 

Completed Land Use

Before 

Control 

Columbia Golden Straw Ln. and Davis 

Rd. 

2000 Residential/urban TWSC

Bel Air S. Tollgate Rd. and W. 

MacPhail Rd. 

2012 Residential/urban TWSC

Baltimore Canterbury Rd. and W. 39th St. 2013 University/urban TWSC

Baltimore Guilford Ave. and 22nd St. 2012 Residential/urban AWSC

Baltimore Guilford Ave. and E. 24th St. 2012 Residential/urban AWSC

Stevensville Thompson Creek Rd. and U.S. 

50 eastbound ramps

2007 Commercial/urban AWSC

CHARACTERISTICS OF SELECTED MR LOCATIONS

A comparable group of MRs was installed at locations with either TWSC or AWSC (table 3).

Table 3. Traffic control type before MR installation.

State AWSC TWSC Unclear Total 

Maryland 3 3 0 6 

Michigan 6 0 0 6 

Washington 0 9 6 15 

Total 9 12 6 27 

Similarly, table 4 shows the number of sites of analysis available at comparison sites. 

Table 4. Traffic control type at comparison sites. 

State AWSC TWSC Total 

Maryland 9 9 18 

Michigan 17 0 17 

Washington 12 35 47 

Total 38 44 82 

The research team collected other site characteristics that would potentially be accounted for in 

the statistical contrast between the MRs and comparison sites. These characteristics included 

land use, proximity to school zones, the presence of the bus stop, bike lanes, crosswalks, median 

type, and signs and markings, among others. Most of the MRs and comparison sites were in 

urban areas and in residential locations, and some sites were at commercial and mixed land use

locations. Furthermore, most of the MRs and their comparison sites were located away from 

school zones, did not have crosswalks, and did not have pedestrian crossing signs (table 5). 
24 

Table 5. Other characteristics of treated and comparison sites.

State

Within School Zone Crosswalk Present Pedestrian Crossing Signs

No Yes No Yes No Yes

Maryland 22 2 11 14 11 13

Michigan 23 0 23 0 23 0

Washington 59 3 44 19 45 19

Total 104 5 78 33 79 32

If a site had at least one period for a given condition (such as having crosswalks or not having 

them), they are counted in the corresponding cell. As a result, the totals for the two columns 

under each variable in table 5 do not necessarily add up to the same value, because sites that had 

a change for a feature (e.g., crosswalk present) are counted under both the Yes and No columns. 

Table 6, table 7, and table 8 show summary statistics of the assembled databases. Table 6 shows 

that the average total entering volumes (i.e., both average major and average minor AADT 

combined) for the sites in Washington are approximately 7,800 vehicles per day (vpd). 

Table 6. Descriptive statistics—Washington data.

Variable Mean Std Dev Median Minimum Maximum

Year 2011 4.9 2011 2003 2019

MR.Install date 2014.03 3.82 2014 2006 2019

MajAADT (vpd) 5,588.71 3,128.41 5,602 642.87 1,5138

MinAADT (vpd) 2,222.36 1,628.96 1,707.21 240 9,555

Approaches 3.81 0.4 4 3 4

lanes_maj (approach) 2.1 0.43 2 2 3

lanes_min (approach) 1.94 0.44 2 1 3

spd_maj (mph) 30.19 6.37 30 20 50

spd_min (mph) 27.5 6.1 25 15 35

diagonal_length (ft) 75.4 17.14 71.5 43 125.08

maj_ln width (ft) 12.2 2.02 12 10 15

min_ln width (ft) 12.3 2.84 12 9 15

MR_diameter (ft) 70.35 12.2 63.31 58.36 97.2

MR.Install date = MR installation date; MajAADT = major AADT; MinAADT = minor AADT; lanes_maj = major 

lanes; lanes_min = minor lanes; spd_maj = speed limit on the major approaches; spd_min = speed limit on the minor 

approaches; diagonal_length = diagonal length; maj_ln width = major line width; min_ln width = minor line width; 

MR_diameter = MR diameter. 

The diagonal length (diagonal_length) variable was collected to capture the overall footprint of 

the intersection, regardless of whether it was a roundabout or comparison site. This variable was 

considered as an alternative to the diameter in the model selection, as described in the Panel 

Analysis on Multistate Data section.

Table 7 shows that the average amount of entering traffic (approximately 7,700 vpd) in the 

Michigan dataset is comparable to that observed for Washington. 
25 

Table 7. Descriptive statistics—Michigan data. 

Variable Mean Std Dev Median Minimum Maximum

Year 2016 2.01 2016 2013 2019

MR.Install date 2016.74 1.08 2017 2015 2018

MajAADT (vpd) 4,206.49 2,292.63 3,341 253 7,598

MinAADT (vpd) 3,566.95 2,135.23 3,062 439 8,397

Approaches 4 0 4 4 4

lanes_maj 2.09 0.41 2 2 4

lanes_min 2.09 0.41 2 2 4

spd_maj (mph) 46.96 3.84 45 35 55

spd_min (mph) 43.7 5.77 45 25 55

diagonal_length (ft) 83.47 12.02 83.11 61.5 108

maj_ln width (ft) 11.91 1.62 12 10 15

min_ln width (ft) 11.78 1.75 11 10 15

MR_diameter (ft) 87.97 7.97 88.02 69.32 98.98

Similarly, table 8 shows the statistics for Maryland data, which had an average entering volume 

of approximately 7,500 vpd, which was comparable with the other two States. 

