Reducing Roadway Departure Crashes 

at Horizontal Curve Sections on 

Two-Lane Rural Highways 

http://safety.fhwa .dot.gov 
REDUCING ROADWAY DEPARTURE CRASHES AT HORIZONTAL CURVE 

SECTIONS ON TWO-LANE RURAL HIGHWAYS 

FINAL REPORT 

FHWA PUBLICATION NUMBER: FHWA-SA-19-005 

JANUARY 2019 
Notice 

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

Transportation 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 

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i 
I I I 

TECHNICAL DOCUMENTATION PAGE 

1. Report No. 

FHWA-SA-19-005 

2. Government 

Accession No. 

3. Recipient's Catalog No. 

4. Title and Subtitle 

Reducing Roadway Departure Crashes at Horizontal Curve Sections on Two-lane Rural 

Highways 

5. Report Date 

January 2019 

6. Performing Organization 

Code 

7. Author(s) 

Donnell, Eric; Porter, Richard J.; Li, Lingyu, Hamilton, Ian; Himes, Scott C.; Wood, 

Jonathan 

8. Performing Organization 

Report No. 

9. Performing Organization Name and Address 

Thomas D. Larson Pennsylvania Transportation Institute 

Pennsylvania State University

201 Transportation Research Building 

University Park, PA 16802 

 VHB 

 940 Main Campus Dr.

 Suite 500 

 Raleigh, NC 27606 

 

 

10. Work Unit No. 

11. Contract or Grant No. 

DTFH61-12-C-00032 

12. Sponsoring Agency Name and Address 

U.S. Department of Transportation 

Federal Highway Administration 

1200 New Jersey Avenue, SE 

Washington, DC 20590 

13. Type of Report and Period 

Safety Evaluation 

14. Sponsoring Agency Code: 

FHWA-HSA 

15. Supplementary Notes. 

The Federal Highway Administration (Office of Safety) managed this study. The technical representative was Joseph 

Cheung. 

16. Abstract 

While several proven safety countermeasures and strategies exist to mitigate roadway departure crashes on 

horizontal curve sections of two-lane rural highways, there are several countermeasures or strategies that have yet 

to be proven via a rigorous safety evaluation. The purpose of this research was to identify several of these 

strategies or countermeasures, and to perform a statistical assessment of their safety effectiveness. This report 

details the following three evaluations: (1) observational before-after study of curve ahead warning pavement 

markings, (2) cross-sectional study of delineators on guiderail along horizontal curves, and (3) cross-sectional 

study of the safety effects of geometric design consistency. The findings from these evaluations indicate that the 

expected number of roadway departure crashes are associated with the horizontal curve radius, radii of adjacent 

horizontal curves, and the tangent lengths between curves. Further, the expected number of roadway departure 

crashes is associated with side friction demand on horizontal curves. Guiderail with delineators are expected to 

reduce total, fatal plus injury, run-off-road (ROR), and nighttime crashes along horizontal curves that are four 

degrees or sharper. Horizontal curve warning pavement markings are associated with fewer expected total, fatal 

plus injury, ROR, nighttime, nighttime ROR, and nighttime fatal plus injury crashes on two-lane rural highways. 

17. Key Words: Traffic safety, horizontal curves, roadway 

departure, design consistency, delineators, guiderail, curve 

warning pavement markings, empirical Bayes, propensity scores 

18. Distribution Statement 

No restrictions. 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 

Unclassified 

21. No. of Pages: 

170 

22. Price 

N/A 

Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized 

ii 
SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2 

ft2 square feet 0.093 square meters m2 

yd2 square yard 0.836 square meters m2 

ac acres 0.405 hectares ha 

mi

2 

square miles 2.59 square kilometers km2 

VOLUME 

fl oz fluid ounces 29.57 milliliters ml 

gal gallons 3.785 liters l 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 l shall be shown in m3 

MASS oz ounces 28.35 grams g 

lb pounds 0.454 kilograms kg 

T shorttons(20001b) 0.907 megagrams (or "metric ton") Mg (or "t") 

OF Fahrenheit 

TEMPERATURE (exact degrees) 

5 (F-32)/9 Celsius oc or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux Ix 

fl foot-lamberts 3.426 candelalm2 cd/m2 

FORCE and PRESSURE or STRESS 

lbf poundforce 4 .45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA 

mm2 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac 

km2 square kilometers 0.386 square miles m, ·2 

VOLUME 

ml milliliters 0.034 fluid ounces fl oz 

l liters 0.264 gallons gal m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz 

kg kilograms 2.202 pounds lb 

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

•c Celsius 

TEMPERATURE (exact degrees) 

1.8C+32 Fahrenheit OF 

ILLUMINATION 

IX IUX 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-lamberts fl 

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2 

'SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003) 

iii 
TABLE OF CONTENTS 

CHAPTER 1. INTRODUCTION ....................................................................................................1 

Integrating Speed Management within Roadway Departure, Intersection, and Pedestrian and 

State of the Practice for Shoulder and Center Line Rumble Strip Implementation on NonDevelopment of Crash Modification Factors for the Application of the SafetyEdgeSM 

Effectiveness of Traffic Signs, Pavement Markings, and Other Roadway Treatments in 

Effectiveness of Traffic Signs, Pavement Markings, and Other Roadway Treatments in 

Applications of Speed-Activated Traffic Control Devices on Horizontal Curves and Other 

CHAPTER 4. ROADWAY DEPARTURE SAFETY EFFECTS OF DESIGN CONSISTENCY 

Strategic Approach to Roadway Departure Crashes ................................................................... 2 

Objectives of Current Study ........................................................................................................ 4 

Organization of the Report .......................................................................................................... 4 

CHAPTER 2. LITERATURE REVIEW .........................................................................................5 

Low-Cost Treatments for Horizontal Curve Safety .................................................................... 5 

Other FHWA Roadway Departure Safety Management Resources ........................................... 6 

Factors Influencing Speed and Safety on Rural and Suburban Roads .................................... 6 

Bicyclist Safety ........................................................................................................................ 7 

Freeway Facilities .................................................................................................................... 7 

Treatment on Two-Lane Rural Roads ..................................................................................... 7 

Other Research Related to Roadway Departure Crashes ........................................................ 8 

Reducing Operating Speeds on Horizontal Curves ............................................................ 8 

Reducing Roadway Departure Crashes on Horizontal Curves ......................................... 14 

Effects of Roadway and Roadside Features on Safety and Driver Speed Choice ............ 18 

Locations ........................................................................................................................... 25 

Summary of Literature Review Findings .................................................................................. 28 

CHAPTER 3. OVERVIEW OF SAFETY EVALUATIONS ........................................................30 

........................................................................................................................................................32 

Research Objective .................................................................................................................... 32 

Methodology ............................................................................................................................. 32 

Data ........................................................................................................................................... 33 

Road Segments ...................................................................................................................... 33 

Roadway Data ................................................................................................................... 34 

Crash Data ............................................................................................................................. 39 

Results and Discussion .............................................................................................................. 40 

iv 
Design Consistency Effects ................................................................................................... 45 

CHAPTER 5. QUANTIFYING RELATIONSHIPS BETWEEN EXPECTED FREQUENCIES 

OF ROADWAY DEPARTURE CRASHES AND HORIZONTAL ALIGNMENT USING THE 

CHAPTER 6. SAFETY EVALUATION OF GUIDERAIL AND CURVE DELINEATORS ON 

Other Effects .......................................................................................................................... 46 

A Closer Look at Estimated Radius Effects .......................................................................... 47 

Conclusions and Recommendations .......................................................................................... 48 

SHRP2 ROADWAY INFORMATION DATABASE ..................................................................50 

Overview of Data Source .......................................................................................................... 50 

Data Collection .......................................................................................................................... 51 

Horizontal Curve Collection ............................................................................................. 51 

Tangent Collection ............................................................................................................ 52 

Crash Data ............................................................................................................................. 52 

AADT Collection .............................................................................................................. 54 

Summary ........................................................................................................................... 54 

Data Assessment for Modeling ................................................................................................. 57 

Radius Functional Form ........................................................................................................ 58 

Results and Discussion .............................................................................................................. 60 

Radius and Normal Crown Effects ................................................................................... 67 

Friction Demand Effects ................................................................................................... 69 

Design Consistency Effects .............................................................................................. 72 

Other Effects ..................................................................................................................... 73 

Comparison with Utah/Washington Analysis ................................................................... 74 

Conclusions and Recommendations .......................................................................................... 78 

HORIZONTAL CURVE ALONG TWO-LANE RURAL HIGHWAYS .....................................81 

Background ............................................................................................................................... 81 

Delineators ............................................................................................................................. 81 

Guardrail ................................................................................................................................ 83 

Study Sites and Roadway inventory data .................................................................................. 85 

Description of Data ................................................................................................................... 86 

Methodology ............................................................................................................................. 95 

Propensity Scores-Potential Outcomes Framework .............................................................. 95 

v 
Counterfactual Framework .................................................................................................... 96 

Estimating Propensity Scores ................................................................................................ 98 

Matching Algorithms............................................................................................................. 98 

Matching Considerations ....................................................................................................... 99 

Estimating Treatment Effect ................................................................................................ 100 

Analysis Results ...................................................................................................................... 101 

Safety Effects of Guiderail with Delineators (GD) ............................................................. 101 

Safety Effect of Guiderail (G only) ..................................................................................... 111 

Disaggregate Analysis ......................................................................................................... 124 

Summary of Results............................................................................................................. 127 

Discussion and Conclusions .................................................................................................... 129 

CHAPTER 7. HORIZONTAL CURVE WARNING PAVEMENT MARKINGS .....................131 

Background ............................................................................................................................. 131 

Analysis Method ..................................................................................................................... 132 

SPF Estimation .................................................................................................................... 134 

Data ......................................................................................................................................... 134 

Results ..................................................................................................................................... 135 

Conclusions ............................................................................................................................. 147 

CHAPTER 8. CONCLUSIONS AND FUTURE RESEARCH NEEDS ....................................149 

ACKNOWLEDGEMENTS .........................................................................................................151 

REFERENCES ............................................................................................................................153 

vi 
LIST OF FIGURES 

Figure 1. Photo. Optical speed bars (Katz 2004). ........................................................................... 9 

Figure 2. Photo. Horizontal curve warning and speed advisory pavement marking (Retting and 

Figure 3. Illustration. Horizontal curve warning and speed advisory pavement marking (Retting 

Figure 6. Graph. Recommended CMFs using lane width and shoulder width combinations (Gross 

Figure 9. Graphic. Illustration of analysis curve, upstream elements, and downstream elements. 

Figure 16. Graph. CMF for changing radius (normal crown versus superelevated versus HSM 

Figure 18. Equation. CMF for a combination of posted speed limit, superelevation rate, and 

Figure 22. Equation. CMF calculation based on increase in posted speed limit and increase in 

Farmer 1998). ................................................................................................................................ 10 

and Farmer 1998). ......................................................................................................................... 11 

Figure 4. Photo. On-pavement marking (Hallmark et al. 2012). .................................................. 13 

Figure 5. Photo. Chevrons with retroreflective posts (Hallmark et al. 2012). .............................. 14 

et al. 2009). ................................................................................................................................... 20 

Figure 7. Photo. DSDS sign. (Hallmark et al. 2013). ................................................................... 26 

Figure 8. Equation. General form of NB regression model. ......................................................... 32 

....................................................................................................................................................... 34 

Figure 10. Chart. Comparison of alternative superelevation estimates. ....................................... 36 

Figure 11. Equation. Side friction demand. .................................................................................. 45 

Figure 12. Graph. HSM and model derived CMFs for horizontal curve radius. .......................... 47 

Figure 13. Graph. Observed to predicted crash ratio by radius. ................................................... 59 

Figure 14. Graph. Comparison of CMFs by functional form. ...................................................... 60 

Figure 15. Equation. CMF for horizontal curvature. .................................................................... 68 

CMF). ............................................................................................................................................ 68 

Figure 17. Graph. Comparison of CMFs by curves included in analysis. .................................... 69 

curve radius. .................................................................................................................................. 70 

Figure 19. Graph. CMF for total crashes by speed versus HSM. ................................................. 70 

Figure 20. Graph. CMF for RwD-KABCO crashes from North Carolina radius. ........................ 71 

Figure 21. Equation. CMF for increasing radius to 1,000 ft. ........................................................ 72 

radius. ............................................................................................................................................ 72 

Figure 23. Equation. CMF calculation for increased speed with no change in radius. ................ 72 

Figure 24. Graph. Box plot of AADT in the delineator with guiderail dataset. ........................... 90 

Figure 25. Graph. Box plot of degree of curvature in the delineator with guiderail dataset.* ..... 90 

vii 
Figure 26. Graph. Box plot of curve advisory speed in the delineator with guiderail dataset. ..... 91 

Figure 27. Graph. Box plot of posted speed limit in the delineator with guiderail dataset. ......... 91 

Figure 28. Graph. Box plot of AADT in the guiderail dataset. .................................................... 94 

Figure 29. Graph. Box plot of degree of curvature in the guiderail dataset.* .............................. 94 

Figure 30. Graph. Box plot of posted speed limit in the guiderail dataset. .................................. 95 

Figure 31. Graph. Box plot of curve advisory speed in guiderail dataset. .................................... 95 

Figure 32. Equation. Counterfactual framework. ......................................................................... 96 

Figure 33. Equation. Estimate of average treatment effect of treated. ......................................... 97 

Figure 34. Equation. Estimate of average treatment of untreated. ................................................ 97 

Figure 35. Equation. Propensity score logit model. ...................................................................... 98 

Figure 36. Equation. NB regression model. ................................................................................ 100 

Figure 37. Equation. Variance of NB distribution. ..................................................................... 100 

Figure 38. Graph. Propensity score distributions before matching (GD). .................................. 107 

Figure 39. Graph. Propensity score distributions after matching (GD). ..................................... 107 

Figure 40. Graph. ASMD before and after matching (GD). ....................................................... 108 

Figure 41. Graph. Propensity score distributions before matching (G only). ............................. 118 

Figure 42. Graph. Propensity score distributions after matching (G only). ................................ 118 

Figure 43. Graph. ASMD before and after matching (G only). .................................................. 120 

Figure 44. Photo. Horizontal curve warning pavement marking (Retting and Farmer, 1998). .. 131 

Figure 45. Equation. Expected number of crashes in the before period EB analysis. ................ 133 

Figure 46. Equation. EB weighting factor. ................................................................................. 133 

Figure 47. Equation. Index of effectiveness. .............................................................................. 134 

Figure 48. Equation. Standard deviation of index of effectiveness. ........................................... 134 

Figure 49. Equation. SPF. ........................................................................................................... 134 

viii 
LIST OF TABLES 

Table 1. Roadway departure strategies to support crash emphasis areas. ...................................... 2 

Table 2. Crash reduction estimates for proven roadway departure countermeasure treatments or 

Table 8. Descriptive statistics for design consistency and roadway variables in Washington State 

Table 9. Descriptive statistics for roadway departure crash counts in Washington State (2008-

strategies (FHWA 2018). ................................................................................................................ 3 

Table 3. CMFs for traffic engineering treatments. ....................................................................... 17 

Table 4. Select horizontal curve CMFs......................................................................................... 18 

Table 5. CMFs for roadway and roadside features. ...................................................................... 19 

Table 6. Select rural two-lane highway CMFs. ............................................................................ 22 

Table 7. Operating speed models. ................................................................................................. 24 

and Utah. ....................................................................................................................................... 38 

2012). ............................................................................................................................................ 39 

Table 10. Descriptive statistics for roadway departure crash counts in Utah (2008-2014). ......... 40 

Table 11. RwD-KABCO model estimation results for Alternative 1 (1/R). ................................ 41 

Table 12. RwD-KABCO model estimation results for Alternative 2 (with fd). ........................... 42 

Table 13. RwD-KABC model estimation results for Alternative 1 (with 1/R). ........................... 43 

Table 14. RwD-KABC model estimation results for Alternative 2 (with fd). .............................. 44 

Table 15. Collision codes for roadway departure crashes. ........................................................... 53 

Table 16. Roadway departure crash summary statistics for Indiana (2008-2013). ...................... 53 

Table 17. Roadway departure crash summary statistics for Pennsylvania (2008-2013). ............. 53 

Table 18. Indiana horizontal curve summary statistics. ................................................................ 55 

Table 19. Pennsylvania horizontal curve summary statistics. ...................................................... 56 

Table 20. Design consistency analysis for Pennsylvania. ............................................................. 58 

Table 21. Design consistency analysis for Indiana. ...................................................................... 58 

Table 22. Correlation among predictors of interest. ..................................................................... 61 

Table 23. RwD-KABCO for inverse radius and normal crown. ................................................... 62 

Table 24. RwD-KABC for inverse radius and normal crown. ..................................................... 63 

Table 25. RwD-KABCO for friction demand. .............................................................................. 64 

Table 26. RwD-KABC for friction demand. ................................................................................ 65 

Table 27. RwD models for design consistency. ............................................................................ 66 

Table 28. RwD-KABC for design consistency. ............................................................................ 67 

ix 
Table 29. Results comparison. ...................................................................................................... 77 

Table 30. Summary of reference and treatment study sites. ......................................................... 86 

Table 31. Study sites of the safety evaluations. ............................................................................ 86 

Table 32. Descriptive statistics of continuous variables in the guiderail with treatment delineators 

dataset. .......................................................................................................................................... 88 

Table 33. Descriptive statistics of continuous variables with reference delineators dataset. ....... 88 

Table 34. Descriptive statistics of categorical variables with treatment delineators dataset. ....... 89 

Table 35. Descriptive statistics of categorical variables with reference delineators dataset. ....... 89 

Table 36. Descriptive statistics of continuous variables in the guiderail only dataset. ................ 92 

Table 37. Descriptive statistics of categorical variables in the guiderail only dataset. ................ 93 

Table 38. Potential outcomes framework. .................................................................................... 97 

Table 39. Statistical output of the cross-sectional NB regression for total crashes (GD). ......... 101 

Table 40. Statistical output of the cross-sectional NB regression for fatal and injury (GD). ..... 102 

Table 41. Statistical output of the cross-sectional NB regression for ROR crash (GD). ............ 102 

Table 42. Statistical output of the cross-sectional NB regression for nighttime crash (GD). ..... 103 

Table 43. Propensity score matching configuration (GD). ......................................................... 103 

Table 44. Statistical output of propensity score model estimation (GD). ................................... 104 

Table 45. Summary of variables before matching (GD). ............................................................ 105 

Table 46. Summary of variables after matching (GD). .............................................................. 106 

Table 47. Mean and ASMD before and after matching (GD). ................................................... 108 

Table 48. Statistical output of NB model estimation after matching (GD). ............................... 109 

Table 49. Statistical output of NB model estimation for fatal and injury after matching (GD). 110 

Table 50. Statistical output of NB model estimation for ROR crash after matching (GD). ....... 110 

Table 51. Statistical output of NB model estimation for nighttime crash after matching (GD). 111 

Table 52. CMF estimates of guiderail with delineators (GD). ................................................... 111 

Table 53. Statistical output of the cross-sectional NB regression for total crashes (G only). .... 112 

Table 54. Statistical output of the cross-sectional NB regression for fatal and injury (G only). 112 

Table 55. Statistical output of the cross-sectional NB regression for ROR crash (G only). ...... 114 

Table 56. Statistical output of the cross-sectional NB regression for nighttime crash (G only). 115 

Table 57. Propensity score matching configuration (G only). .................................................... 116 

Table 58. Statistical output of propensity score model estimation (G only). ............................. 116 

x 
Table 59. Summary of variables before matching (G only). ...................................................... 117 

Table 64. Statistical output of NB model estimation for fatal and injury after matching (G only). 

Table 66. Statistical output of NB model estimation for nighttime crash after matching (G only). 

Table 70. Disaggregate analysis for CMF estimates using a degree of curvature greater than or 

Table 71. Disaggregate analysis for CMF estimates using a degree of curvature less than four, for 

Table 74. Disaggregate analysis for CMF estimates degree of curvature greater than or equal to 

Table 75. Disaggregate analysis for CMF estimates for degree of curvature less than four, for 

Table 77. Summary of CMF estimates for all sites of guiderail with delineator, guiderail only, 

Table 78. Summary of CMF estimates for degree of curvature greater than or equal to four of 

Table 79. Summary of CMF estimates for degree of curvature less than four of guiderail with 

Table 60. Summary of variables after matching (G only). ......................................................... 117 

Table 61. Mean and ASMD difference before and after matching (G only). ............................. 119 

Table 62. Mean and ASMD covariates before and after matching (G only). ............................. 119 

Table 63. Statistical output of NB model estimation for total crashes after matching (G only). 121 

..................................................................................................................................................... 122 

Table 65. Statistical output of NB model estimation for ROR crash after matching (G only). .. 123 

..................................................................................................................................................... 124 

Table 67. CMF estimates of guiderail with delineators (G only). .............................................. 124 

Table 68. Summary mean for each degree of curvature category (GD). .................................... 125 

Table 69. Summary standard deviation for each degree of curvature category (GD). ............... 125 

equal to four, for crash type using propensity score matching (GD). ......................................... 126 

crash type using propensity score matching (GD). ..................................................................... 126 

Table 72. Summary mean for each degree of curvature category (G only). ............................... 126 

Table 73. Summary standard deviation for each degree of curvature category (G only). .......... 127 

four, for crash types using propensity score matching (G only). ................................................ 127 

crash types using propensity score matching (G only). .............................................................. 127 

Table 76. Expected CMFs of the countermeasures for each crash type. .................................... 128 

and delineators. ........................................................................................................................... 128 

guiderail with delineator, guiderail only, and delineators. .......................................................... 128 

delineator, guiderail only, and delineators. ................................................................................. 128 

Table 80. Variable descriptions. ................................................................................................. 136 

Table 81. Descriptive statistics for reference group (21, 902 curves). ....................................... 137 

Table 82. Descriptive statistics for reference group indicator variables (21, 902 curves). ......... 137 

xi 
Table 83. Descriptive statistics for treated group in the before period (263 curves). ................. 138 

Table 84. Descriptive statistics for treated group in the before period indicator variables (263 

Table 86. Descriptive statistics for treated group in the after period indicator variables (263 

curves). ........................................................................................................................................ 138 

Table 85. Descriptive statistics for treated group in the after period (263 curves). .................... 139 

curves). ........................................................................................................................................ 139 

Table 87. Estimated SPFs for total crashes.* .............................................................................. 140 

Table 88. Estimated SPFs for fatal and injury crashes.* ............................................................ 141 

Table 89. Estimated SPFs for ROR crashes.* ............................................................................. 142 

Table 90. Estimated SPFs for nighttime crashes.* ..................................................................... 143 

Table 91. Estimated SPFs for nighttime ROR crashes.* ............................................................ 144 

Table 92. Estimated SPFs for nighttime fatal and injury crashes.* ............................................ 145 

Table 93. EB analysis results. ..................................................................................................... 146 

Table 94. EB analysis results cont. ............................................................................................. 147 

xii 
LIST OF ABBREVIATIONS 

AADT average annual daily traffic 

AASHTO American Association of State Highway and Traffic Officials 

ANOVA univariate analyses of variance 

ASMD absolute standardized mean difference 

ATE average treatment effect 

ATT average treatment effect for the treated 

ATU average treatment effect for the untreated 

CMF crash modification factor 

CRR-M modified change radius rate 

CTRE Center for Transportation Research and Education 

DSDS dynamic speed display signs 

DSFS dynamic speed feedback signs 

EB empirical Bayes 

FB full Bayes method 

FHWA Federal Highway Administration 

FI fatal and injury crashes 

GD guiderail with delineators 

GIS geographic information systems 

G only guiderail only 

HFST high friction surface treatment 

HPMS Highway Performance Monitoring System 

HSIS Highway Safety Information System 

HSM Highway Safety Manual 

IHSDM Interactive Highway Safety Design Model 

IRI International Roughness Index 

K-S Kolmogorov-Smirnov test 

LED light-emitting diode 

MLE maximum likelihood estimation 

MUTCD Manual on Uniform Traffic Control Devices 

NB negative binomial 

xiii 
NDS Naturalistic Driving Study

NN nearest neighbor matching 

PC point of curvature

PDO property damage only

PennDOT Pennsylvania Department of Transportation 

PMD post-mounted delineator 

PT point of tangency 

QQ quantile-quantile 

RwD-A incapacitating injury roadway departure crashes 

RwD-B non-incapacitating injury 

RwD-C possible injury 

RwD-K fatal roadway departure crashes 

RwD-KABC fatal-plus-injury roadway departure crashes 

RwD-KABCO total (i.e., all severities) roadway departure crashes 

RwD-O no injury

RID Roadway Information Database 

ROR run-off-the-road 

RTR ratio of tangent length to radius 

SB standardized bias 

SDCWS sequential dynamic curve warning system 

SHRP Strategic Highway Research Program 

SPF safety performance function

SVROR single-vehicle run-off-road

TDR traffic data recorder

UDOT Utah Department of Transportation

VIEDA Variable Introduction Exploratory Data Analysis 

xiv 
CHAPTER 1. INTRODUCTION 

Roadway departure crashes are defined as those in which a vehicle “crosses an edge line or a 

centerline, or otherwise leaves the traveled way.” (FHWA 2014) In 2016, there were 

approximately 7.28 million police-reported crashes, resulting in 37,461 fatalities and more than 

3.1 million injuries, on highways and streets in the United States. (NHTSA 2018) The Federal 

Highway Administration (FHWA) estimates that more than 50 percent of traffic fatalities result 

from roadway departure crashes. Vehicles are more likely to depart the roadway at locations 

where the alignment changes. Research by Glennon et al. (1985) estimated that the average crash 

rate along horizontal curve sections of two-lane rural highways is three times higher than on 

tangent roadway sections, and that the severity of roadway departure crashes along horizontal 

curves is greater than the severity of roadway departure crashes along tangent roadway sections. 

A Guide for Reducing Collisions on Horizontal Curves further illustrates the problem associated 

with roadway departure crashes along horizontal curves. (Torbic et al. 2004) The authors’ found 

that nearly 25 percent of people who die each year on the Nation’s roadways are killed in vehicle 

crashes at curves. About 75 percent of all fatal crashes occur in rural areas, and approximately 76 

percent of the curve-related fatal crashes involve single-vehicles leaving the roadway and 

striking trees, utility poles, rocks, or other fixed objects or overturning. FHWA (2014) estimates 

that more than 70 percent of fatal roadway departure crashes involve overturning vehicles, 

opposite direction crashes, or collisions with trees. Among the risk factors for these three crash 

types are the following: 

 Overturn Crashes: 76 percent are in rural areas, 72 percent occur on roads with posted 

speed limits of 50 mph or higher, and 43 percent are reported on horizontal curve 

sections. 

 Opposite Direction Crashes: 83 percent are on undivided roads, 68 percent occur in 

rural areas, 68 percent occur on roadways with posted limits of 50 mph or higher, and 

32 percent are reported on horizontal curve sections. 

 Roadside Trees and Shrubs: 68 percent are in rural areas, 52 percent occur on roads 

with posted speed limits of 50 mph or higher, and 46 percent are reported on horizontal 

curve sections. 

Collectively, these statistics indicate that roadway departure crashes along horizontal curves on 

two-lane rural highways are a significant safety issue. To mitigate this crash type, safety 

countermeasures aim to keep vehicles on the roadway, reduce the likelihood of a crash when 

vehicles leave the roadway or cross into opposing travel lanes, or reduce the severity of a 

roadway departure crash. 

1 
Emphasis Area Strategies to Keep 

Vehicles on Road 

Strategies to Reduce 

Potential for Crashes 

Strategies to Minimize 

Crash Severity 

Overturn Crashes 







Curve delineation 

Friction treatments in 

curves 

Edge line or shoulder 

rumble strips 







Safety EdgeSM 

Maintain clear zones 

Traversable roadside 

slopes 

 Barriers to shield 

fixed objects and 

slopes 

Opposite Direction 

Crashes 





Centerline rumble 

strips 

Friction treatments in 

curves 

 Increase separation 

between opposing 

lanes in curves 

 Median barriers 

Roadside Trees and 

Shrubs 







Edge line and 

shoulder rumble 

strips 

Curve delineation 

Friction treatments in 

curves 

 Clear zone 

improvements and 

maintenance, 

particularly along the 

outside of horizontal 

curves 

 Barriers to shield 

fixed objectives 

STRATEGIC APPROACH TO ROADWAY DEPARTURE CRASHES 

In 2013, the FHWA developed a roadway departure strategic plan (FHWA 2017a). The areas of 

emphasis for the plan are overturning crashes, opposite direction crashes, and collisions with 

roadside trees and shrubs. Table 1 provides a list of strategies that are recommended to support 

the safety emphasis areas. 

Table 1. Roadway departure strategies to support crash emphasis areas. 

In order to address horizontal curve locations with roadway departure crash issues, the FHWA 

Office of Safety has identified several proven countermeasures. A number of these 

countermeasures are infrastructure-based treatments or strategies that are intended to reduce 

serious injuries and fatalities on horizontal curves of two-lane rural highways. The treatments or 

strategies include the following: 

 Roadside Design Improvements Along Horizontal Curves. This strategy includes 

several treatments that are designed to either provide for a safe recovery in the event of 

a roadway departure, or to reduce the impact severity in a roadway departure crash. 

The treatments include: (1) an unobstructed, traversable clear zone, (2) slope flattening, 

(3) adding or widening shoulders, (4) cable barrier, (5) guardrail, and (6) concrete 

barrier. 

 Enhanced Delineation and Friction for Horizontal Curves. This strategy includes 

several treatments to keep vehicles on the roadway, including enhanced delineation, 

such as pavement markings, post-mounted delineators, larger and more visible signs, 

and dynamic or flashing sequential signs. Additionally, restoring pavement friction and 

applying the high-friction surface treatment (HFST) is identified as a roadway surface 

roadway departure safety treatment. 

2 
 Longitudinal Rumble Strips and Stripes. Installation of rumble strips along the edge 

line, shoulder, or centerline is a strategy to keep the vehicle on the roadway. 

 Safety EdgeSM. This treatment produces a pavement edge of approximately 30 degrees 

relative to the pavement cross-slope during the paving process, enabling vehicles that 

depart the roadway to more effectively recover. 

Among the safety countermeasures or strategies identified above, several have crash reduction 

benefits that are documented based on empirical research. These benefits are shown in table 2. 

Table 2. Crash reduction estimates for proven roadway departure countermeasure 

treatments or strategies (FHWA 2018). 

Treatment of Strategy Crash Type Crash Reduction 

Estimate (percent) Source 

Increase clear zone from 

3.3 to 16.7 ft Total crashes 22 FHWA (2017b) 

Increase clear zone from 

16.7 to 30 ft Total crashes 44 FHWA (2017b) 

Install chevron signs Fatal and injury crashes 16 FHWA (2017c) 

Install chevron signs Lane departure crashes at night 25 FHWA (2017c) 

HFST Total crashes 24 FHWA (2017c) 

HFST Wet road crashes 52 FHWA (2017c) 

Shoulder rumble strips Single-vehicle run-off road 

crashes 15 FHWA (2017d) 

Shoulder rumble strips Single-vehicle run-off-road fatal 

and injury crashes 29 FHWA (2017d) 

Centerline rumble strips Total crashes 9 FHWA (2017d) 

Centerline rumble strips Fatal and injury crashes 12 FHWA (2017d) 

Centerline rumble strips 

Total target (head-on and 

opposite direction sideswipe) 

crashes 

30 FHWA (2017d) 

Centerline rumble strips Fatal and injury target crashes 44 FHWA (2017d) 

Safety EdgeSM Fatal and injury crashes 11 FHWA (2017e) 

3 
OBJECTIVES OF CURRENT STUDY 

While several proven safety countermeasures and strategies exist to mitigate roadway departure 

crashes on horizontal curve sections of two-lane rural highways, there are several 

countermeasures or strategies that have yet to be proven via a rigorous safety evaluation. The 

purpose of this research was to identify several of these strategies or countermeasures, and to 

perform a statistical assessment of their safety effectiveness. This report details the following 

three evaluations: 

 Observational before-after study of curve ahead warning pavement markings. 

 Cross-sectional study of delineators on guiderail along horizontal curves. 

 Cross-sectional study of the safety effects of geometric design consistency. 

ORGANIZATION OF THE REPORT 

The remainder of the report is organized into six subsequent chapters: 

 Chapter 2 is a synthesis of literature related to the safety and operational effects of 

treatments intended to mitigate roadway departure crashes along horizontal curves of 

two-lane rural highways. 

 Chapter 3 provides an overview of the three safety evaluations that were completed in the 

present study. 

 Chapters 4 and 5 summarize two cross-sectional studies that evaluated the relationship 

between geometric design consistency and safety on two-lane rural highways. 

 Chapter 6 describes a propensity scores-potential outcomes evaluation of delineators on 

guiderail along horizontal curves. 

 Chapter 7 describes the methodology and results of a horizontal curve ahead warning 

pavement markings evaluation. 

 Chapter 8 contains the overall findings from the research effort, as well as 

recommendations for future research. 

4 
CHAPTER 2. LITERATURE REVIEW 

This chapter of the report is organized into three sections. The first describes two publications 

that were published as part of the current study, both of which include countermeasures that are 

intended to mitigate roadway departure crashes along horizontal curves of two-lane rural 

highways. The second section summarizes several Federal Highway Administration (FHWA) 

publications that were developed as part of other research efforts, but also provides information 

that supports the roadway departure program. The third section is a summary of existing research 

describing the relationship between traffic control devices and other roadway features, and their 

association with driver speed choice and safety. 

LOW-COST TREATMENTS FOR HORIZONTAL CURVE SAFETY 

In addition to the evaluations described in Chapters 4, 5, and 6 of this report, two other 

publications were developed by the research team to support the FHWA roadway departure 

program. FHWA provided the overall framework for the Low-Cost Treatments for Horizontal 

Curve Safety 2016 report, which presents summary information for countermeasures that 

transportation agencies may consider applying on two-lane highways experiencing roadway 

departure crashes along horizontal curves. (Albin et al. 2016) For each countermeasure, the 

following information is documented (if available): 

 General description of the countermeasure. 