Table 8. Descriptive statistics—Maryland data. 

Variable Mean Std Dev Median Minimum Maximum

Year 2017 1.42 2017 2015 2019

MR.Install date 2011.33 1.98 2012 2007 2013

MajAADT (vpd) 4,964.06 3,978.39 3,727.5 877 14,375

MinAADT (vpd) 2,640.98 2,600.72 1,470.25 329 10,052

Approaches 4 0 4 4 4

lanes_maj 2.08 0.4 2 2 4

lanes_min 2 0.29 2 1 3

spd_maj (mph) 28.12 4.54 25 25 40

spd_min (mph) 26.25 3.62 25 15 35

diagonal_length (ft) 67.91 10.8 65.5 55 93

maj_ln width (ft) 12.96 1.60 13 11 15

min_ln width (ft) 12.68 1.90 12 10 15

MR_diameter (ft) 60.79 17.4 62.03 39.06 88.42

Finally, table 9, table 10, and table 11 show crash statistics for the three States. The statistics 

were generated for yearly periods of analysis so that the statistics would correspond to crashes 

per year. 
26 

Table 9. Crash descriptive statistics—Washington data (crashes per year).

Crash Type Mean Std Dev Minimum Maximum

Total 0.57 1.18 0 11

FI 0.17 0.52 0 5

PDO 0.39 0.9 0 7

MV_Total 0.51 1.1 0 11

MV_FI 0.15 0.49 0 5

MV_PDO 0.36 0.86 0 7

Total_Ped_&_Bicycle 0.01 0.1 0 1

Total_Bus_&_Truck 0.03 0.18 0 2

MV_Total = multivehicle total; MV_FI = multivehicle FI; MV_PDO = multivehicle PDO; Total_Ped_&_Bicycle = 

total pedestrian and bicycle; Total_Bus_&_Truck = total bus and truck.

Table 10. Crash descriptive statistics—Michigan data (crashes per year).

Crash Type Mean Std Dev Minimum Maximum

Total 2.57 3.39 0 24

FI 0.48 0.84 0 4

PDO 2.08 3.12 0 23

MV_Total 2.43 3.3 0 24

MV_FI 0.46 0.79 0 4

MV_PDO 1.98 3.04 0 23

Total_Ped_&_Bicycle 0 0 0 0

Total_Bus_&_Truck 0.08 0.27 0 1

Table 11. Crash descriptive statistics—Maryland data (crashes per year).

Crash Type Mean Std Dev Minimum Maximum

Total 0.72 1.01 0 5

FI 0.16 0.45 0 2

PDO 0.57 0.81 0 4

MV_Total 0.58 0.93 0 5

MV_FI 0.13 0.41 0 2

MV_PDO 0.45 0.78 0 4

Total_Ped_&_Bicycle 0.03 0.18 0 1

The crash statistics show that the frequency of pedestrian/bicycle and bus/truck crashes is small, 

and, thus, no meaningful analysis of these crashes could be supported. 

CHAPTER SUMMARY

This chapter documents the data collection and assembled database for this study. Various 

summary statistics are presented for the three databases developed: Washington, Michigan, and 

Maryland. The next chapter describes the statistical evaluations of these datasets and the derived 

CMF estimates.
27 

CHAPTER 4. SAFETY-EFFECTIVENESS EVALUATIONS 

This chapter describes the statistical analysis and presents the results of the safety-effectiveness 

evaluations of MR installations, including estimated CMFs of interest. 

As described in chapter 3, the research team assembled a three-State database for the statistical 

evaluation. The research team conducted multiple types of analyses on the ITS-CG data 

structure. First, FB evaluations were done for Washington for each crash type separately, and 

second, a GLMM estimation was done on all the panel data from three States combined, to 

maximize the size of the dataset and thus boost the statistical power of the estimation.

WASHINGTON RASH ANALYSIS 

The research team conducted the safety evaluation of MR in Washington by FB before–after 

analysis with comparison groups. Because the literature suggested that the safety effects 

associated with MR implementation significantly vary with previous intersection control types 

(whether TWSC or AWSC) (Green 1977, Ibrahim and Metcalfe 1993, Pulugurtha, Mishra, and 

Mathew 2021), the team considered CMFs for MR for TWSC and AWSC separately.

The Washington data contained 15 MR sites. The yearly crash data were obtained at each of the 

15 sites for 2003 to 2019. The implementation year when the MR was installed at each site varies 

between 2006 and 2019. Table 12 gives the number of sites in Washington for each 

implementation year. As can be seen from table 12, the base condition for the before period is 

missing (no old photo existed for those sites) for 6 out of 15 MRs in the database, and those sites 

were excluded from the before–after evaluation. The remaining nine sites all had TWSC as the 

before condition. Consequently, CMF was developed based on before–after analysis of those 

nine sites with TWSC as the before condition. 