 Design elements or materials to use when deploying the countermeasure. 

 How to apply the countermeasure. 

 The effectiveness of the countermeasure. 

 The relative cost (low, medium, or high) of the countermeasure. 

The guide offers two strategies for implementing safety countermeasures, including the sitespecific approach and the systemic approach. The countermeasures are organized into several 

basic categories, including: pavement markings, signs, pavement surface countermeasures, 

roadside improvements, and treatments along curves within at-grade intersections. In FHWA’s 

Low-Cost Treatments for Horizontal Curve Safety 2016 there are eight case study examples of 

safety improvement programs and countermeasures included in the guide. (Albin et al. 2016) 

One sign application with potential safety improvements along horizontal curves on two-lane 

rural highways was the Sequential Dynamic Curve Warning System (SDCWS). The SDCWS is a 

series of horizontal curve chevron signs with solar-powered flashing lights embedded in the 

signs. The flashing lights can be simultaneous or a sequence of lights moving toward or away 

from the driver. A driving simulator study at the University of Utah’s Utah Traffic Lab identified 

several SDCWS settings that impacted operating speeds and lane keeping behavior along a 

simulated version of a two-lane rural highway in Pennsylvania with 17 horizontal curves. Sixtyeight participants were recruited to participate in the study to examine effective flash rates, speed 

activation thresholds, and flashing sequences when deploying SDCWS along horizontal curves 

on two-lane rural highways. Based on the outcome of the simulator study, an outdoor field study 

was completed at three sites in Wisconsin to further assess the potentially effective flash rates 

5 
and flashing patterns identified in the simulator study. Four different conditions were studied in 

the field, including a speed-activation threshold that was either 5 or 10 mph above the curve 

advisory speed, two different flash rates (simultaneous and away from the driver), and two 

different flashing patterns (three flashes per second and one flash per second). 

Based on the indoor driving simulator study, a flashing sequence away from the driver at a low 

flash rate (1 Hz), or a simultaneous flashing pattern with a high flash rate produced the greatest 

speed reduction effects on drivers approaching horizontal curves at higher speeds on two-lane 

rural highways. The flashing sequence away from the driver also produced the lowest probability 

of a lane departure event. These two conditions were then evaluated in the field at three locations 

in Wisconsin. In addition to the flashing pattern and flash rate, the speed-activation threshold 

was also varied in the field to either 5mph or 10mph above the curve advisory speeds. 

The field study found that, among the conditions tested, the simultaneous flashing pattern, set to 

activate at a rate of 3 Hz when a driver approached the curve more than 5 mph above the curve 

advisory speed, produced the most desirable outcome based on the speed metrics considered in 

the present study. However, a flashing pattern away from the driver with a flashing rate of 1 Hz 

set to activate when approach speeds exceed the curve advisory speed by any amount appears to 

be another effective setting when the present field study results are assessed in conjunction with 

findings from the driving simulator study and a previous study by Smadi et al. (2015) 

OTHER FHWA ROADWAY DEPARTURE SAFETY MANAGEMENT RESOURCES 

In addition to the two reports identified above, FHWA published four other reports that support 

the roadway departure program. Each of these is summarized below. 

Factors Influencing Speed and Safety on Rural and Suburban Roads 

This informational report summarizes a variety of treatments that to support speed management 

along horizontal curves and tangents of rural and suburban roads. (Boodlal et al. 2015) Included 

is a detailed review of design features and current practices associated with methods to manage 

operating speeds. The remainder of the report describes three studies undertaken to evaluate the: 

(1) operational effects of the high-friction surface treatment on horizontal curves of two-lane 

rural highways, (2) operational effects of optical speed bars on rural and suburban roads, and (3) 

safety effects of lane and shoulder width combinations on two-lane rural highways. 

The main findings from this research effort are as follows: 

 No consistent differences in various driver speed metrics could be found after a highfriction surface was applied to horizontal curves on two-lane rural highways. Friction 

tests confirmed that the friction supply increased considerably at the locations treated 

with the high-friction surface treatment, and that the friction levels remained high for a 

period one year after the treatment was applied – no additional friction measurements 

were recorded. 

 A before-after field study of the optical speed bar treatment showed that this treatment 

was not associated with statistically significant changes in driver operating speeds. 

6 
 The results of the lane and shoulder with safety evaluation showed complex interactions 

between expected crash frequency and cross-section dimensions for rural, two-lane roads. 

For narrower total paved widths, the safety evaluation found that the optimal lane width 

appears to be 12 ft. As total paved widths become larger, there is not necessarily a safety 

benefit from using a wider lane, and in some cases, using a narrower lane appears to 

result in lower expected crash frequencies. 

Integrating Speed Management within Roadway Departure, Intersection, and Pedestrian 

and Bicyclist Safety 

Neuner et al. (2016) identifies current practices related to speed management within the FHWA 

key focus areas of roadway departure, intersection, and pedestrian safety. In the roadway 

departure focus area, national trends identified overturn or rollover crashes, opposite direction 

crashes, and collisions involving trees as the most harmful event in 75 percent of roadway 

departure crashes. Other trend analyses found that rural areas, roadways with posted speed limits 

equal to 50 mph or greater, horizontal curves, and adverse weather conditions are locations in 

which roadway departure crashes frequently occur. Several strategies were identified to mitigate 

roadway departure crashes, including the following: 

 Establishing appropriate speed limits. 

 Deploy pavement marking, rumble strip, static or dynamic horizontal curve signing, highfriction surface treatment, Safety EdgeSM, or pavement widening safety countermeasures. 

 Deploy safety countermeasures to reduce crash severity, such as removing, shielding, or 

delineating fixed objects; increasing the clear zone width, or flattening side slopes. 

State of the Practice for Shoulder and Center Line Rumble Strip Implementation on NonFreeway Facilities 

Himes et al. (2017) summarized the current state-of-the-practice related to centerline and 

shoulder rumble strip use and developed a decision support guide to inform transportation 

agencies on the application of centerline and shoulder rumble strip installation. The literature 

review details research related to rumble strip design, noise and vibration characteristics 

associated with the designs, impacts on bicyclists and motorcyclists, pavement condition 

impacts, pavement marking (rumble stripe) visibility, and the operational and safety 

effectiveness of centerline and shoulder rumble strips. The report also describes agency practices 

regarding rumble strip installation criteria and patterns. 

Development of Crash Modification Factors for the Application of the SafetyEdgeSM 

Treatment on Two-Lane Rural Roads 

The SafetyEdgeSM is a low-cost treatment that is constructed using a paver attachment, enabling 

the pavement edge to be paved and compacted at a 30-degree angle. When this treatment is 

implemented, it permits a vehicle that has departed the paved roadway to make a smooth return 

to the travel lane after one or more wheels have left the pavement. An observational before-after 

7 
safety evaluation developed crash modification factors for this treatment. A multi-State study 

found that drop-off related crashes are expected to decrease by approximately 34.5 percent; runoff-road related crashes are expected to decrease by approximately 21 percent; opposite direction 

crashes are expected to decrease by approximately 18.7 percent; and fatal plus injury crashes are 

expected to decrease by approximately 10.8 percent after implementing the SafetyEdgeSM on 

two-lane rural highways. (FHWA n.d.) A benefit-cost analysis found that the treatment can be 

applied cost-effectively. 

Other Research Related to Roadway Departure Crashes 

In addition to the research reports that are noted above, all of which support the FHWA roadway 

departure program, there is a large body of published research that also identifies methods or 

practices to manage vehicle operating speeds or safety along horizontal curves sections of twolane rural highways. This literature is summarized below, and organized into sections that are 

related to treatments that are associated with operating speeds on horizontal curves, treatments 

that are related to roadway departure crashes on horizontal curves, and the relationship between 

roadway and roadside design features on operating speeds and safety. 

Effectiveness of Traffic Signs, Pavement Markings, and Other Roadway Treatments in 

Reducing Operating Speeds on Horizontal Curves 

Katz (2004) investigated the potential for peripheral transverse (i.e., optical speed bars) 

pavement markings to reduce vehicle operating speeds approaching and within horizontal curves. 

Each curve treatment had a slightly different pattern, which is illustrated in figure 1. The pattern 

spacing was based on a desired speed reduction from the approach tangent to the advisory speed 

for the horizontal curve. The speed bars were applied such that they intruded into the travel lane, 

perpendicular to the edge of the travel lane. Three curves were selected for inclusion in the study 

based on complaints that speeding had been cited as a safety problem. One curve was located on 

an interstate (in New York) and two were on two-lane rural highways (in Mississippi and Texas). 

No comparison site locations were included in the study. Vehicle operating speed data were 

collected before the peripheral transverse lines were installed, immediately after installation, and 

six months after installation. Speeds were collected at a location upstream of the curve and just 

prior to the point of curvature (PC) of the curve to permit speed reductions (i.e., rates of 

deceleration) to be computed. 

The results indicated that deployment of the optical speed bar markings resulted in a statistically 

significant decrease in vehicle speeds at the curve speed measurement locations for both the New 

York and Mississippi test locations in the immediate and extended after periods. No statistically 

significant change in speed was found at the upstream data collection location for the New York 

or Mississippi horizontal curves for either after period. The Texas curve had a statistically 

significant decrease in speed at the upstream location but no statistical difference in either after 

period from the before period at the curve. Speed changes at the curve locations in the after 

period (adjusted using the differences in the upstream speeds) included a 9.5-mph decrease for 

the immediate after period and 4-mph decrease in the extended period for the New York curve, 

8 
4.6-mph decrease for the immediate after period and 1.8-mph decrease in the extended after 

period for the Mississippi curve, and a 13.6-mph increase for the immediate after period and 6.6-

mph increase in the extended after period for the Texas curve. 

Figure 1. Photo. Optical speed bars (Katz 2004). 

The impacts of optical speed bars on vehicle operating speeds along horizontal curves were also 

investigated by Gates et al. (2008) The speed bars were 18 inches long by 12 inches wide and 

were painted perpendicular to the edge line of a single horizontal curve on Interstate 43 in 

Milwaukee, Wisconsin. Speeds were measured two months before, one week after, and six 

months after the speed bars were painted. Speeds were collected 850 ft upstream of the PC (350 

ft upstream of the start of speed bars), 100 ft downstream of the PC, and 700 ft downstream of 

the PC (200 ft downstream from the end of the speed bars). No comparison locations were 

included in the observational before-after study. 

The findings from the field study indicated that mean speed reductions of 0.05 to 5 mph were 

statistically significant when comparing the before to the immediate and long-term after periods. 

The findings also indicated that light condition may influence vehicle operating speeds, but the 

authors indicated that the magnitude was too small to be practically significant. 

Speed bars that were 24 inches long, 8 inches wide, and had two bars spaced 8 inches apart 

(making the marked area 24 inches by 24 inches) were spaced every 100-150 ft and were 

analyzed along horizontal curves in Arizona by Latoski (2009) in an observational before-after 

study. No comparison locations were included in the analysis. Curve operating speed data were 

collected before, immediately after, and three months after installation of the optical speed bars. 

Vehicle speeds were collected at a location approximately three quarters of a mi downstream of 

the terminal end of the speed bars for one week at each time period. Speeds were not collected at 

any other locations. 

The findings indicated that the mean speeds and 85th-percentile speeds in the after periods, for 

both weekdays and weekends, had statistically significant reductions (at the 99-percent 

significance level). The reductions in speed were the greatest at nighttime (with reductions of up 

to 5.5 mph) and the lowest during the daytime (as low as 1.3-mph reduction). 

The operational effectiveness of zig-zag pavement markings at roadway crossings with multi-use 

paths was analyzed by Dougald (2010). The analysis involved a 45-mi-long multi-use path in 

Virginia with over 70 crossings, two of which received the treatment. The zig-zag pattern was 

9 
intended to indicate to motorists on a two-lane highway that they were approaching a multi-use 

path crossing. To estimate the effectiveness of the zig-zag markings, speed data were collected 

before installation, one week after installation, six months after installation, and one year after 

installation at both treatment locations. Speed data were also collected at two similar locations 

that did not receive the treatment – these data were collected at the same time as the treatment 

site data were collected. Motorist attitudinal changes were also assessed through surveys. These 

surveys targeted motorists, pedestrians, and bicyclists that were familiar with the zig-zag 

markings. 

The findings indicated that the markings increased the awareness of motorists approaching the 

crossings as evidenced by reduced mean operating speeds. These findings were based on simple 

comparisons of the descriptive statistics of the before and after data and no statistical analysis 

was provided. Also, the survey results indicated that awareness was increased and a higher 

tendency to yield resulted after the markings were installed. Only descriptive statistics were used 

for the survey results. An interesting finding from the survey was that motorists had limited 

understanding of the markings and, that motorists, pedestrians, and cyclists were confused as to 

who had the right-of-way at the crossing locations. 

Another pavement marking scheme that has been used in an attempt to reduce vehicle operating 

speeds approaching horizontal curves on two-lane rural highways has been an on-pavement 

“sign” with a curve ahead warning arrow and speed advisory. An example of this treatment is 

shown in figure 2 and figure 3. 

Figure 2. Photo. Horizontal curve warning and speed advisory pavement marking (Retting 

and Farmer 1998). 

10 
T 

+•=--::... 

~ I'"' . ew,-

.,,.,.. SI.ow 

"" t __ 

--- Figure 3. Illustration. Horizontal curve warning and speed advisory pavement marking 

(Retting and Farmer 1998). 

A speed evaluation of this treatment by Retting and Farmer (1998) involved an arrow curved to 

the left with the word “slow” panted before it at a location approximately 220 ft before the PC of 

a left-hand horizontal curve. A single curve on a two-lane suburban highway in northern Virginia 

with paved roadway width of 20 ft received the treatment. A separate curve on the same highway 

was used as a control. The posted speed limit was 35 mph, while an advisory speed of 15 mph 

was posted approximately 500 ft before the curve with the treatment. 

Vehicle operating speeds were collected at locations 90 ft prior to the PC as well as at a location 

650 ft prior to the PC of the treated curve. Speeds at the control curve were collected 100 ft prior 

to the PC. Speeds were collected five months prior to installation of the pavement markings and 

two weeks after installation. The results indicated a statistically significant decrease in the mean 

speed at the location 90 ft prior to the PC, based on a comparison of the curve with the treatment 

and the control curve in the before and after periods. The magnitude of the reduction was 7 

percent (2.4 mph). 

A driving simulator was recently used to evaluate the effectiveness of several low-cost 

treatments on operating speeds for the following two scenarios: 1) two-lane rural horizontal 

curves at night and 2) traffic calming measures for rural towns during the day (Molino et al., 

2010). All drivers partcipating in the study viewed all of the treatment conditions. All drivers 

were between the ages of 18 and 88 years old (mean age of 57.6 years old). There was an even 

distribution between male and female drivers. A total of 36 drivers participated in the study. 

Treatments that were analyzed for the rural town traffic calming included parked cars along both 

sides of the road, chicanes, and bulb-outs (curb and gutter or painted types). Treatments for rural 

horizontal curves included post-mounted delineators (PMDs), light-emitting diode (LED) 

enhanced PMDs, and edge lines added were there were none previously. 

11 
Operating speed and acceleration profiles were collected on the approach to and at the curve 

treatment locations along rural town road segments. The results of the analysis for the rural town 

traffic calming treatments indicated that chicanes reduced driver speeds by 6 mph, parked cars 

on both sides of the road reduced driver speeds by 4 mph, and bulb-outs reduced driver speeds 

by 1 mph. Results for the horizontal curves indicated that the LED enhanced PMDs were 

associated with a 9-mph reduction in driver speeds, PMDs were associated with 7-mph 

reductions in driver speeds, and edge lines were associated with driver speed reductions of 2 

mph. All speed reductions were statistically significant. 

A simulator was also used by Charlton (2007) to analyze the effects of warning signs on driver 

speed traversing horizontal curves in New Zealand. The warning sign scenarios included: 1) 

advance curve warning signs and advisory speeds, 2) advance curve warning signs followed by 

chevron sight boards, 3) advance curve warning signs followed by chevrons through the curve, 

and 4) advance curve warning signs followed by chevron sight boards and then chevrons through 

the curve. Data from 48 drivers were collected, imbalanced between male and female (17 men, 

31 women). The findings indicated that the advance warning signs with advisory speeds were 

ineffective. Further, the results indicated that chevrons produced statistically significant 

reductions in driver operating speeds. No estimates were reported for the magnitude of the speed 

reductions. 

The effect of chevron signs on vehicle operating speeds and lateral vehicle lane position was 

investigated by Ré et al. (2010) Two horizontal curves on two-lane rural highways with 10 ft 

lanes in Texas were used in the evaluation. Both had posted speed limits of 70 mph during the 

day and 65 mph at night, one had an advisory speed of 45 mph, and the other location had an 

advisory speed of 50 mph. For the treatment, chevron signs were placed every 160 ft between the 

PC and point of tangency (PT) of the curves. Two sign configurations were tested -- the first 

included chevron signs mounted on non-reflective posts, and the second included chevron signs 

mounted on retroreflective posts. 