Table 12. Number of MR sites and comparison sites in Washington for each 

implementation year.

Implementation 

Year

Number of MR 

Sites

Number of MR Sites with a 

Known Before Condition 

(TWSC)

Number of 

Comparison Sites

2006 2 — 6

2012 2 2 6

2013 2 1 6

2014 3 2 9

2015 — — 2

2016 1 1 3

2017 2 1 6

2018 1 — 3

2019 2 2 6

Total 15 9 47

—No data.
28 

The treatment group for MR (with TWSC as the before condition) in Washington consists of 

crashes from intersections where MRs were installed during 2012, 2013, 2014, 2016, 2017, and 

2019. The year with the installation of MR is included in the after period. 

The team fitted a Poisson-gamma mixture model with a change point as described in chapter 2, 

to total, FI, PDO, multivehicle total (MV_Total), multivehicle FI (MV_FI), and multivehicle

PDO (MV_PDO) crashes. This model included appropriate indicator functions for site type 

(specifying whether a segment is a treatment site or a comparison site) and period (specifying 

whether the site belongs to the before or the after period) as well as time trend for each site type 

and other covariates. Exposure was accounted for by the variables logAADT_Maj and 

logAADT_Min (log of major approach AADT and log of minor approach AADT, respectively). 

Additionally, the following variables were included as model covariates: 

• Approaches—Number of approaches. 

• PedCross01—Whether there is a pedestrian crossing sign: 1 = yes; 0 = no. 

• SchoolZone01—Whether there is a school zone within 250 ft: 1 = yes; 0 = no. 

• diag1—Length of the first diagonal in feet. 

• diag2—Length of the second diagonal in feet. 

• spd_maj—Speed limit on the major approaches. 

The research team followed the steps for implementing FB before–after evaluations with six 

comparison groups (corresponding to implementation years 2012, 2013, 2014, 2016, 2017, and 

2019 with G=6) as presented in chapter 2. To manage the issue of a limited sample size, the team 

incorporated prior knowledge obtained from previous studies documented in the CMF 

Clearinghouse on the safety effects of roundabouts into the analysis through a prior distribution 

(FHWA 2022b). For the prior distribution of β5 in the analysis, the research team used an 

informative prior distribution derived based on the CMFs for roundabouts provided on the CMF

Clearinghouse website as well as previous studies (Kennedy, Hall, and Barnard 1998; Green 

1977; Walker and Pitnam 1989; Lalani 1975; Ibrahim and Metcalfe 1993) on MRs to 

compensate for the small sample size. Previous studies on MRs indicated crash reductions of 

roughly 30 to 79 percent, which would correspond to CMF value of 0.21–0.7 (Green 1977; 

Lalani 1975; ). The CMF Clearinghouse provides the following CMFs for roundabouts: 0.42 

(with adjusted standard error (Std Err) 0.13 and unadjusted Std Err 0.07) for conversion of stopcontrolled intersection into single-lane roundabout, 0.56 (with adjusted Std Err 0.1 and 

unadjusted Std Err 0.05) for convert unsignalized intersection to roundabout, and 0.53 (with 

unadjusted Std Err 0.061) for conversion of intersection into single-lane roundabout. Because the 

CMF will be roughly on the same scale as exp(β5), the normal distribution with a mean of −0.8 

(for total, PDO, MV_Total, and MV_PDO crashes) or −0.9 (for FI and MV_FI crashes), and Std 

Dev of 0.1 was used for the prior distribution for β5. For the prior distributions of the other 

regression coefficients, however, proper but diffuse priors, such as a normal distribution with 

mean of 0 (or other nonzero constant for β0) and Std Dev of 1, were used to reflect the lack of 

precise knowledge on the parameters a priori. The inferences on the parameters of interest were 

made based on the samples from the posterior distribution obtained by the MCMC algorithm 

coded in MATLAB® (MathWorks 2022). 

Table 13, table 15, table 17, table 19, table 21, and table 23 summarize the results from the FB 

analysis based on 5,000 posterior samples collected for 100,000 iterations by subsampling every 
29 

10th sample after discarding the first 50,000 draws. The estimated CMF and index of 

effectiveness were obtained by accounting for the changes in unmeasured factors between the 

before and the after period using the comparison ratio following steps 4–6 described in the 

section, Steps for Implementing FB Before–After Evaluations with Multiple Comparison 

Groups, in chapter 2. The corresponding uncertainty estimates for each table for the estimated 

CMF, the posterior Std Dev, and 95 percent (or 90 percent) credible interval are provided in 

table 14, table 16, table 18, table 20, table 22, and table 24. The results indicate that there have 

been statistically significant reductions in total, FI, PDO, MV_Total, and MV_PDO crashes after 

conversion to MRs from TWSC intersections. Reductions for total and PDO crashes were 

statistically significant with 95 percent probability, and reductions for FI, MV_Total, and 

MV_PDO crashes were significant with 90 percent probability. 

Table 13. Results for FB evaluation of total crashes for MR sites with TWSC as the before 

condition in Washington. 

Regression 

Coefficients Variable Estimate

Uncertainty 

Estimates

Lower Limit 

of 95-percent

Credible 

Interval

Upper Limit of 

95-percent

Credible 

Interval

β0 Intercept −4.5163 1.3567 −7.0911 −1.7200 

β1 Trt −0.9762 0.7097 −2.4647 0.4220 

β2 Time 0.0872 0.0214 0.0449 0.1316 

β3 Trt×time 0.1168 0.0271 0.0660 0.1704 

β4 After −0.2386 0.2212 −0.6715 0.1885 

β5 Trt×After −0.7595 0.0968 −0.9539 −0.5757 

β6 logAADT_Maj 0.7959 0.3893 0.1077 1.5535 

β7 logAADT_Min 0.0538 0.3269 −0.6154 0.7182 

β8 Approaches −2.9383 0.6861 −4.3563 −1.6534 

β9 PedCross01 −0.9240 0.6339 −2.1438 0.3774 

β10 SchoolZone01 2.8451 0.9931 1.1580 4.9494 

β11 diag1 0.0190 0.0117 −0.0027 0.0429 

β12 diag2 0.0181 0.0115 −0.0033 0.0412 

β13 spd_maj 0.1189 0.0364 0.0537 0.2014 

Table 14. MR CMF and uncertainty estimates for table 13. 

CMF Estimate

CMFTWSC ( ) 0.6330 

Std Dev 0.1512 

95-percent credible interval (0.3807, 0.9713) 

90-percent credible interval (0.4157, 0.8956) 

(percent reduction) 36.70 

= the estimated CMF, per FB procedure described in chapter 2. 

Std Dev = the posterior standard deviation for θ. 

= the estimated percent crash reduction. 

CMFTWSC = CMF of MR with TWSC as the before condition. 
30 

Table 15. Results for FB evaluation of FI crashes for MR sites with TWSC as the before 

condition in Washington. 

Regression 

Coefficients Variable Estimate

Uncertainty 

Estimates

Lower Limit 

of 95-percent 

Credible 

Interval

Upper Limit of 

95-percent 

Credible 

Interval

β0 Intercept −2.8003 0.9452 4.7607 −0.9262 

β1 Trt −0.7077 0.5305 −1.8295 0.2539 

β2 Time 0.0501 0.0302 −0.0130 0.1083 

β3 Trt×time 0.1040 0.0392 0.0298 0.1866 

β4 After −0.2396 0.2950 −0.7931 0.3188 

β5 Trt×After −0.8979 0.0919 −1.0778 −0.7112 

β6 logAADT_Maj −0.2411 0.2932 −0.8118 0.3621 

β7 logAADT_Min 0.3922 0.2729 −0.1747 0.9115 

β8 Approaches −2.1133 0.4149 −3.0429 −1.3591 

β9 PedCross01 −0.9540 0.6402 −2.3349 0.2295 

β10 SchoolZone01 1.9136 0.6919 0.5683 3.3282 

β11 diag1 0.0163 0.0102 −0.0050 0.0343 

β12 diag2 0.0145 0.0110 −0.0056 0.0368 

β13 spd_maj 0.1420 0.0281 0.0862 0.2020 

Table 16. MR CMF and uncertainty estimates for table 15. 

CMF Estimate

CMFTWSC ( ) 0.5773 

Std Dev 0.2114 

95-percent credible interval (0.2616, 1.0672) 

90-percent credible interval (0.3019, 0.9577) 

(percent reduction) 42.27 
31 

Table 17. Results for FB evaluation of PDO crashes for MR sites with TWSC as the before 

condition in Washington. 

Regression 

Coefficients Variable Estimate

Uncertainty 

Estimates

Lower Limit 

of 95-percent 

Credible 

Interval

Upper Limit 

of 95-percent 

Credible 

Interval

β0 Intercept −8.6456 1.0573 −10.7568 −6.5717 

β1 Trt −0.5725 0.5237 −1.6307 0.4614 

β2 Time 0.0954 0.0242 0.0505 0.1400 

β3 Trt×time 0.0980 0.0265 0.0458 0.1478 

β4 After −0.1331 0.2349 −0.5985 0.3055 

β5 Trt×After −0.7514 0.0936 −0.9369 −0.5572 

β6 logAADT_Maj 0.7636 0.3338 0.1845 1.4837 

β7 logAADT_Min 0.0371 0.3029 −0.5959 0.5899 

β8 Approaches −1.6871 0.4411 −2.7441 −0.9767 

β9 PedCross01 −0.8500 0.5291 −1.9080 0.2061 

β10 SchoolZone01 1.5275 0.7161 0.2429 3.0469 

β11 diag1 0.0186 0.0094 −0.0013 0.0390 

β12 diag2 0.0149 0.0095 −0.0049 0.0338 

β13 spd_maj 0.0983 0.0299 0.0414 0.1660 

Table 18. MR CMF and uncertainty estimates for table 17. 