Speed and lane position data were collected at the PC, midcurve, and 1 mi upstream of the curve 

(both directions) for each treatment location. The upstream data collection locations were used as 

control locations. Data were collected before installation of the signs, 10 days after installation of 

the signs (with retroreflective posts), and 10 days after installation of chevron signs without 

retroreflective posts. Prior to the analysis, the data were separated into daytime and nighttime 

observations for each observation period. 

The results of the lane position analysis indicated that both types of signs were associated with 

vehicles moving away from the centerline by approximately 15 inches from the before period to 

the after period. Additionally, lower variance in lane position was found after the chevron signs 

were deployed at the treatment sites. The speed data analysis indicated that both types of 

chevrons produced statistically significant reductions in speeds at the PC and midcurve locations. 

The magnitude of the reductions in mean operating speeds due to the chevrons was 1.28 mph 

(for non-retroreflective posts) and 2.2 mph (with retroreflective posts). The 85th-percentile 

operating speeds were also reduced by 1.3 mph (for non-retroreflective posts) and 2.2 mph (with 

12 
retroreflective posts). There was not a statistically significant change in the speed variance for 

any location resulting from implementation of the chevron signs. 

The operating speed effects of adding retroreflective posts to existing chevrons and on-pavement 

curve markings were also evaluated by Hallmark et al. (2012) This study added retroreflective 

posts to existing chevrons at four horizontal curves and on-pavement curve markings at two 

horizontal curves (a total of six horizontal curves) on two-lane rural highways in Iowa. 

Examples of these treatments are shown in figure 4 and figure 5. No comparison locations were 

used in the evaluation. 

Speed data at each of the treatment locations were collected one month before installation, one 

month after installation, and 12 months after installation of the treatments. Vehicle speeds were 

collected at the PC, midcurve, and PT for each of the locations. The results indicated that both 

the added retroreflective posts and on-pavement curve markings were moderately effective in 

reducing both the mean and 85th-percentile operating speeds both the short-term and long-term. 

Some of the sites showed little to no change in operating speeds while the majority had 

statistically significant decreases in the percentage of passenger cars exceeding the speed limit 

by more than 10 mph (up to 50-percent reduction during the day and 41-percent reduction at 

night). 

Figure 4. Photo. On-pavement marking (Hallmark et al. 2012). 

13 
Figure 5. Photo. Chevrons with retroreflective posts (Hallmark et al. 2012). 

Effectiveness of Traffic Signs, Pavement Markings, and Other Roadway Treatments in 

Reducing Roadway Departure Crashes on Horizontal Curves 

Table 3 is a summary of the crash modification factors (CMFs) that have been reported in the 

American Association of State Highway and Traffic Officials (AASHTO) Highway Safety 

Manual (2010) for treatments that may be applied to horizontal curves on two-lane rural 

highways. These treatments may be considered “proven” as a result of a rigorous, scientific 

safety evaluation. 

A study by Srinivasan et al. (2009) used an empirical Bayes (EB) observational before-after 

study to determine the safety effects of new chevrons, advance warning signs, horizontal arrows, 

and improved existing signs using fluorescent yellow sheeting at horizontal curves on two-lane 

rural roads. Data from Connecticut and Washington were used for the analysis. Horizontal 

curves in Connecticut received improved signing via improved existing or new signs with 

fluorescent yellow sheeting. The signs included chevrons, advance warning signs, and horizontal 

arrows. The road data included 89 treated horizontal curves and 334 horizontal curves in the 

reference group. Crash data for the years 1995-2006 were used for the analysis. The results 

indicated statistically significant decreases of 17.8 percent for all crashes, 17.7 percent for lane 

departure crashes, 35.3 percent for nighttime crashes, and 34.2 percent for nighttime lane 

departure crashes. CMFs for these estimates are shown in 

14 
table 4. 

Horizontal curve treatment locations in Washington involved only installation of chevrons where 

there were none previously or where the number of chevrons was increased. For the analysis, 

139 horizontal curves received the treatment and approximately 4,000 horizontal curves were 

included in the reference group. Crash data for the years 1993-2007, excluding 1997 and 1998, 

were used for the analysis. Analysis results indicated non-significant reductions in total and lane 

departure crashes and statistically significant reductions of 24.5 percent for nighttime crashes 

and 22.1 percent for nighttime lane departure crashes. CMF estimates from this study are shown 

in 

15 
table 4. 

Pratt et al. (2014) investigated the effects of pavement surface treatments on safety using data 

from Texas. A total of 501 horizontal curves on rural highways were included in the evaluation, 

101 curves were treated with the HFST, and 400 randomly chosen curves were identified as a 

reference group. Cross-sectional statistical models were estimated for total, wet-weather, run-offroad, and wet-weather run-off-road crashes for two-lane rural highways. The findings indicate 

that, as the skid number on a road increases, the expected crash frequency decreases. The 

benefits of a high skid resistance on a paved surface appeared to be more significant for wetweather run-off-road and wet-weather crashes, relative to total crashes. The authors’ developed a 

decision-support tool to estimate the potential safety benefit of installing high-friction surface 

treatments along horizontal curves. 

16 
Table 3. CMFs for traffic engineering treatments. 

CMF Area Type Facility Type Crash Type CMF (S.E.) Source 

Install combination 

horizontal alignment / 

advisory speed signs 

Rural 

/Suburban All types Injury crashes 0.87 (0.09) Elvik and Vaa (2004) 

Install combination 

horizontal alignment / 

advisory speed signs 

Rural 

/Suburban All types Non-injury 

crashes 0.71 (0.2) Elvik and Vaa 

(2004) 

Install changeable speed 

warning sign 

Rural 

/Suburban 

All types 

Arterials 

All types and 

severities 0.54 (0.2) Elvik and Vaa (2004) 

Place standard edge line 

markings Rural Two-lane Injury crashes 0.97 (0.04) Elvik and Vaa (2004) 

Place standard edge line 

markings Rural Two-lane Non-injury crashes 0.97 (0.1) Elvik and Vaa (2004) 

Place wide (8 in.) edge 

line markings Rural Two-lane Injury crashes 1.05 (0.08) Elvik and Vaa (2004) 

Place wide (8 in.) edge 

line markings Rural Two-lane Non-injury crashes 0.99 (0.2) Elvik and Vaa (2004) 

Place centerline pavement 

markings Rural Two-lane Injury crashes 0.99 (0.06) Elvik and Vaa (2004) 

Place centerline pavement 

markings Rural Two-lane Non-injury crashes 1.01 (0.05) Elvik and Vaa (2004) 

Place center and edge line 

markings Rural Two / Multilane Injury crashes 0.76 (0.1) Elvik and Vaa (2004) 

Install edge lines, 

centerlines, PMDs Rural Two / Multilane Injury crashes 0.55 (0.1) Elvik and Vaa (2004) 

Install snowplowable, 

permanent RPMs Rural Two-lane and freeways Nighttime crashes 

0.67–1.43 

(depending on 

AADT) 

Elvik and Vaa 

(2004) 

Install centerline rumble 

strips Rural Two-lane All crashes 0.86 (0.05) 0.91 (0.04) 

Persaud et al. 

(2003) & 

Torbic et al. 

(2009) 

Install centerline rumble 

strips Rural Two-lane Fatal and injury 0.88 (0.03) Torbic et al. (2009) 

Install centerline rumble 

strips Rural Two-lane All injury crashes 0.85 (0.08) Persaud et al. (2003) 

Install centerline rumble 

strips Rural Two-lane Head-on and sideswipe crashes 0.79 (0.1) Persaud et al. (2003) 

Install centerline rumble 

strips Rural Two-lane 

Head-on and 

sideswipe injury 

crashes 

0.75 (0.2) Persaud et al. 

(2003) 

Install automated speed 

enforcement All types All types Injury crashes 0.83 (0.01) AASHTO (2010) 

Install changeable speed 

warning signs for 

individual drivers 

All types All types All crashes 0.54 (0.2) Elvik and Vaa 

(2004) 

Note: SVROR = Single-vehicle run-off-road. 

17 
Table 4. Select horizontal curve CMFs. 

Treatment Roadway Type Crash 

Types 

Expected CMF 

(S.E.) 

Source 

Improve signs with 

fluorescent sheeting 

Two-lane rural 

highway All 0.822 (0.077) 

Srinivasan et al. 

(2009) 

Improve signs with 

fluorescent sheeting 

Two-lane rural 

highway 

Run-offroad 0.823 (0.084) 

Srinivasan et al. 

(2009) 

Improve signs with 

fluorescent sheeting 

Two-lane rural 

highway Nighttime 0.647 (0.105) 

Srinivasan et al. 

(2009) 

Improve signs with 

fluorescent sheeting 

Two-lane rural 

highway 

Nighttime 

run off road 0.658 (0.115) 

Srinivasan et al. 

(2009) 

Add chevrons Two-lane rural 

highway All 0.957 (0.089) 

Srinivasan et al. 

(2009) 

Add chevrons Two-lane rural 

highway 

Run off 

road 0.941 (0.088) 

Srinivasan et al. 

(2009) 

Add chevrons Two-lane rural 

highway Nighttime 0.755 (0.127) 

Srinivasan et al. 

(2009) 

Add chevrons Two-lane rural 

highway 

Nighttime 

run off road 0.779 (0.101) 

Srinivasan et al. 

(2009) 

Effects of Roadway and Roadside Features on Safety and Driver Speed Choice 

Safety 

Similar to the CMFs shown in table 3, the Highway Safety Manual (HSM) includes a collection 

of CMFs for roadway and roadside design features on rural two-lane highways that may 

influence roadway departure crashes. (AASHTO 2010) These are presented in table 5. The 

CMFs for lane width, shoulder width and type, and roadside hazard rating in table 5 apply to 

SVROR and opposite-direction crashes; however, algorithms are included in the HSM to convert 

these target crash CMFs to total crashes. 

Similarly, in the NCHRP Report 500 Volume 6, Neuman et al. (2003) provided suggested 

treatments for reducing run-off-road crashes. Treatments were separated into categories by the 

objective of the countermeasures. Categories included: 1) keeping vehicles from encroaching 

into the roadside, 2) minimizing the likelihood of crashing into an object or overturning if the 

vehicle travels beyond the edge of the shoulder, and 3) reduce the severity of the crash. Of the 

suggested countermeasures, there are tried (implemented and may even be accepted as standards, 

but there are no valid evaluations of their effectiveness), experimental (no properly designed 

studies have been done and have not been implemented and accepted as a standard), and proven 

(properly designed evaluations have found to be effective). 

18 
 

 

 

Suggested treatments for keeping vehicles from encroaching into the roadside, with ratings 

according to the report, included: 1) installing shoulder rumble strips [tried], 2) installing edge 

line rumble strips or edge line profile marking on road sections with narrow or no paved 

shoulders [experimental], 3) install center lane rumble strips [experimental], 4) provide enhanced 

shoulder or in-lane delineation and marking for sharp curves [proven, tried, and experimental], 5) 

provide improved highway geometry for horizontal curves [proven], 6) provide enhanced 

pavement markings [tried], 7) provide skid-resistant pavement surfaces [tried], 8) eliminate 

shoulder drop-offs [experimental], and 9) widen and/or pave shoulders [proven]. Treatments 

suggested to minimize the likelihood of crashing into an object or overturning if the vehicle 

travels beyond the edge of the shoulder included: 1) designing safer side slopes and ditches to 

prevent rollovers [proven], 2) remove or relocate objects in hazardous locations [proven], and 3) 

delineate trees or utility poles with retroreflective tape [experimental]. Finally, in order to reduce 

the severity of crashes, the report suggested either improving the design of roadside hardware 

[tried] or improving the design and application of barrier and attenuation systems [tried]. 

Table 5. CMFs for roadway and roadside features. 

CMF 

Area 

Type 

Facility 

Type Notes CMF (S.E.) 

Modify lane width Rural Two-lane None 

See figure 

13-1 from 

HSM 

Add or widen paved 

shoulder Rural Two-lane None 

See figure 

13-5 from 

HSM 

Increase the distance 

to roadside features Rural Two-lane 

and freeways 3.3 ft–16.7 ft offset 0.78 (0.02) 

Increase the distance 

to roadside features Rural Two-lane and freeways 16.7 ft–30.0 ft offset 0.56 (0.01) 

Reduce roadside 

hazard rating Rural Two-lane 

0.6869 0.0668 RHR  e CMF  0.4865 e 

See figure 

13-8 from 

HSM 

Modify horizontal 

curve radius Rural Two-lane 

80.2    (1.55 L ) c    (0.012 S )  R  CMF  1.55 L c 

See figure 

13-9 from 

HSM 

Improve 

superelevation Rural Two-lane Improve superelevation variance (SV) < 0.01 1.00 (N/A) 

Improve 

superelevation Rural Two-lane Improve SV 0.01 ≤ SV < 0.02 1.00 + 6 (SV – 0.01) 

Improve 

superelevation Rural Two-lane Improve SV > 0.02 1.06 + 3 (SV – 0.02) 

Change vertical grade Rural Two-lane Increase vertical grade by 1 % 

(SVROR) 1.04 (0.02) 

Gross et al. (2009) used a case-control study to analyze the effect of lane width – shoulder width 

combinations on crash frequency. Data for the study came from Pennsylvania and Washington 

States and consisted of two-lane rural road segments (intersections were not included in the 

19 
1.3 ,---------------------------

28-ft 1.2 r----.::..:....;..;............,...-rr,,..... ;-;-.;-;- . · -=--=• • -=--= • . --:-: ..--:-: •• ::-: • •=--------------

············· 

··········· IL 

:!: 

0 

-c 1.1 

QI 

"C 

C 

~ E 1 

0 

u 

QI 

D:: 

30-ft 

26-ft ----------------- • _ • _ . _ -------- 32-ft - • -- • - • _ ------. 30-ft Total Width 

28-ft Total Width 

34-ft ' - - - - • - 26-ft Total Width 

36-ft ~ ----- '\ ~ - - 32-ft Total Width 

36-ftTotal Width 

' ' 0.9 -t---------------------------

' -·-· - • - 34-ft Total Width 

0.8 --t---------.------..---------~------

9 10 11 12 13 

Lane Width (ft) 

analysis). Roadway and crash data covered five years for Pennsylvania and six years for 

Washington. Cases for this study were defined as road segments that had at least one reported 

crash during one analysis year. Controls were taken from road segments that did not have any 

reported crashes during the same year. The final recommended CMFs are shown in figure 6, and 

are relative to a 36-ft baseline with 12-ft travel lanes and 6-ft shoulders. As shown, 34 ft total 

width with either 11 or 12 ft lanes lower crash frequency compared to the baseline, 36 ft total 

width with 11 ft lanes are the same, and all other combinations result in higher crash frequencies 

than the baseline. 

Figure 6. Graph. Recommended CMFs using lane width and shoulder width combinations 

(Gross et al. 2009). 

Centerline rumble strips on two-lane rural roads were evaluated for potential safety benefits by 

Persaud et al. (2004) An EB before-after methodology was employed to analyze roadway and 

crash data from California, Colorado, Delaware, Maryland, Minnesota, Oregon, and Washington. 

A total of 98 treated curves along 210 mi of roadway were used. Highway Safety Information 

System (HSIS) crash and roadway inventory data were used to calibrate the safety performance 

functions (SPFs) which were used for the analysis. The results of the analysis indicated that, for 

all States combined, centerline rumble strips resulted in a statistically significant reduction in 

crashes. Results for individual States varied from significant reductions (all crash types in 

California, Colorado, and Washington, opposing direction in Colorado and Minnesota) to 

insignificant reductions, no change, or an insignificant increase in crashes for all other locations 

and crash types. Composite results indicated a 12-percent reduction in all crashes, 25-percent 

reduction in opposing direction crashes, 15-percent reduction in total crashes at night, and 8-

20 
percent reduction in total crashes during the day. CMFs from the composite results are shown in 

table 6. 

Park et al. (2012) estimated the safety effects of wider edge lines on two-lane rural roads using 

data from Kansas, Michigan, and Iowa were used for analysis. Analysis methods were 

determined based on the data available for each State and included an EB before-after study 

(Kansas), interrupted time series design and generalized linear segmented regression (Michigan), 

and cross-sectional analysis (Illinois). All road data were non-intersection, non-interchange 

segments and crash data were for non-winter months only. 

For Kansas, data included 2,801 road segments with crashes for the years 2001-2008. Treated 

segments received wider painted edge lines (change from 4 inches to 6 inches) during the years 

2005-2007. Of the total segments, 263 were used to develop the SPFs (i.e., reference group) and 

the rest received the treatment and were used for estimation of the safety effects of the wider 

edge lines. Results from the Kansas data analysis indicated a 17.5-percent reduction in total 

crashes, 28.6-percent reduction in daytime crashes, 30.2-percent reduction in single vehicle 

crashes, and 18.5-percent reduction in fixed object crashes. All of the reported crash reductions 

were statistically significant. CMFs from the estimates are shown in table 6. 

Data from Michigan included 253 total road segments with crash data for the years 2001-2009. 