CMF Estimate

CMFTWSC ( ) 0.5977 

Std Dev 0.1462 

95-percent credible interval (0.3540, 0.9341) 

90-percent credible interval (0.3884, 0.8623) 

(percent reduction) 40.23 
32 

Table 19. Results for FB evaluation of MV_Total crashes for MR sites with TWSC as the 

before condition in Washington. 

Regression 

Coefficients Variable Estimate

Uncertainty 

Estimates

Lower Limit of 

95-percent 

Credible 

Interval

Upper Limit 

of 95-percent 

Credible 

Interval

β0 Intercept −4.4562 1.1626 −6.6909 −2.0749 

β1 Trt −0.8073 0.5840 −1.9630 0.3981 

β2 Time 0.0762 0.0212 0.0365 0.1195 

β3 Trt×time 0.1276 0.0264 0.0788 0.1805 

β4 After −0.1216 0.2140 −0.5489 0.2882 

β5 Trt×After −0.7704 0.0892 −0.9608 −0.6053 

β6 logAADT_Maj 0.5168 0.3619 −0.1162 1.3486 

β7 logAADT_Min 0.0999 0.2891 −0.5420 0.6598 

β8 Approaches −2.4914 0.5983 −3.8241 −1.5337 

β9 PedCross01 −0.6885 0.5559 −1.7534 0.4606 

β10 SchoolZone01 1.8898 0.7850 0.4563 3.7072 

β11 diag1 0.0173 0.0090 −0.0018 0.0348 

β12 diag2 0.0191 0.0097 0.0014 0.0407 

β13 spd_maj 0.1172 0.0303 0.0630 0.1852 

Table 20. MR CMF and uncertainty estimates for table 19. 

CMF Estimate

CMFTWSC ( ) 0.6802 

Std Dev 0.1621 

95-percent credible interval (0.4073, 1.0458) 

90-percent credible interval (0.4422, 0.9698) 

(percent reduction) 31.98 
33 

Table 21. Results for FB evaluation of MV_FI crashes for MR sites with TWSC as the 

before condition in Washington. 

Regression 

Coefficients Variable Estimate

Uncertainty 

Estimates

Lower Limit 

of 95-percent 

Credible 

Interval

Upper Limit of 

95-percent 

Credible 

Interval

β0 Intercept −2.6538 0.9399 −4.3873 −0.7207 

β1 Trt −0.7655 0.5424 −1.8407 0.2512 

β2 Time 0.0465 0.0305 −0.0146 0.1058 

β3 Trt×time 0.1122 0.0416 0.0383 0.1994 

β4 After −0.2441 0.3133 −0.8660 0.3521 

β5 Trt×After −0.8962 0.0933 −1.0919 −0.7143 

β6 logAADT_Maj −0.1564 0.2987 −0.7235 0.4781 

β7 logAADT_Min 0.3267 0.2851 −0.2633 0.8655 

β8 Approaches −2.3596 0.4333 −3.3062 −1.5895 

β9 PedCross01 −0.7024 0.7151 −2.1196 0.7363 

β10 SchoolZone01 1.7498 0.7138 0.3416 3.1752 

β11 diag1 0.0126 0.0110 −0.0096 0.0320 

β12 diag2 0.0179 0.0115 −0.0041 0.0422 

β13 spd_maj 0.1519 0.0316 0.0907 0.2180 

Table 22. MR CMF and uncertainty estimates for table 21. 

CMF Estimate

CMFTWSC ( ) 0.5980 

Std Dev 0.2328 

95-percent credible interval (0.2556, 1.1408) 

90-percent credible interval (0.2966, 1.0174) 

(percent reduction) 40.20 
34 

Table 23. Results for FB evaluation of MV_PDO crashes for MR sites with TWSC as the 

before condition in Washington. 

Regression 

Coefficients Variable Estimate

Uncertainty 

Estimates

Lower Limit 

of 95-percent 

Credible 

Interval

Upper Limit 

of 95-percent 

Credible 

Interval

β0 Intercept −8.4140 1.0395 −10.4963 −6.3436 

β1 Trt −0.5982 0.5203 −1.7023 0.4434 

β2 Time 0.0888 0.0261 0.0390 0.1420 

β3 Trt×time 0.1111 0.0278 0.0566 0.1650 

β4 After 0.0007 0.2489 −0.4946 0.5091 

β5 Trt×After −0.7682 0.0922 −0.9496 −0.5922 

β6 logAADT_Maj 0.6021 0.3265 −0.0057 1.3292 

β7 logAADT_Min 0.1487 0.3101 −0.4929 0.7527 

β8 Approaches −1.7576 0.4620 −2.7889 −0.9891 

β9 PedCross01 −0.4764 0.5472 −1.5742 0.5816 

β10 SchoolZone01 1.0436 0.7363 −0.3949 2.5529 

β11 diag1 0.0207 0.0097 0.0014 0.0398 

β12 diag2 0.0138 0.0105 −0.0105 0.0319 

β13 spd_maj 0.1085 0.0347 0.0526 0.1909 

Table 24. MR CMF and uncertainty estimates for table 23. 

CMF Estimate

CMFTWSC ( ) 0.6389 

Std Dev 0.1610 

95-percent credible interval (0.3648, 1.0109) 

90-percent credible interval (0.4091, 0.921) 

(percent reduction) 36.11 

CONSOLIDATED RESULTS

Table 25 presents consolidated results for estimations in the CMFs and percent crash reductions. 

Again, it can be seen from the table that CMFs for MR converted from TWSC intersections are 

statistically significant for total, FI, PDO, MV_Total, and MV_PDO crashes. 
35 

Table 25. CMFs for MR converted from TWSC for different crash types. 

Total FI PDO MV_Total MV_FI MV_PDO

CMFTWSC 0.6330** 0.5773* 0.5977** 0.6802* 0.5980 0.6389*

Std Dev 0.1512 0.2114 0.1462 0.1621 0.2328 0.1610

95-percent 

credible interval

(0.3807, 

0.9713) 

(0.2616, 

1.0672) 

(0.3540, 

0.9341) 

(0.4073, 

1.0458) 

(0.2556, 

1.1408 ) 

(0.3648, 

1.0109)

90-percent 

credible interval

(0.4157, 

0.8956) 

(0.3019, 

0.9577) 

(0.3884, 

0.8623) 

(0.4422, 

0.9698) 

(0.2966, 

1.0174 ) 

(0.4091, 

0.921)

Crash reduction 

(percent) 36.70** 42.27* 40.23** 31.98* 40.20 36.11*

*Statistically significant results at 90-percent level.

**Statistically significant results at 95-percent level.

Std Dev = the posterior standard deviation (uncertainty estimate) for CMF. 

The next section summarizes an analysis effort based on the complete multistate dataset as an 

alternative approach to deal with the small sample issue. 

PANEL ANALYSIS ON MULTISTATE DATA

The research team conducted the next round of safety evaluations of MR in the multistate panel 

data. Similar to the FB analysis, an explicit account for the longitudinal structure and comparison 

groups was used to assess the change in crash frequency at MR installations, given the prior 

traffic control types at those locations. 

The research team performed a panel analysis, including all data for the MR intersection 

operation compared with the other control types available, namely TWSC and AWSC. The 

response variables in these analyses were the same as presented in the FB analysis. All 

estimations in these models were performed using GLMMs.

Particular challenges for these analyses included the multiple dates of installation of the MRs, 

the availability of data from additional MR sites whose prior condition could not be confirmed or 

represented in the dataset (in Washington and Maryland), and the availability of additional 

comparison sites initially collected to be matched and contrasted with an MR but whose MR 

location had to be removed from the dataset due to unavailable traffic volume data. The data 

from unmatched locations could only be used in this analysis of the complete multistate panel 

data. The research team developed overlap PS weights so that the analysis results would be 

indicative of the overlap population between the treated and comparison sites. 

The model estimates for the multistate panel data are shown in table 26. 
36 

Table 26. Model estimates from panel multistate data by crash type. 

Parameter

Total, Estimate 

(Std Err)

FI, Estimate

(Std Err)

PDO, Estimate

(Std Err)

MV_Total, Estimate

(Std Err)

MV_FI, Estimate

(Std Err)

MV_PDO, 

Estimate

(Std Err)

(Intercept) −6.453 (1.914)‡ −8.332 (2.453)‡ −5.886 (1.91)† −7.829 (2.511)† −7.1139 (2.5638)† −6.103 (1.988)†

log(MajAADTfc + 

MinAADTfc) 0.3112 (0.2158) — 0.243 (0.2162) 0.4104 (0.2858) 0.1972 (0.289) 0.2569 (0.225)

log(MajAADTfc) — 0.3335 (0.3878) — — — — 

log(MinAADTfc) — 0.0709 (0.3355) — — — — 

MinAADTfc — — — −4.701E-5 (9.425E-5) — — 

I(TR_CTRL = MR) −0.0184 (0.3046) −0.2211 (0.6503) −0.0266 (0.3473) −0.0311 (0.3712) 0.1214 (0.6492) −0.3758 (0.3757)

I(TR_CTRL = AWSC) 0.1336 (0.2741) 0.3086 (0.5405) 0.1086 (0.3028) 0.3826 (0.3552) 0.5924 (0.5471) 0.0392 (0.3191)

I(TR_CTRL =TWSC) −0.0895 (0.2555) 0.1322 (0.4851) −0.3289 (0.2901) −0.2593 (0.328) 0.2245 (0.5143) −0.458 (0.3023)

MR_diameter −0.0076 (0.0038)* −0.0907 (0.0396)* −0.0091 (0.0042)* −0.0101 (0.005)* −0.0894 (0.0388)* −0.0064 (0.0045)

spd_maj 0.086 (0.0168)‡ 0.0818 (0.0202)‡ 0.0823 (0.0162)‡ 0.1084 (0.0199)‡ 0.083 (0.0189)‡ 0.0845 (0.0166)‡

spd_min — — — −0.0396 (0.0193)* — — 

lane_min — — — 0.4413 (0.3195) — — 

rel.yr 0.0639 (0.0091)‡ 0.0388 (0.0166)* 0.0752 (0.0108)‡ 0.0652 (0.0092)‡ 0.0338 (0.018)§ 0.081 (0.0112)‡

MR_diameter:

MinAADTfc 3.9E-6 (6.4E-7)‡ — 4.2E-6 (7.0E-7)‡ 4.4E-6 (8.8E-7)‡ 0.0118 (0.0047)* 4.22E-6 (7.2E-7)‡

log(MinAADTfc):

MR_diameter — 0.0122 (0.0048)* — — — — 

—Not applicable.