For Michigan, edge lines for almost all State-owned roads changed from 4 inches to 6 inches in 

width in 2004. Therefore, almost no comparable roads for 2004-2009 were available for use as a 

comparison or reference group. Interrupted time series analysis of the data indicated a 

statistically significant reduction of 19.4 percent for all crashes, 18.8-percent reduction in 

nighttime crashes, and 18.7-percent reduction in single-vehicle crashes. 

Crash data for 6,531 road segments for the period 2001-2006 were used for the Illinois analysis. 

From these segments, 5,343 had 4 inch centerlines and 4 inch edge lines. The remaining 1,188 

segments had centerlines and edge lines that were 5 inches wide. Before the analysis was 

conducted, all animal-related crashes were removed from the data files (approximately 50 

percent of the crashes). The analysis results indicated a 30.1-percent reduction in total crashes, 

29.1-percent reduction in daytime crashes, 29.9-percent reduction in nighttime crashes, 37.0-

percent reduction in single-vehicle crashes, and 29.5-percent reduction in fixed object crashes. 

CMFs for these crash reductions are shown in table 6. 

21 
Table 6. Select rural two-lane highway CMFs. 

Treatment Crash Types CMF (S.E.) Significant 

Centerline rumble strips All 0.86 (0.03) Yes 

Centerline rumble strips Opposing 

direction 0.75 (0.087) Yes 

Centerline rumble strips Daytime 0.92 (0.048) Yes 

Centerline rumble strips Nighttime 0.85 (0.028) Yes 

Widen edge lines (from 4 in to 6 in) All 0.825 (0.028) Yes 

Widen edge lines (from 4 in to 6 in) Daytime 0.714 (0.043) Yes 

Widen edge lines (from 4 in to 6 in) Single vehicle 0.698 (0.044) Yes 

Widen edge lines (from 4 in to 6 in) Fixed object 0.815 (0.066) Yes 

Widen edge lines (from 4 in to 5 in) All 0.699 (0.043) Yes 

Widen edge lines (from 4 in to 5 in) Daytime 0.709 (0.052) Yes 

Widen edge lines (from 4 in to 5 in) Nighttime 0.701 (0.07) Yes 

Widen edge lines (from 4 in to 5 in) Single vehicle 0.630 (0.048) Yes 

Widen edge lines (from 4 in to 5 in) Fixed object 0.705 (0.064) Yes 

The impact of pavement conditions on crash severity at horizontal curves was investigated by 

Buddhavarapu et al. (2012) The study used crash data from an unspecified number of horizontal 

curves on two-lane highways in Texas, along with pavement condition (skid index, distress 

index, and International Roughness Index) and other roadway characteristic data for the analysis. 

The skid index was a measure of longitudinal surface friction. The distress index served as a 

measure of the extent of surface distress on the pavement (such as cracking, edge drop offs, 

rutting, and raveling). The International Roughness Index (IRI) is a measure of the roughness of 

longitudinal road profiles (higher IRI values indicate lower ride quality). Data for the years 

2006-2009 were used for statistical modeling. 

The modeling results indicated that the longitudinal skid index did not have a statistically 

significant effect on crash severity. Further, the results indicated that the distress index and IRI 

were both statistically significant with positive and negative signs, respectively. The 

interpretation of the parameter estimate for distress index was that the probability of a crash 

being more severe is greater at horizontal curves with less distressed pavements than at 

horizontal curves with more distressed pavement. Also, the interpretation of the parameter 

estimate for IRI is that as the ride quality decreases (less smooth ride), the probability of crashes 

being more severe is reduced. 

Speed Choice 

Edge line treatments were analyzed to determine the effect on operating speeds along rural twolane highways by Tsyganov et al. (2006) This study evaluated differences between road 

22 
segments with and without road edge lines in Texas. The research methods included laboratory 

testing of the effects of edge lines on vehicle speeds and lane position for various lane widths 

using t-tests. Findings indicated that edge lines were associated with speed increases of 

approximately 5 mph. However, this increase was not statistically significant. Findings for lane 

position indicated that there were no significant differences in the lane position of vehicles 

resulting from edge line applications. 

Other roadway and roadside features and characteristics along or near horizontal curves that have 

been researched for impacts on speed choice include curve radii, degree of curvature, grade, 

length of curve, posted speed limit, available sight distance, paved width, gravel shoulder width, 

clear zone, superelevation, land use, roadside hazard rating, crest vertical curves, curvature 

change rate, and deflection angle. Each of these features/characteristics have been used in 

regression models to predict operating speed parameters. Table 7 shows the operating speed 

parameter that was modeled (dependent variable) in the first column, the independent variables 

(the aformentioned features/characteristics) used in the respective models in the second column, 

the country the data used came from in the third column, and references are shown in the last 

column. 

23 
Table 7. Operating speed models. 

Model Predictors Country Reference

V85 Radius USA Taragin (1954)

V85 Radius USA Glennon et al. (1986) 

V85 Degree of curvature USA Islam & Seneviratne 

(1994) 

V85 Radius USA Voigt (1996) 

V85 Radius USA Passetti & Fambro (1999) 

V85 Radius, K, grade USA Fitzpatrick et al. (2000) 

V85 Degree of curvature, length of curve USA Ottesen & Krammes 

(2000) 

μV,Tangent, 

σV,Tangent 

Percentage trucks, posted speed, grade, 

residential land use, sight distance, 

intersections, paved width, gravel 

shoulder width, untreated shoulder 

width, clear zone, flat curve (radius > 

1,700 ft) 

USA Medina & Tarko (2005) 

μV,Curve, σV,Curve 

Sight distance, residential land use, 

superelevation USA Medina & Tarko (2005) 

Deceleration 

Rate 

Left-hand curve, radius, approach 

tangent length, curve length, roadside 

hazard rating 

USA Hu & Donnell (2010) 

Acceleration 

Rate 

Left-hand curve, radius, approach 

tangent length, curve length, roadside 

hazard rating, departure tangent length 

USA Hu & Donnell (2010) 

VPosted, μV, σV 

Access points, traffic volume, 

residential land use, industrial land use, 

curb and gutter, grade, on-street 

parking, median or turning lane, 

shoulder width, at-grade rail crossing, 

left-hand curve, crest curve, wooded 

adjacent land, percentage trucks 

USA Himes et al. (2011) 

V85,Tangent, 

V85,Curve 

Radius, length of curve, preceding 

tangent length India Jacob & Anjaneyulu (2012) 

μV, σV Radius, length of curve India Jacob & Anjaneyulu 

(2012) 

ΔV85 Radius, length of curve, tangent velocity India Jacob & Anjaneyulu 

(2012) 

V85 μV Germany Koeppel (1984) 

μV Pavement width, curvature change rate Germany Koeppel (1984) 

24 
V85 Radius, pavement width Germany Lippold (1997) 

V85 Curvature change rate, Venv Italy Cafiso et al (2008) 

Venv Pavement width, curvature change rate Italy Cafiso et al (2008) 

V85 

Radius, tangent length preceding the 

curve, deflection angle UK Bird & Hashim (2005) 

V85 Radius Greece Kanellaidis et al. (2000) 

V85 Curvature change rate Greece Xenakis (2008) 

Note: V85 = 85th percentile operating speed, μV = mean operating speed, σV, = speed variance, VPosted = 

posted speed limit, ΔV85 = the change in 85th percentile operating speed, and Venv = environmental speed. 

Applications of Speed-Activated Traffic Control Devices on Horizontal Curves and Other 

Locations 

Hallmark et al. (2013) analyzed the impacts of two different dynamic speed feedback signs 

(DSFS) on operating speeds of two lane rural roads at locations with sharp horizontal curves. An 

example of dynamic speed display signs (DSDS) is shown in figure 7. A total of 22 locations 

were used, with locations in Arizona, Florida, Iowa, Ohio, Oregon, Texas, and Washington. The 

sites were selected based on several criteria. First, the locations had to have a high number of 

crashes and no adverse geometric conditions (such as a major intersection or railroad crossing). 

The sites also had to have known speeding problems (defined as free flow vehicle speed 

distributions with the 85th percentile speed being 5 or more mph greater than the posted speed). 

The final locations (from a pool of sites that met all criteria) were selected based on the number 

and type of crashes, speeding conditions, and practicality of installing the signs at the locations. 

The two different DSFS that were evaluated were 1) a sign that displayed the vehicles speed (a 

speed display sign), and 2) a curve display sign. The curve display signs were programmed to 

only turn on and display a message if it detected a vehicle exceeding a set threshold. The speed 

display signs were also activated when they detected vehicles exceeding a set threshold. The 

speed display signs would then show the vehicles speed unless the vehicle was traveling at 20 or 

more mph greater than the speed limit, in which case it would display the actual posted speed. 

This was done to discourage drivers from using the speed display sign to test their speeds. 

Speed measurements were conducted at each site using pneumatic tubes and counters before 

installation as well as 1 month, 12 months, and 24 months after installation. Data collection 

lasted for 48 hours per site per period, when possible, and occurred on weekdays. The collection 

of speeds 24 months after installation was used to determine if the speed reductions lasted over 

time, if there were any to begin with. 

Summary statistics indicated that speed reductions due to the installation of the signs ranged 

from 0.6 mph to 6.5 mph in the mean speeds and 1 mph to 8 mph in the 85th-percentile speeds at 

the PC. At the midcurve, speed changes for the mean speed ranged from an increase of 3.7 mph 

to a decrease of 7.9 mph. The change in speeds for the 85th-percentile at the midcurve ranged 

from an increase of 3 mph to a decrease of 9 mph. It was also noted that problems encountered 

during the study period included one sign stopped functioning, software issues, wiring 

25 
replacement issues, needs to realign or replace solar panels, replacement of fuses, and issues with 

vandalism. 

Figure 7. Photo. DSDS sign. (Hallmark et al. 2013). 

A subsequent report by Hallmark et al. (2015) described a safety evaluation of the 22 DSDS sites 

that were included in the operating speed evaluation reported above. In this evaluation, 29 

control site locations (DSDS was not deployed at these curve locations) were included. Crash 

data were collected for up to 4 years before and up to 3 years after implementing the signs. The 

results showed that the CMFs for total crashes was 0.95 (with 0.01 standard error) for both 

directions of travel, and 0.93 (with 0.02 standard error) for the direction in which the sign was 

present. The single-vehicle crash CMF was 0.95 (with 0.01 standard error) for both directions of 

travel, and 0.95 (with 0.02 standard error) for the direction toward the sign. All the CMFs were 

statistically significant. 

An analysis of DSDS installed in several permanent locations, including two “sharp horizontal 

curves” was performed by Jeihani et al. (2012) The analysis looked at the impacts of DSDS on 

vehicle speeds. Speed data for this study were collected before installations of DSDS, 

approximately one week after installation, and approximately four months after installation. All 

speed data were collected using hand-held lidar guns at a control point upstream of the locations 

as well as adjacent to the location of the DSDS. The collection one week after installation was 

used to estimate the initial effect of DSDS. The collection four months after DSDS installation 

was used to determine how well the initial impacts on speeds were maintained. Summary 

statistics as well as simple linear regression were used to analyze the data. The summary 

statistics indicated that for the two sharp curves, in the speeds collected one week after the 

installation of the signs, the speed changes ranged from 3.5-mph reduction to an increase of 0.6 

mph for the mean auto speeds and 2.4-mph decrease to an increase of 1.3 mph for trucks mean 

26 
speeds. For the 85th-percentile speeds, the speed changes for passenger cars ranged from 4-mph 

decrease to no change and speeds changes for trucks ranged from 3-mph decrease to no change. 

Also, for the sharp horizontal curves, the speed data was disaggregated to develop regression 

models for cars and large trucks separately at each time point and location. Findings indicated 

that the car model for one of the curves at four months after installation was significantly 

different from the before period and one week after period and that vehicle speeds had been 

reduced. All other models for the sharp curves were not statistically different. 

Tribbett et al. (2000) analyzed the effectiveness of dynamic curve warning signs installed by 

CALTRANS at five separate locations along Interstate 5 in the Sacramento River Canyon. 

Interstate 5 in Sacramento River Canyon is a rural, winding, four-lane freeway (two lanes in each 

direction). The purpose of the signs was to provide advance notice to motorists of alignment 

changes and speed advisories. The signs were able to display both text and diagrammatic 

warnings. The signs were equipped with radar technology, so the speed of approaching vehicles 

could be identified. Based on the detected speeds, the display message would change. 

This project investigated the impacts of dynamic curve warning signs on crash frequency, erratic 

maneuvers, operating speeds, public acceptance, public response, and maintenance requirements. 

The operating speeds were collected at nine months prior to installation of the signs, shortly after 

installation, three months after installation, and eight months after installation. 

The immediate impacts of the dynamic curve warning signs on operating speeds were a 

reduction in speed. Over time, vehicle operating speeds increased until there was no statistically 

significant difference between the speeds before and after installation of the signs. The authors 

noted that curves on steep grades seemed to have the largest speed reductions. For the crash 

analysis, the findings indicated that crash frequency was reduced. Erratic behaviors were the 

same in the before and after periods for all but one of the locations. The one location with a 

difference in erratic behavior indicated that erratic behavior was reduced in the after period. 

Public response and acceptance were reported as favorable. There were reportedly few 

maintenance difficulties with the signs. 

DSDS were also analyzed for speed reductions in transitions zones of two-lane highways in 

Pennsylvania by Cruzado and Donnell (2009). Data were collected at 12 transition zones at 

locations before implementation, during the first week of DSDS use, and one week after the 

DSDS was removed from the transition zone. Speeds were collected at positions one-half mi 

prior to the DSDS, at the DSDS location, and 500 ft downstream of the DSDS location. Only the 

speeds of free-flow vehicles were included in the analysis. The results indicated average 

reductions in operating speeds of 6 mph while DSDS was in use. The results of the analysis of 

the data after the DSDS was removed indicated that the benefits faded after the DSDS devices 

were removed. 

Further research into DSDS impacts on operating speeds was undertaken by Ullman and Rose 

(2005). This project investigated the impacts of DSDS at various locations including a school 

speed zone, two sharp horizontal curves, and two approached to signalized intersections on highspeed roadways (all in Texas). Speed data for each location were collected before installation, 1-

3 weeks after installation, and 2-4 months after installation of the DSDS. Speed sensors were 

27 
placed at locations 2,000-3,000 ft upstream of the DSDS as well as near the DSDS. The authors’ 

reported that the DSDS could yield 1-to 4-mph reductions in the average and 85th-percentile 

operating speeds, but that over time the effect diminishes. 

SUMMARY OF LITERATURE REVIEW FINDINGS 

Existing literature on treatments and characteristics that have been found to impact safety, 

operating speed, or both, along rural horizontal curves or two-lane rural highways were 

identified and summarized in the literature review. 

Numerous treatments were evaluated by different researchers attempting to find treatments that 

reduce operating speeds at horizontal curves. Treatments that were found to have an impact on 

operating speeds included optical speed bars, curve arrows painted on the road with the word 

“slow” painted beneath them, post mounted delineators, LED enhanced post mounted 

delineators, adding edge lines, chevrons, and chevrons with retroreflective posts. Magnitudes of 

reductions attributed to the treatments ranged from being too small for practical purposes (0.05 

mph for optical speed bars) to 9 mph for LED enhanced post mounted delineators. 

Various traffic signs, pavement markings, and other treatments were also analyzed by 

researchers for their effectiveness in reducing crash frequency at horizontal curves. Treatments 

that were found to be effective included advisory speeds, chevrons, horizontal arrows, improving 

existing signs using fluorescent yellow sheeting, and sequential flashing beacons. CMFs from 

these treatments ranged from 0.524 for all crash types on freeways or expressways using a 

combination of chevron signs, curve warning signs, and flashing beacons, to 0.974 for all crash 

types when using chevron signs on freeways or expressways. For two-lane rural highways, 

CMFs ranged from 0.647 for nighttime crashes by improving existing signs with yellow 

fluorescent sheeting to 0.957 for all crash types when adding chevrons. 

Other roadway treatments that have been found to influence safety on two-lane rural highways 

include modifying lane width, modifying shoulder width, changing the lane width and shoulder 

in combination, pavement resurfacing, improving signing, repainting pavement markings, adding 

centerline rumble strips, and widening edge lines. CMFs for these treatments ranged from 0.64 

for wet weather crashes after pavement resurfacing project to 1.02 for all crash types for 

pavement resurfacing projects. 

Impacts of edge lines on operating speed were analyzed and found to be associated with a 5-mph 

reduction on operating speeds, but the decrease was not statistically significant. Other factors 

have been shown to influence operating speeds on two-lane highways, including curve radii, 

degree of curve, grade, length of horizontal curve, posted speed limit, available sight distance, 

paved roadway width, gravel shoulder width, clear zone, superelevation, land use, roadside 

hazard rating, crest curves, curvature change rate, and deflection angle. 

Research analyzing the impacts of various speed activated traffic control devices had varying 

results on operating speeds. DSDS were found to be associated with a statistically significant 

reduction in operating speeds of 1-4 mph in short term applications, but that the effect dissipated 

over time. 