§

Significant at the 90.0-percent confidence level.

*Significant at the 95.0-percent confidence level.

†

Significant at the 99.0-percent confidence level.

‡

Significant at the 99.9-percent confidence level. 

MajAADTfc = Major AADT; MinAADTfc = Minor AADT; TR = Treatment; CTRL = control; rel.yr = relative year. 
37 

Next, the research team estimated the corresponding CMFs by contrasting the MR estimate to 

the estimates for the other two traffic control types at average values for the roundabout diameter 

and minor AADT, as the effects of the countermeasures on these variables were found to be 

interrelated. Table 27 shows the resulting CMFs for conversions of TWSC intersections to MR. 

Table 27. CMFs for TWSC-to-MR conversion from panel multistate data. 

Crash Type Estimate Std Err z Value p Value Significance

Total 1.1015 0.0967 0.1859 0.6030 — 

FI 0.6855 −0.3776 0.3497 0.2803 — 

PDO 1.3000 0.2624 0.2140 0.2202 — 

MV_Total 1.1552 0.1443 0.2034 0.4782 — 

MV_FI 0.7833 −0.2442 0.3730 0.5127 — 

MV_PDO 1.2676 0.2372 0.2236 0.2888 — 

—Not applicable.

As can be seen in table 27, none of the estimates for TWSC-to-MR conversions was statistically 

significant in the multistate data. Similar to table 27, table 28 shows the CMFs corresponding to 

AWSC intersections converted to MRs from the multistate data.

Table 28. CMFs for AWSC-to-MR conversion from panel multistate data. 

Crash Type Estimate Std Err z Value p Value Significance

Total 0.8813 −0.1263 0.1852 0.4952 — 

FI 0.5746 −0.5541 0.4157 0.1825 — 

PDO 0.8393 −0.1751 0.1990 0.3788 — 

MV_Total 0.6080 −0.4976 0.2455 0.0427 * 

MV_FI 0.5422 −0.6122 0.4072 0.1327 — 

MV_PDO 0.7710 −0.2600 0.2105 0.2168 — 

—Not applicable.

*Significant at the 95.0-percent confidence level.

All estimates in table 28 are smaller than 1, suggesting there are crash reductions for this type of 

conversion. However, only for MV_Total crashes was this result statistically significant.

CHAPTER SUMMARY

This chapter documents the statistical evaluations and steps taken to develop CMFs from the 

three-State safety data available for this study. The analysis developed FB for Washington and 

GLMM statistical models for crash frequencies for the multistate joint database. The CMFs for 

MR converted from TWSC intersections were statistically significant for total, FI, PDO, 

MV_Total, and MV_PDO crashes. The CMF estimates showed directions with intuitive 

interpretations and reasonable magnitudes. In the multistate database, only a CMF estimate from 

AWSC to MR conversions yielded statistically significant results. 

The next chapter documents an economic analysis that considers the results in the evaluations 

documented in this chapter. 

39 

CHAPTER 5. ECONOMIC ANALYSIS

The research team conducted an economic analysis to estimate B/C ratios for the evaluated MR

installations at TWSC locations using the statistically significant severity shift factors developed 

from the multistate database. The research team adopted the procedures recommended in 

FHWA’s technical document, Crash Costs for Highway Safety Analysis (Harmon, Bahar, and 

Gross 2018). 

BENEFITS AND COSTS ESTIMATES

To perform a B/C analysis, the research team took results from the analyses documented in 

chapter 4, in combination with additional information on costs and other benefits of MR 

installations. 

The research team estimated MR installation costs based on various sources. A Transportation 

Research Board webinar showed a range of MR installations in Michigan for 2017 that was 

between $840,000 and $900,000 (Gillum 2017). According to another source, the installation 

cost for the MRs ranges between $250,000 and $465,000 in Texas (Melton and Shumard 2019). 

Finally, according to a 2010 FHWA technical summary (Rodegerdts, Scarbrough, and Bansen, 

2010), MR construction costs widely depends on the extent of modification to the location 

necessary for the conversion and the materials used in the construction. The cost estimates 

offered in 2010 by the FHWA report ranged from $50,000 up to $250,000. For the economic 

evaluation, the research team adopted the value of $300,000 in 2020 to represent a national 

average. 