28 
29 
CHAPTER 3. OVERVIEW OF SAFETY EVALUATIONS 

Based on the findings from the literature review, there are countermeasures being used to 

mitigate roadway departure crashes on two-lane rural highways that have not been extensively 

evaluated. The purpose of the remaining chapters of this report are to document efforts that were 

undertaken in the present study to evaluate three roadway treatment or design practices that focus 

on “preventing the vehicle from the leaving the roadway.” The three evaluations reported in 

subsequent chapters are as follows: 

 Chapters 4 and 5: Safety-Design Consistency Relationship – this evaluation was 

completed in two parts. The first part considered the safety effects of geometric design 

consistency using data from Utah and Washington. A subsequent update to the original 

evaluation used the Strategic Highway Research Program (SHRP) 2 Roadway Inventory 

Database (RID) to estimate cross-sectional models of expected crash frequency as a 

function of geometric design consistency variables. The study used high-accuracy 

roadway data collected explicitly for research purposes to consistency the effects of 

design decision-making on roadway departure crashes. 

 Chapter 6: Guiderail with Post-Mounted Delineators – this evaluation also used the 

SHRP 2 RID information to estimate the safety effects of guiderail with delineators, 

guiderail only, and delineators only placed along horizontal curves of two-lane rural 

highways. A propensity scores-potential outcomes framework was used to estimate crash 

modification factors (CMFs) for each treatment type on total crashes, fatal plus injury 

crashes, run-off-road crashes, and nighttime crashes. 

 Chapter 7: Horizontal Curve Pavement Marking Warnings – an observational before-after 

safety evaluation, using the empirical Bayes (EB) method, was completed to evaluate the 

safety performance of horizontal curve warning pavement markings on two-lane rural 

highways. CMFs for total, fatal plus injury, and run-off-road crashes were developed. 

30 
31 
CHAPTER 4. ROADWAY DEPARTURE SAFETY EFFECTS OF DESIGN 

CONSISTENCY 

Design consistency in the context of highway and street design refers to the conformance of 

highway geometry to driver expectancy. Various design practices are used to achieve design 

consistency. Highway designers, for example, seek to make design decisions that are consistent 

with previous experience (e.g., exit ramp on right). Designers also coordinate horizontal and 

vertical alignments. Several alternatives for quantifying design consistency on rural, two-lane 

highways were explored during previous Federal Highway Administration (FHWA)-sponsored 

research, including operating speed profiles and alignment indices. Operating speed profiles are 

currently used in the Design Consistency Module of the Interactive Highway Safety Design 

Model (IHSDM) to “flag” different levels of rural, two-lane design consistency. 

While design consistency has safety implications and is intuitively linked to roadway departure 

crashes, only a few studies have been published that sought to link measures of design 

consistency to safety (Fitzpatrick et al., 2000; Ng & Sayed, 2004; Wu et al., 2013). These studies 

offered a starting point for additional analysis, but did not necessarily provide generalizable 

safety findings related to roadway departure crashes on horizontal curves along rural, two-lane 

roads in the U.S. The availability of detailed horizontal and vertical alignment data in Utah and 

Washington offered the potential to explore this relationship at a greater level of breadth and 

depth. 

RESEARCH OBJECTIVE 

The objective of this research was to explore and estimate relationships between alternative 

measures of design consistency and the expected number of roadway departure crashes along 

horizontal curves on rural, two-lane, two-way roads. 

METHODOLOGY 

The relationships between alternative measures of design consistency and the expected number 

of roadway departure crashes were explored using a negative binomial (NB) regression modeling 

approach. Figure 8 illustrates the general form of an NB regression model of the expected 

number of roadway departure crashes along horizontal curve “i.” 

E(Yi) = μi = EXP(Xiβ+εi) 

Figure 8. Equation. General form of NB regression model. 

where: Yi = a random variable representing the number of roadway departure crashes along the th 

horizontal curve; 

E(Yi) = μi = expected number of roadway departure crashes along the th horizontal curve; 

Xi = a matrix of explanatory variables characterizing the th horizontal curve and 

associated with λi, including measures of design consistency; 

32 
β = a vector of parameters to be estimated that quantify the relationships between the 

explanatory variables and μi; and 

εi = a disturbance term, where EXP(εi) is gamma-distributed with a mean equal to one and 

variance equal to αi. 

NB regression models include the specification of “additional dispersion” (additional when 

compared to a Poisson model) that is common to crash data. Statistical road safety modelers 

often specify this additional dispersion as a dispersion parameter multiplied by the expected 

number of crashes squared (NB-2 model) and treat the dispersion parameter as fixed across 

observations. In the NB-2 model with a fixed dispersion parameter (α), the variance in the 

number of crashes is written as Var(Yi) = μi + αμi

2

. 

Model estimation for this analysis was carried out using maximum likelihood as implemented in 

Stata 14.0. 

DATA 

Road Segments 

The road segments used for analysis and modeling each consisted of one horizontal curve (i.e., 

each observation was defined by the observed number of roadway departure crashes occurring 

on an individual horizontal curve during the observation period). The analysis also considered 

characteristics of the “upstream” horizontal tangent, “upstream” horizontal curve, “downstream” 

horizontal tangent, and “downstream” horizontal curve. Figure 9 illustrates these elements of the 

analysis. The final database consisted of 249 observations from Washington State and 421 

observations from Utah. Data on the starting and ending locations of each horizontal curve and 

tangent was drawn from databases developed for a concurrent FHWA “Predisposing Factors” 

project. (Porter et al. 2018) 

33 
Upstream 

Tangent 

• 

Upstream •• 

Curve ••• 

•• •• •••••••••• 

Study 

Curve 

• • • • • •• I I If Downstream / 

• Curve i --

, Downstream ._ - -' 

Tangent 

Figure 9. Graphic. Illustration of analysis curve, upstream elements, and downstream 

elements. 

Roadway Data 

Traffic and roadway characteristics corresponding to each analysis curve as well as the upstream 

and downstream tangents and curves were also drawn from databases developed for the 

concurrent FHWA “Predisposing Factors” project. Some additional calculation steps specific to 

this analysis were needed in some cases. 

The elements in the FHWA “Predisposing Factors” project databases that were of interest to this 

analysis came from the Highway Safety Information System (HSIS) for Washington State and 

from the Utah Department of Transportation (UDOT) Data Portal for Utah, with two exceptions. 

UDOT staff members overseeing UDOT’s LiDAR data efforts did not post information on 

horizontal curvature and superelevation, knowing that data for these elements needed additional 

processing and quality control. The processing and quality control for horizontal curvature 

occurred primarily during the concurrent FHWA “Predisposing Factors” project. Processing and 

quality control for superelevation took place as part of this effort and is described in the 

following section of this report. 

Superelevation 

Cross slope measurements at a frequency of 0.1 mi were available in UDOT’s processed LiDAR 

data files. “Noise” in the cross slope measurements became immediately evident. Multiple 

measurements for a given curve, made in either in the same or opposite travel directions at 

locations all likely to be at “full superelevation,” were different. That said, cross slope 

measurements generally looked reasonable for given radius-posted speed limit combinations 

(information on design speed was not available). 

34 
Several alternative “simple” data smoothing approaches were tested to arrive at an estimate of 

design superelevation rate for each horizontal curve: 

1. Alternative 1: Take the averages of all cross-slope measurements made along the 

horizontal curve separately for both the increasing milepost and decreasing milepost 

directions. Select the average cross slope (i.e., increasing milepost or decreasing 

milepost) that is closest to the expected design superelevation rate assuming the posted 

speed limit equals the design speed, maximum superelevation equals 6 percent, and 

superelevation and side friction are distributed according Method 5 (with values drawn 

from the 2011 version of A Policy on Geometric Design of Highways and Streets). 

2. Alternative 2: Take the averages of all cross-slope measurements made between the onequarter point and three-quarter point of the horizontal curve separately for both the 

increasing milepost and decreasing milepost directions. Select the average cross slope 

(i.e., increasing milepost or decreasing milepost) that is closest to the expected design 

superelevation rate assuming the posted speed limit equals the design speed, maximum 

superelevation equals 6 percent, and superelevation and side friction are distributed 

according Method 5 (with values drawn from the 2011 version of A Policy on Geometric 

Design of Highways and Streets). 

3. Alternative 3: Take one overall average of all cross-slope measurements made between 

the one-quarter point and three-quarter point of the horizontal curve in both the 

increasing milepost and decreasing milepost directions. 

4. Alternative 4: Take one overall average of all cross-slope measurements made along the 

horizontal curve in both the increasing milepost and decreasing milepost directions. 

The four alternative superelevation rate estimates were then compared to the expected design 

superelevation rate assuming the posted speed limit equals the design speed, maximum 

superelevation equals 6 percent, and superelevation and side friction are distributed according 

Method 5 (with values drawn from the 2011 version of A Policy on Geometric Design of 

Highways and Streets). Figure 10 contains the results of these comparisons. The figure shows, 

for example, that for Alternative 1: 

 57.8 percent of the superelevation estimates are within 1 percent of the expected design 

superelevation rate. 

 77.5 percent of the superelevation estimates are within 1.5 percent of the expected design 

superelevation rate. 

 88.0 percent of the superelevation estimates are within 2 percent of the expected design 

superelevation rate 

 94.7 percent of the superelevation estimates are within 2.5 percent of the expected design 

superelevation rate. 

The research team concluded that Alternative 3 likely produces the most robust superelevation 

estimates since it utilizes measurements from both travel directions at locations where the cross 

slope is at full superelevation. Estimates from Alternative 3 were used during the statistical 

modeling. 

35 
-

Figure 10. Chart. Comparison of alternative superelevation estimates. 

Design Consistency Measures 

A Policy on Geometric Design of Highways and Streets (the Green Book) includes “General 

Controls for Horizontal Alignment,” some of which are related to achieving horizontal alignment 

design consistency: 

 “Sharp curves should not be introduced at the ends of long tangents.” 

 “Where sharp curvature is introduced, it should be approached, where practical, by a 

series of successively sharper curves.” 

This study seeks to further inform users of this guidance. Two alignment indices that capture 

these design principles for achieving a consistent alignment are explored: 

1. Ratio of tangent length to radius (RTR): the average length of the upstream and 

downstream tangents divided by the radius of the analysis curve. Estimated regression 

parameters corresponding to this variable are expected to be positive. Horizontal curves 

following longer tangents are expected to experience a larger number of roadway 

departure crashes than horizontal curves following shorter tangents. This effect is 

expected to be more pronounced for sharper curves, and less pronounced for flatter 

curves. 

2. Modified change radius rate (CRR-M): the average radius of the upstream and 

downstream horizontal curves divided by the radius of the analysis curve. Estimated 

regression parameters corresponding to this variable are also expected to be positive. 

Horizontal curves following flatter curves are expected to experience a larger number of 

roadway departure crashes than horizontal curves following sharper curves. This effect is 

36 
expected to be more pronounced for sharper curves that follow flatter curves, and less 

pronounced for flatter curves that follow other flatter curves. 

Summary 

Table 8 provides a summary of variables available for modeling. The information in table 8 is 

applicable to both Washington and Utah datasets. 

37 
Table 8. Descriptive statistics for design consistency and roadway variables in Washington 

State and Utah. 

Notation Variable Mean S.D. Minimum Maximum 

L Segment length (mi) 0.169 0.109 0.02 1.143 

AADT Annual average daily traffic (veh/day) over the 

observation period 

1,614 1,667 90.71 12,021 

UTind Indicator variable for segment location (= 1 if 

segment in Utah; 0 if segment in Washington) 

0.628 0.484 0 1 

Lc Horizontal curve length (ft) 893.9 577.6 105.6 6,035 

R Horizontal curve radius (ft) 2,231 1,333 318.3 8,873 

e Superelevation (percent) 4.48 1.93 0.09 10 

Defl Deflection angle (degrees) 29.07 22.20 2.112 177.5 

SpLmt Speed limit (mph) 55.21 6.632 30 65 

fd Side friction demand (assuming speed = speed 

limit) 

0.078 0.057 -0.002 0.407 

UpTL Length of upstream tangent (ft) 2,042 2,370 301.0 16,780 

DnTL Length of downstream tangent (ft) 2,079 2,305 300.5 15,835 

AvUDTL Average of upstream and downstream tangent 

length (ft) 

2,060 1,929 308.7 15,333 

UpR Radius of upstream horizontal curve (ft) 2,247 1,362 250 9,950 

DnR Radius of downstream horizontal curve (ft) 2,292 1,514 318 11,460 

AvUDR Average of upstream and downstream curve 

radius (ft) 

2,269 1,164 433 7,925 

RTR Ratio of tangent length to radius (ft/ft) 1.037 0.828 0.083 5.782 

CRR-M Modified change radius rate (ft/ft) 1.216 0.667 0.156 4.333 

38 
Crash Data 

Crash data for Washington State were obtained from the HSIS for 2008-2012 (five years). Crash 

data for Utah were obtained from UDOT for 2008-2014 (seven years). Roadway departure 

crashes were identified as non-intersection crashes in which a vehicle crosses an edge line, 

centerline, or leaves the traveled way. In mapping this definition to variables on the Utah and 

Washington crash reports, roadway departure crashes were identified as those meeting both of 

the following criteria: 

1. Non-intersection (i.e., not at-intersection or intersection-related); and 

2. The first harmful event for at least one of the involved vehicles is a) ran-off-road (right or 

left), b) crossed centerline or median, c) went airborne, or d) hit fixed object. 

The focus of the analysis was roadway departure crashes along horizontal curves on rural, twolane highways. Each observation was represented by a single horizontal curve from the point of 

curvature (PC) to the point of tangency (PT). Roadway departure crashes occurring between the 

PC and PT of each curve were included in the analysis. The observed number of roadway 

departure crashes for each curve over the observation period were determined by severity: 

 Fatal roadway departure crashes (RwD-K). 

 Incapacitating injury roadway departure crashes (RwD-A). 

 Non-incapacitating injury (RwD-B). 

 Possible injury (RwD-C). 

 No injury (RwD-O). 

These counts were ultimately aggregated for modeling due to the low numbers into the following 

categories: 

 Total (i.e., all severities) roadway departure crashes (RwD-KABCO). 

 Fatal-plus-injury roadway departure crashes (RwD-KABC). 

Table 9 and table 10 include summaries of descriptive statistics for the roadway departure crash 

counts associated with the horizontal curves included in this analysis. 

Table 9. Descriptive statistics for roadway departure crash counts in Washington State 

(2008-2012). 

Crash Type N Mean S.D. Min Max Rate 

(crashes/mi/year) 

Rate 

(crashes/MVM) 

RwDKABCO 

249 0.498 1.082 0 12 0.750 0.788 

RwD_KABC 249 0.221 0.571 0 5 0.333 0.350 

39 
 Table 10. Descriptive statistics for roadway departure crash counts in Utah (2008-2014). 

Crash Type N Mean Standard 

deviation 

Min Max Rate 

(crashes/mi/year) 

Rate 

(crashes/MVM) 

RwDKABCO 421 0.390 0.998 0 12 0.292 0.778 

RwD_KABC 421 0.192 0.675 0 9 0.144 0.384 

RESULTS AND DISCUSSION 

Table 11, table 12, table 13, and table 14 summarize the model estimation results for the RwDKABCO and RwD-KABC, respectively. Each table provides model estimation results for two 

different model specification alternatives. Variables capturing segment length, traffic volume, 

design consistency (modified change radius rate and ratio of tangent length to radius), and State 

(a State of Utah indicator variable) are included in both model specifications. The impact of 

horizontal curve radius is captured differently by the two models: 

 Alternative 1 includes horizontal curvature effects through the specification of the 

inverse of horizontal curve radius (1/R). 

 Alternative 2 includes horizontal curvature effects through the specification of side 

friction demand, which captures interactions between posted speed limit, horizontal 

curve radius, and superelevation. 

40 
Table 11. RwD-KABCO model estimation results for Alternative 1 (1/R). 

Notation Variable Parameter 

estimate 

S.E. 

Ln(L*T) Natural logarithm of segment length multiplied by time 

period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.914** 0.103 

1/R Inverse of horizontal curve radius (ft-1) 860.36** 185.74 

fd Side friction demand (assuming speed = speed limit) -- -- 

CRR-M Modified change radius rate (ft/ft) 0.253** 0.118 

RTR Ratio of tangent length to radius (ft/ft) 0.037 0.096 

UTind Indicator variable for segment location (= 1 if segment in 

Utah; 0 if segment in Washington) 

0.101 0.181 

Constant Model constant -8.521** 0.848 

alpha Dispersion parameter 0.752** 0.192 

Note: Alternative 1 (with 1/R): Likelihood ratio chi-squared, 5df = 154.67 (p < 0.0001); Pseudo R2 = 

0.133; Likelihood ratio of alpha chi-squared, 1df = 44.08 (p < 0.001); ** statistically significant at 95 

percent confidence level; * statistically significant at 85 percent confidence level; n/a not applicable; – not 

statistically significant. 

41 
Table 12. RwD-KABCO model estimation results for Alternative 2 (with fd). 

Notation Variable Parameter estimate S.E. 

Ln(L*T) Natural logarithm of 

segment length 

multiplied by time 

period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of 

AADT 

0.924** 0.105 

1/R Inverse of horizontal 

curve radius (ft-1) 

-- -- 

fd Side friction demand 

(assuming speed = 

speed limit) 

4.292** 1.474 

CRR-M Modified change 

radius rate (ft/ft) 

0.372** 0.119 

RTR Ratio of tangent length 

to radius (ft/ft) 

0.049 0.101 

UTind Indicator variable for 

segment location (= 1 

if segment in Utah; 0 if 

segment in 

Washington) 

0.047 0.188 

Constant Model constant -8.484** 0.869 

alpha Dispersion parameter 0.919** 0.208 

Note: Alternative 2 (with fd): Likelihood ratio chi-squared, 5df = 142.76 (p < 0.0001); Pseudo R2 = 

0.123; Likelihood ratio of alpha chi-squared, 1df = 61.00 (p < 0.001); ** statistically significant at 95 

percent confidence level; * statistically significant at 85 percent confidence level; n/a not applicable; – not 

statistically significant. 

42 
Table 13. RwD-KABC model estimation results for Alternative 1 (with 1/R). 

Notation Variable Parameter 

Estimate 

S.E. 

Ln(L*T) Natural logarithm of segment length 

multiplied by time period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.807** 0.142 

1/R Inverse of horizontal curve radius (ft-1) 801.18** 259.56 

fd Side friction demand (assuming speed = 

speed limit) 

-- -- 

CRR-M Modified change radius rate (ft/ft) 0.249* 0.169 

RTR Ratio of tangent length to radius (ft/ft) 0.176+ 0.126 

UTind Indicator variable for segment location (= 1 

if segment in Utah; 0 if segment in 

Washington) 

0.072 0.257 

Constant Model constant -8.579** 1.178 

alpha Dispersion parameter 1.299** 0.432 

Note: Alternative 1 (with 1/R): Likelihood ratio chi-squared, 5df = 72.57 (p < 0.0001); Pseudo R2 = 

0.1015; Likelihood ratio of alpha chi-squared, 1df = 27.62 (p < 0.001); ** statistically significant at 95 

percent confidence level, * statistically significant at 85 percent confidence level, + statistically 

significant at 80 percent confidence level, n/a not applicable; – not statistically significant. 

43 
Table 14. RwD-KABC model estimation results for Alternative 2 (with fd). 

Notation Variable Parameter 

Estimate 

S.E. 

Ln(L*T) Natural logarithm of 

segment length 

multiplied by time 

period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of 

AADT 

0.816** 0.145 

1/R Inverse of horizontal 

curve radius (ft-1) 

-- -- 

fd Side friction demand 

(assuming speed = 

speed limit) 

4.573** 2.047 

CRR-M Modified change 

radius rate (ft/ft) 

0.369** 0.166 

RTR Ratio of tangent length 

to radius (ft/ft) 

0.185+ 0.133 

UTind Indicator variable for 

segment location (= 1 

if segment in Utah; 0 

if segment in 

Washington) 

0.049 0.266 

Constant Model constant -8.617** 1.208 

alpha Dispersion parameter 1.568** 0.464 

Note: Alternative 2 (with fd): Likelihood ratio chi-squared, 5df = 68.49 (p < 0.0001); Pseudo R2 = 0.096; 

Likelihood ratio of alpha chi-squared, 1df = 36.86 (p < 0.001), ** statistically significant at 95 percent 

confidence level, * statistically significant at 85 percent confidence level, + statistically significant at 80 

percent confidence level, n/a not applicable; – not statistically significant. 

44 
2ݐ݉ܮ݌ܵ

݂݀ൌቆ െ 0.01݁ቇ 15ܴ

Figure 11. Equation. Side friction demand. 

where: 

݂݀ = estimated side friction demand; 

ܵܮ݌݉ݐ = speed limit (mph); 

ܴ = horizontal curve radius (ft); and 

݁ = superelevation (percent). 

Models that estimate horizontal curvature effects through the specification of the inverse of 

horizontal curve radius had slightly better fits, as measured by Pseudo R-squared, for both the 

RwD-KABCO and RwD-KABC models. Estimated regression parameters for both inverse 

radius and side friction demand variables were in the direction expected and statistically 

significant at the 95-percent confidence level for both the RwD-KABCO and RwD-KABC 

models. Alternative 2 includes horizontal curvature effects through the specification of side 

friction demand, which captures interactions between posted speed limit, horizontal curve radius, 

and superelevation, as shown in figure 11. 

Design Consistency Effects 

Estimated regression parameters for the modified change radius rate (CRR-M) were positive and 

statistically significant at either the 95-percent or 85-percent confidence level in all models. The 

results indicate that the expected number of roadway departure crashes increases as CRR-M 

increases. In other words, the expected number of roadway departure crashes on a horizontal 

curve not only increases as a function of that curve’s radius, but also as a function of the radii on 

the upstream and downstream curves. The expected number of roadway departure crashes on the 

subject curve increases as the radius of that curve decreases. The sensitivity between the 

expected number of roadway departure crashes and radius is highest for smaller radii and the 

sensitivity continually decreases as the radii get larger and larger. Flatter upstream and 

downstream radii result in a higher number of roadway departure crashes on the subject curve, 

likely because drivers enter the subject curve after becoming used to the flatter radii and higher 

operating speeds of the surrounding curves. Sharper upstream and downstream radii result in a 

lower number of roadway departure crashes on the subject curve, likely because drivers enter the 

subject curve after becoming used to the sharper radii and lower operating speeds of the 

surrounding curves. The magnitudes of the CRR-M effects were similar for both the total and 

fatal-plus-injury crash models. 

Estimated regression parameters for the RTR were positive, but were only statistically significant 

at the 85-percent confidence level in the fatal-plus-injury models. The results indicate that the 

expected number of fatal-plus-injury roadway departure crashes increases as RTR increases. In 

other words, the expected number of roadway departure crashes on a horizontal curve not only 

45 
increases as a function of that curve’s radius, but also as a function of the upstream and 

downstream tangent lengths. The expected number of roadway departure crashes on the subject 

curve increases as the radius of that curve decreases. The sensitivity between the expected 

number of roadway departure crashes and radius is highest for smaller radii and the sensitivity 

continually decreases as the radii get larger and larger. Longer upstream and downstream 

tangents result in a higher number of roadway departure crashes on the subject curve, likely 

because drivers enter the subject curve after becoming used to the longer tangent section of 

alignment and higher operating speeds. Shorter upstream and downstream tangents result in a 

lower number of roadway departure crashes on the subject curve, likely because drivers enter the 

subject curve without enough time to increase their speed or get used to driving on the tangent 

section of alignment. The fact that RTR is more related to fatal-plus-injury crashes than total 

crashes makes intuitive sense, as it is likely the design consistency measure most related to curve 

entering speeds. 

Other Effects 

The models demonstrate multiple other roadway departure safety effects in addition to those 

from the design consistency measures: 

 Segment length and time period were included in the model as offset variables (i.e., 

setting those variables to unity provides an estimate of expected number of roadway 

departure crashes per mi per year). 

 The models also include horizontal curve length as a covariate, and the estimated 

parameters indicate that the expected number of roadway departure crashes decrease as 

curve length increases. Curve length captures an interaction between deflection angle and 

curve radius, and the negative parameters seem to indicate that curve radius is the more 

important part of that interaction. Main effects of deflection angle were tested, but were 

very small and never statistically significant. 

 The positive regression parameters associated with 1/R indicate that the expected number 

of roadway departure crashes on the subject curve increases as the radius of that curve 

decreases. The sensitivity between the expected number of roadway departure crashes 

and radius is highest for smaller radii and the sensitivity continually decreases as the radii 

get larger and larger. This result is expected and is statistically significant at the 95-

percent confidence level for both the total and fatal-plus-injury crash models. 

 The positive regression parameters associated with side friction demand indicate that the 

expected number of roadway departure crashes on the subject curve increases as the side 

friction demand increases. Side friction demand increases as the speed limit increases or 

as the radius of curve and/or superelevation decrease. This result is expected and is 

statistically significant at the 95-percent confidence level and 85-percent level for the 

total crash model and fatal-plus-injury crash model, respectively. 

 Models included a State of Utah indicator variable to capture other unmeasured 

differences between Utah and Washington. The estimated parameter was always positive 

(indicating a higher number, on average, of reported roadway departure crashes in Utah) 

but never statistically significant. 

46 
 

I 

I 

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,: 

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·' l

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· ',· ~::.:~;.:;.a,;:.i;=,.,..,.,. _____ ~·----~--======~- :; ...... ______ ..... ,, ... 

14 

12 

10 

Cra

8 

CMF Total 

CMF HSM 

6 CMF MODEL 

CMF MODEL 2 SD 

4 

2 

0 

Curve Radius (ft)

shes 

0 2000 4000 6000 8000 10000 

A Closer Look at Estimated Radius Effects 

This section provides additional discussion of model findings with respect to curve radius. The 

estimated coefficient for the inverse curve radius variable in the reported models leads to a radius 

CMF that is larger than the radius of curve CMF provided for rural, two-lane highways in the 

Highway Safety Manual (HSM). 

Figure 12 illustrates a comparison of CMFs derived from the RwD-KABCO model reported in 

this chapter to the CMF in the HSM. Since the HSM provides a CMF for total crashes, the RwDKABCO CMF was converted to a total crash CMF (shown as CMF MODEL). Figure 12 shows 

that the CMF derived from the RwD-KABCO model in this chapter is consistently larger than 

the HSM CMF. However, when considering a range defined by two-standard deviations from the 

model coefficient (shown as CMF MODEL 2 SD), the HSM CMF falls within the range of the 

confidence interval of the CMF derived in this effort. Further analysis revealed that the 

difference in study curve radii is likely responsible for much of the difference in the CMF 

magnitudes. The data used to develop the HSM CMF included curves with curve radii less than 

1,000 ft, noted to be commonly as small as 200 ft. As noted in table 8, the average curve radius 

for this dataset was more than 2,200 ft. Overall, this comparison adds some confidence in the 

RwD-KABCO model results. 

Figure 12. Graph. HSM and model derived CMFs for horizontal curve radius. 

47 
CONCLUSIONS AND RECOMMENDATIONS 

This research explored and estimated relationships between alternative measures of design 

consistency and the expected number of roadway departure crashes along horizontal curves on 

rural, two-lane, two-way roads. The relationships between alternative measures of design 

consistency and the expected number of roadway departure crashes were explored using a NB 

regression modeling approach and observing the regression parameter estimates corresponding to 

the measures. Data used for model estimation were drawn from a concurrent FHWA 

“Predisposing Factors” project. (Porter et al. 2018) The data were adaptable to, but not originally 

collected for, studying design consistency. A few points regarding the methodology are worth 

noting in this context: 

1. The study design was cross sectional. Whether estimated regression parameters from 

cross sectional studies can ever represent safety effects estimates is a matter of ongoing 

debate. More recent safety research has implemented cross sectional study designs 

intended to “mimic” randomized experiments and strengthen confidence in safety effects 

estimates, such as the propensity scores – potential outcomes framework. Road safety 

researchers have limited experience using the propensity scores – potential outcomes 

framework for treatments represented by continuous variables, such as alternative 

measures of design consistency. The adapted data and analysis scope did not support the 

use of the propensity scores – potential outcomes framework. 

2. The sample of horizontal curves will impact the identified association between design 

consistency and expected number of roadway departure crashes. Since the modeling 

technique is non-linear, including larger radii curves will impact the coefficient estimates, 

which can lead to larger CMFs for small radii curves upon application. 

The analysis results showed that the expected number of roadway departure crashes on a 

horizontal curve changes not only as a function of that curve’s radius, but also as a function of 

the radii on the upstream and downstream curves and the upstream and downstream tangent 

lengths. More specifically, for a subject curve with a given set of characteristics: 

 Flatter upstream and downstream radii result in a higher number of roadway departure 

crashes on the subject curve, likely because drivers enter the subject curve after becoming 

used to the flatter radii and higher operating speeds of the surrounding curves. 

 Sharper upstream and downstream radii result in a lower number of roadway departure 

crashes on the subject curve, likely because drivers enter the subject curve after becoming 

used to the sharper radii and lower operating speeds of the surrounding curves. 

 Longer upstream and downstream tangents result in a higher number of roadway 

departure crashes on the subject curve, likely because drivers enter the subject curve after 

becoming used to the longer tangent section of alignment and higher operating speeds. 

 Shorter upstream and downstream tangents result in a lower number of roadway 

departure crashes on the subject curve, likely because drivers enter the subject curve 

without enough time to increase their speed or get used to driving on the tangent section 

of alignment. 

48 
Such findings are intuitive given the concept of design consistency and represents a potential 

advancement to existing predictive methods in the HSM, which estimates the expected number 

of crashes on a segment as a function of the characteristics of only that segment. Future work 

should attempt to replicate this analysis with a dataset specifically collected for that purpose. 

49 
CHAPTER 5. QUANTIFYING RELATIONSHIPS BETWEEN EXPECTED 

FREQUENCIES OF ROADWAY DEPARTURE CRASHES AND HORIZONTAL 

ALIGNMENT USING THE SHRP2 ROADWAY INFORMATION DATABASE 

The objective of this study is to explore the transferability of previous findings (see Chapter 4 of 

this report) regarding the application of alignment indices as an indicator of the relationship 

between design consistency and safety. In keeping with past recommendations, the present study 

leveraged high-accuracy roadway data explicitly collected for research purposes. The following 

sections of this paper provide a brief overview of the data and methods applied to investigate the 

effect of design consistency on roadway departure crashes, as well as the conclusions and 

practical applications of design consistency for practitioners. 

OVERVIEW OF DATA SOURCE 

The project team obtained a copy of the Strategic Highway Research Program (SHRP) 2 RID 2.0 

from the Center for Transportation Research and Education (CTRE) at Iowa State University. 

This dataset is derived from photogrammetry for assets (via windshield survey) and automated 

alignment processing using differential global positioning systems and inertial navigation. data 

collection effort. The SHRP 2 RID project team collected data in nine States along roads that 

were most frequently driven by participants in the previously conducted SHRP 2 Naturalistic 

Driving Study (NDS). These States include the following: 

 Florida. 

 Indiana. 

 New York. 

 North Carolina. 

 Pennsylvania. 

 Washington. 

In addition to its compatibility with the NDS, the Roadway Information Database (RID) provides 

the opportunity to use its high-quality roadway inventory data for research on the effects of 

roadway design and traffic control strategies on highway safety. The RID includes a variety of 

high-resolution roadway attributes in geographic information systems (GIS) format. These data 

include the following: 

 Horizontal curvature: 

o Radius. 

o Length. 

o Point of curvature (PC). 

o Point of tangency (PT). 

o Direction of curve (left or right based on driving direction). 

 Vertical grade. 

 Cross-slope/superelevation. 

 Lanes: number, width, and type (through, turning, passing, acceleration, car pool, etc.). 

 Shoulder type/curb (and paved width, if it exists). 

50 
 All Manual on Uniform Traffic Control Devices (MUTCD) signs. 

 Guardrails/barriers. 

 Intersections: location, number of approaches, and control (uncontrolled, all-way stop, 

two-way stop, yield, signalized, roundabout). Crossroad ramp termini are coded as 

intersections in the RID. 

 Median presence: type (depressed, raised, flush, barrier). 

 Rumble strip presence: location (center line, edge line, shoulder). 

 Lighting presence. 

These data are supplemented with other existing public datasets. Among them are the Highway 

Performance Monitoring System (HPMS), as well as State-level inventories of crash locations, 

average annual daily traffic (AADT), and incorporated areas. 

DATA COLLECTION 

The road segments used for analysis and modeling each consisted of one horizontal curve (i.e., 

each observation was defined by the observed number of roadway departure crashes occurring 

on an individual horizontal curve during the observation period). The analysis also considered 

characteristics of the “upstream” horizontal tangent, “upstream” horizontal curve, “downstream” 

horizontal tangent, and “downstream” horizontal curve. 

This section outlines the method used for collecting data associated with eligible horizontal 

curves and their associated roadway tangents in Pennsylvania and Indiana. The study team 

identified these two States as the most likely to have rural, two-lane horizontal curves within the 

RID dataset. Eligible study curves met the following criteria: 

 Unincorporated, rural location. 

 Two, undivided through lanes only (no dedicated turn or acceleration lanes). 

 Bidirectional. 

 Subject horizontal curve is not within 300 ft of another horizontal curve (i.e., each 

upstream and downstream tangent approaching a horizontal curve is at least 300 ft in 

eligible tangent roadway length: two through lanes with no dedicated turn lanes). 

Horizontal Curve Collection 

The SHRP 2 RID 2.0 stores horizontal curves in a bidirectional format, with two linear elements 

representing each travel direction along the curve. Attributes associated with each curve 

direction are stored within the existing horizontal curve feature class for each State. The project 

team queried the Pennsylvania and Indiana RID geodatabases to identify eligible rural, two-lane 

curves using the python-based Dynamic Segmentation Tool developed by CTRE. The team then 

compared the reduced curve output dataset against the entire State RID inventory to remove 

rural, two-lane curves that fell within 300 ft of an adjacent horizontal curve (i.e., one or both of 

the approach tangents were less than 300 ft in length). 

The project team assigned a unique ID to each directional pair of eligible curves. This allowed 

the team to merge directional attributes into a single curve observation. The project team utilized 

51 
the unique curve ID to generate average values along the curve and reconcile attribute 

differences between travel directions. The team determined the following attributes for each 

merged curve observation: 

 Average radius. 