For the benefit side, the research team assumed comparable maintenance costs for AWSC and 

TWSC intersections, unlike traditional roundabouts that have landscape in the center and splitter 

islands. Regarding the benefit of reduced congestion, this analysis used the average national 

average of congestion hourly cost per driver of $13.9, as can be extracted from a congestion 

scorecard recently reported by a private company (INRIX 2018). Simulation studies on 

AWSC-to-MR conversion suggest significant delay reductions for AWSC configurations, even 

when operations are near to their saturation levels (Zhang 2012). Assuming such an operation to 

be a conservative estimate for AWSC, but not for TWSC, the yearly benefit is a reduction of 

about 3 delay h per driver. When converting this delay estimate to yearly values, the research 

team made the following conservative assumptions: Because the simulation analyses are 

performed for peak hour conditions, it was assumed that only half of the drivers would 

experience any delay, and that the peak hour estimate represents 50 percent of the total delay of 

an average day.

Economic Effectiveness of MR Installation at TWSC 

The safety benefit of MR installation is derived from the estimated reductions in total crash 

frequency for TWSC conversions (table 25) A statistical life value of $11.6 million is the most 

current value used by U.S. DOT (Putnam and Coes 2021). The total yearly benefit (safety only) 

for MR installation at TWSC locations was estimated as $86,290 in 2020 dollars. In contrast, the 

assumed 2020 cost of construction was $300,000. For a useful life of 10 yr and no salvage value 

at the end of that period, the B/C ratio for the MR installation is estimated as 2.88. 
40 

Economic Effectiveness of MR Installation at AWSC 

The safety benefit of AWSC conversion was estimated as the monetary value of reduction in 

MV_Total crash frequencies for AWSC conversions (per table 28). The total yearly benefits 

(safety and operational combined) for MR installation at AWSC locations was estimated as 

$402,423 in 2020 dollars, whereas the safety-only benefit was $86,074, similar to the benefit of 

TWSC intersections. Using the same 2020 cost of construction estimate ($300,000) and a useful 

life of 10 yr with no salvage value at the end of that period, the B/C ratio for the MR installation 

at AWSC locations is estimated as 13.41 when both safety and operations benefits are 

considered. The B/C ratio was 2.87 when only safety benefits were considered. 

CHAPTER SUMMARY

This chapter describes the assumptions and sources to perform an estimation of the economic 

effectiveness of implementing MRs at locations with either AWSC or TWSC configurations. 

B/C ratios are developed for the two types of conversions. B/C ratios were found to be larger 

than 1.0 (2.88 and 2.87 for AWSC and TWSC conversions, respectively, when only safety 

benefits were considered, and 13.41 for AWSC when operational benefits were also considered), 

indicating more benefits than costs for these implementations. Chapter 6 provides a summary 

and conclusions of the project.
41 

CHAPTER 6. SUMMARY AND CONCLUSIONS

The objective of this study was to perform rigorous safety-effectiveness evaluations of MR 

installations at TWSC and AWSC locations. The study database included three States and had a

longitudinal design, including comparison sites. This data structure allowed ITS-CG evaluations, 

as well as a more general panel evaluation. The analyses were performed using FB models, as 

well as generalized linear mixed binomial models. 

The safety data for these evaluations were compiled for locations of known MR installations 

around the United States where the date of installation and prior intersection condition could be 

known. A set of suitable comparison locations was identified to include allowing the analyses to 

control for extraneous variables. Additionally, geometric features were collected for analysis, as 

well as AADT where available. Model-based AADT imputation was performed at locations 

where AADT was partially available and enough for that task. After data filtering and assembly, 

the study included 15 MR locations from Washington, 6 from Michigan, and 6 from Maryland. 

Crash data from 2003 through 2019 were available from Washington, crash data from Michigan 

represented 2013 through 2019, and crash data from Maryland represented 2015 through 2019. 

The FB analyses were conducted on separated State data subsets on ITS-CG evaluations for 

TWSC-to-MR conversions. Statistically significant crash reductions ranging from 31 up to 

42 percent for various types of crashes were estimated from these analyses. A statistically 

significant reduction of 39 percent in MV_Total crashes at AWSC conversions was found from 

an additional analysis using the complete database, now including additional locations that could 

not be used in the ITS-CG evaluations. 

Finally, the research team performed an economic analysis of MR conversions from either 

AWSC or TWSC. B/C ratios were found to be larger than 1.0 (1.33 for both AWSC and TWSC 

conversions when only safety benefits were considered, and 8.47 for AWSC when operational 

benefits were also considered). These results indicate economic feasibility of MR installations.

43 

ACKNOWLEDGMENTS

The authors gratefully acknowledge the contributions from State DOTs that provided data and 

valuable feedback for completion of this study. The authors specifically acknowledge the 

following PFS and non-PFS States for providing data that were used or considered in the study: 

Washington, Maryland, Michigan, Nevada, Minnesota, and North Carolina DOTs and the 

Kentucky Transportation Cabinet. 

The original maps in figure 1 and figure 4 are the copyrighted property of Google® EarthTM and 

can be accessed from https://earth.google.com/web/ (Google 2019). They were modified to show 

the locations of study sites as callouts and yellow pins. 

45 

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