 Average grade. 

 Average curve length. 

 Presence of a superelevated roadway or normal crown. 

 Indicators for presence of roadway elements. 

o Speed limit. 

o Advisory speed. 

o Curve warning signs. 

o Curve chevrons. 

o Rumble strips. 

o Roadside barriers. 

o Intersections. 

o Lighting. 

Each study curve was associated with an upstream and downstream curve. The order was 

determined by geographic orientation, with upstream curves being south or west of the 

observation curve and downstream curves being north or east of the study curve. The team linked 

the average radius, average grade, and average curve length of the upstream/downstream curves 

with the study curve. Figure 9 illustrates the orientation of study curves with their upstream and 

downstream components. 

Tangent Collection 

The project team defined tangents as the entire stretch of roadway between a study curve and its 

upstream and downstream counterparts. The team did not apply any eligibility criteria to 

identifying tangents besides that which was necessary to determine eligible curves. The team 

only collected the length, the average cross-slope, and the average grade of the tangent. These 

data were associated and oriented with the study curves in the same way as the 

upstream/downstream curves. 

Crash Data 

Pennsylvania and Indiana State crash data between the years 2006 and 2013 (inclusive) were 

provided as part of the RID. This analysis included crashes between 2008 and 2013 (inclusive). 

The project team defined curve-related crashes as those that occurred within 150 ft upstream of 

the PC or PT or those that fell within the limits of the horizontal curve. Applying the Federal 

Highway Administration’s (FHWA) definition of a roadway departure crash, the team identified 

roadway departure crashes using the manner of collision variable associated with each State’s 

crash data. The collision codes included in the roadway departure analysis are provided in table 

15. 

52 
Table 15. Collision codes for roadway departure crashes. 

Pennsylvania Indiana 

0: Non-Collision 2: Head-On 

2: Head-On 4: Sideswipe (same direction) 

5: Sideswipe (same direction) 5: Sideswipe (opposite direction) 

6: Sideswipe (opposite direction) 6: Ran off road 

7: Hit fixed object 13: Non-Collision 

These crash types were sorted into the following two categories for further analysis: (1) the total 

number of roadway departure crashes and (2) the number of fatal and injury roadway departure 

crashes along a given curve. While Pennsylvania crash data included the total (i.e., all severities) 

roadway departure crashes (KABCO) designation for maximum injury severity, the available 

Indiana dataset only referenced fatal, injury, and property damage only (PDO) crashes. The 

project team combined all fatal and injury crashes to allow for comparison between States. Table 

16 and table 17 summarize roadway departure and fatal and injury roadway departure crashes by 

State. 

Table 16. Roadway departure crash summary statistics for Indiana (2008-2013). 

Variable Notation N Mean S.D. Minimum Maximum 

RD Crashes RDWDP_total 466 2.02 3.14 0 28 

FI RD Crashes RDWDP_KABC 466 0.59 1.11 0 8 

The roadway departure and fatal and injury roadway departure crash rates for Pennsylvania were 

1.09 crashes/mi/year and 0.580 crashes/mi/year, respectively. The roadway departure and fatal 

and injury roadway departure crash rates for Indiana were 1.67 crashes/mi/year and 0.49 

crashes/mi/year, respectively. 

Table 17. Roadway departure crash summary statistics for Pennsylvania (2008-2013). 

Variable Notation N Mean S.D. Minimum Maximum 

RD crashes RDWDP_total 423 1.15 1.34 0 7 

FI RD crashes RDWDP_KABC 423 0.61 0.88 0 5 

The roadway departure and fatal and injury roadway departure crash rates for Pennsylvania were 

1.09 crashes/mi/year and 0.580 crashes/mi/year, respectively. The roadway departure and fatal 

and injury roadway departure crash rates for Indiana were 1.67 crashes/mi/year and 0.49 

crashes/mi/year, respectively. 

53 
AADT Collection 

Pennsylvania AADT data were available between 2011 and 2013 (inclusive). Indiana AADT 

data were available between 2009 and 2012 (inclusive). The project team assumed that the 

earliest or latest observed AADT values were valid proxies for any study period years outside of 

the range for which data were available. This approach is consistent with that in the Part C 

“Predictive Method” chapters of the Highway Safety Manual (HSM). (AASHTO 2010) 

Summary 

Table 18 provides the summary statistics for data associated with the study curves in Indiana. 

Table 19 provides the summary statistics for data associated with the study curves in 

Pennsylvania. For both States, the sample size is smaller for the upstream and downstream 

tangents and curves; this is because in some cases, data were only available for one direction 

(upstream or downstream). In those cases, the study curve was dropped from the analysis. 

As with the Utah and Washington analysis, this effort explores two alignment indices that 

capture principles for achieving a consistent alignment: 

1. Ratio of tangent length to radius (RTR): the average length of the upstream and 

downstream tangents divided by the radius of the analysis curve. Estimated regression 

parameters corresponding to this variable are expected to be positive. Horizontal curves 

following longer tangents are expected to experience a larger number of roadway 

departure crashes than horizontal curves following shorter tangents. This effect is 

expected to be more pronounced for sharper curves, and less pronounced for flatter 

curves. 

2. Modified change radius rate (CRR-M): the average radius of the upstream and 

downstream horizontal curves divided by the radius of the analysis curve. Estimated 

regression parameters corresponding to this variable are also expected to be positive. 

Horizontal curves following flatter curves are expected to experience a larger number of 

roadway departure crashes than horizontal curves following sharper curves. This effect is 

expected to be more pronounced for sharper curves that follow flatter curves, and less 

pronounced for flatter curves that follow other flatter curves. 

54 
Table 18. Indiana horizontal curve summary statistics. 

Variable Notation N Mean S.D. Minimum Maximum 

Curve radius (ft) R 466 2,581.8 2,121.5 97.5 16,769.5 

Curve grade (degrees) G 466 1.4 1.4 0.0 7.9 

Curve length (ft) L 466 1,055.1 566.3 129.0 4,059.5 

Curve superelevation (degrees) e 466 3.6 1.8 0.3 9.6 

AADT (veh/day) AADT 466 4,595.4 2,845.2 224.4 27,224.2 

Total curve lane width (ft) Lane_Wid 466 20.0 2.7 11.8 25.7 

Total curve shoulder width (ft) Should_Wid 466 5.9 5.9 0 25.6 

Presence of an intersection Intersect 466 0.4 0.5 0 1 

Normal crown Norm_Cn 466 0.2 0.4 0 1 

Deflection angle (degrees) Defl 466 32.0 18.2 5.3 108.1 

Side-friction demand Fd 466 0.1 0.2 0.0 1.9 

Speed limit (mph) SpLmt 466 51.0 6.1 20.0 55.0 

Length of upstream tangent (ft) UpTL 456 2,635.2 6,664.0 312.0 117,674.7 

Length of downstream tangent (ft) DnTL 456 2,444.6 4,238.0 310.1 39,423.4 

Average length of upstream/ 

downstream tangent (ft) AvUDTL 456 2,539.9 4,051.4 351.1 62,327.8 

Radius of upstream horizontal 

curve (ft) UpR 456 2,728.6 2,429.7 62.0 16,894.5 

Radius of downstream horizontal 

curve (ft) DnR 456 2,494.3 2,178.2 42.0 16,894.5 

Average radius of 

upstream/downstream radius (ft) AvUDR 456 2,611.4 1,791.6 174.0 10,305.8 

Ratio of tangent length to radius 

(ft/ft) RTR 456 1.7 5.0 0.1 74.3 

Modified change radius rate (ft/ft) CRR-M 456 1.5 1.9 0.03 29.6 

55 
Table 19. Pennsylvania horizontal curve summary statistics. 

Variable Notation N Mean S.D. Minimum Maximum 

Average radius R 423 3,423.7 3,155.1 97.5 16,221.0 

Average grade G 423 2.0 1.8 0.0 12.4 

Average curve length L 423 915.3 508.5 141.0 4,457.0 

Curve superelevation (degrees) e 423 3.7 1.9 0.9 10.8 

AADT (veh/day) AADT 423 3,847.2 2,363.8 15.0 12,904.8 

Total curve lane width (ft) Lane_Wid 423 20.9 1.3 17.1 27.0 

Total curve shoulder width (ft) Should_Wid 423 6.2 3.5 0 16.9 

Presence of an intersection Intersect 423 0.6 0.5 0 1 

Normal crown Norm_Cn 423 0.3 0.4 0 1 

Deflection angle (degrees) Defl 423 24.8 18.9 5.4 124.0 

Side-friction demand Fd 423 0.1 0.1 0.0 0.8 

Speed limit (mph) SpLmt 423 47.7 8.0 25.0 55.0 

Length of upstream tangent (ft) UpTL 398 1,811.9 1,823.4 312.1 14,579.4 

Length of downstream tangent (ft) DnTL 398 1,917.7 2,152.2 304.6 15,378.3 

Average of length upstream/ 

downstream tangent (ft) AvUDTL 398 1,864.8 1,524.4 319.6 11,462.6 

Radius of upstream horizontal 

curve (ft) UpR 398 3,218.6 3,187.6 35.0 22,150.5 

Radius of downstream horizontal 

curve (ft) DnR 398 3,062.2 2,820.3 78.0 15,889.0 

Average radius of 

upstream/downstream radius (ft) AvUDR 398 3,140.4 2,307.0 333.5 11,675.8 

Ratio of tangent length to radius 

(ft/ft) RTR 398 0.9 0.9 0.05 8.2 

Modified change radius rate (ft/ft) CRR-M 398 1.4 1.7 0.13 25.9 

56 
DATA ASSESSMENT FOR MODELING 

The information available to the project team for defining roadway departure crashes differed 

between the States, particularly related to the States’ handling of non-collisions. Pennsylvania 

non-collision crashes could be further differentiated to identify specific types of non-collision 

crashes, while the Indiana non-collision crashes could not. Non-collision crashes typically 

include overturn/rollover crashes, struck by falling object crashes, and other non-collision 

crashes. Drawing on wording in the crash coding manuals provided with the RID, other noncollision crashes may include sudden stops causing an occupant to be injured or breakage of a 

vehicle part resulting in property damage or injury. 

In Pennsylvania, non-collision crashes accounted for approximately seven percent of total 

crashes. In Indiana, non-collision crashes accounted for approximately two percent of total 

crashes. In Pennsylvania, overturn-rollover crashes accounted for 65 percent of non-collision 

crashes. In Indiana, the study team could not further differentiate types of non-collision crashes. 

The project team felt that it was important to include overturn/rollover crashes in the dataset, but 

could not separate those crashes from other non-collision crashes that were not related to 

roadway departures in Indiana. Therefore, the project team developed one set of roadway 

departure crashes that included non-collision crashes and one set of roadway departure crashes 

that excluded non-collision crashes to test in the models. 

Because non-collision crashes accounted for a small percentage of overall crashes, the models 

indicated no meaningful differences between the datasets that included or excluded them. 

Therefore, to slightly bolster sample size, and to include all roadway departure crashes, the 

project team opted to include non-collision crashes in the analysis dataset. 

Additionally, the project team examined the data from Pennsylvania and Indiana to determine if 

the two States’ data could be pooled together for analysis. Table 20 and table 21 provide a model 

for design consistency with coefficients estimated separately for Pennsylvania and for Indiana. 

The coefficients for all variables except for the presence of an intersection and the ratio of 

tangent length to radius are similar. The presence of an intersection has no effect in roadway 

departure crashes in Pennsylvania and the ratio of average tangent length to radius has no 

apparent effect in Indiana. With the relative consistency between States, the project team 

determined that the States could be combined for further analysis, with special attention paid to 

pooled model parameters for intersection presence and the ratio of average tangent length to 

radius. 

57 
Table 20. Design consistency analysis for Pennsylvania. 

Measure Coef. L95 U95 

Log-AADT 0.354 0.138 0.571 

Intersection presence -0.017 -0.250 0.216 

Average vertical grade 0.067 0.004 0.130 

Total lane width -0.038 -0.144 0.068 

Total shoulder width -0.024 -0.065 0.017 

CRR_M 0.098 0.018 0.178 

RTR 0.336 0.205 0.466 

Constant -2.357 -4.629 -0.085 

Table 21. Design consistency analysis for Indiana. 

Measure Coef. L95 U95 

Log-AADT 0.383 0.160 0.606 

Intersection presence 0.824 0.570 1.078 

Average vertical grade 0.063 -0.035 0.160 

Total lane width -0.055 -0.103 -0.008 

Total shoulder width -0.052 -0.075 -0.028 

CRR_M 0.107 -0.001 0.215 

RTR 0.007 -0.037 0.051 

Radius Functional Form 

The project team explored the functional form of horizontal curve radius for inclusion in the 

models. The team used Variable Introduction Exploratory Data Analysis (VIEDA) as described 

by Hauer (2014) in his book The Art of Regression Modeling in Road Safety. The project team 

developed a prediction model for roadway departure crashes containing predictors other than 

horizontal curve radius. The base model included an offset variable (accounting for curve length 

and number of data years), AADT, presence of an intersection, average vertical grade, total lane 

width, total shoulder width, and an indicator for Pennsylvania. The project team saved the 

58 
• 

• 

• 

• • 

• • 

predicted number of crashes for each curve over the period and compared the predicted crashes 

to observed crashes, aggregating curves into bins by radius in 500-ft increments. 

Figure 13 provides a plot of the ratio of observed to predicted crashes for each 500-ft bin from 

250 ft to 8,250 ft (as measured by the center of each bin). A value greater than 1.0 indicates that 

the model under-predicts crashes for a set of curves and a value less than 1.0 indicates that the 

model over-predicts crashes for a set of curves. In general, the base model appears to underpredict for smaller radius curves and over-predicts for flatter curves (indicating the horizontal 

curve radius does indeed have an impact on safety performance). The shape generally resembles 

a power function. 

Figure 13. Graph. Observed to predicted crash ratio by radius. 

The project team used this information to compare several functional forms for horizontal curve 

radius, including exponential, power, and polynomial forms. The team also explored the inverse 

of the horizontal curve radius, since the inverse radius flattens toward zero as radius nears 

infinity (allowing for a smooth transition to tangent segments). The inverse radius form allows 

for greater flexibility and range for the impact of the “elbow” in crashes that generally occurs on 

horizontal curves (i.e., once a certain radius threshold is reached, crash frequency increases at a 

faster rate, but the relationship is generally flat for radii above this threshold). Figure 14 

compares crash modification factors (CMFs) developed from models including each functional 

form of horizontal curve radius. The exponential form of horizontal curve radius was found to 

have the worst fit to the data and the least flexibility as a CMF. The power function fit the data 

approximately the same as the inverse curve radius, but the CMF elbow is less flexible. This 

function also includes a long, broad range of CMFs greater than 2.0. A fifth-degree polynomial 

was found to fit the data the best, and provided a generally reasonable CMF across the range of 

horizontal curve radii; however, this functional form provides little practical value, is difficult to 

59 
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1 •• I •••••• 

I ••• • I •• I I ••••••• I •• 

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interpret, and includes small fluctuations in CMFs for larger values of horizontal curve radius. 

Therefore, the project team chose to proceed with the inverse horizontal curve radius 

specification for final models. 

Figure 14. Graph. Comparison of CMFs by functional form. 

RESULTS AND DISCUSSION 

The project team was interested in estimating the safety effects of horizontal curve radius, 

superelevation rate, and design consistency on roadway departure crashes. However, as table 22 

shows, there is substantial correlation among variables of interest. The radius of the study curve 

is included in the calculation of the modified change radius rate, ratio of average tangent length 

to radius, and friction demand. Therefore, it is unsurprising that inverse radius is more than 50 

percent correlated to each of these other characteristics. Due to this complication, the project 

team chose to estimate the safety impacts of these features separately. 

60 
Table 22. Correlation among predictors of interest. 

-- Inverse Radius CRR_M RTR fd 

Inverse Radius 1.000 0.590 0.550 0.880 

CRR_M 0.590 1.000 0.422 0.512 

RTR 0.550 0.422 1.000 0.657 

fd 0.880 0.512 0.657 1.000 

Table 23, 

table 24, table 25, table 26, table 27, and table 28 provide separate models based on the inclusion 

of horizontal curve radius and superelevation, friction demand, and design consistency, 

respectively. Each of the tables include two models, one for roadway departure crashes of all 

severities and one for fatal and injury roadway departure crashes. Each of the models includes 

variables for curve length, AADT, presence of an intersection, total lane width, total shoulder 

width, and an indicator for unobserved differences between Pennsylvania and Indiana. Figure 11 

provides an overview of the calculation of friction demand. 

61 
Table 23. RwD-KABCO for inverse radius and normal crown. 

Notation Variable Parameter 

estimate 

S.E. 

LN(L*T) Natural logarithm of segment length multiplied by time 

period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.598** 0.078 

1/R Inverse of horizontal curve radius (ft-1) 464.66** 55.77 

Norm_Cn Indicator for normal crown (=1 if normal crown; 0 if 

superelevated) 

-0.309** 0.135 

Norm_Cn* 

1/R 

Interaction between indicator for normal crown and inverse 

radius 

610.78** 171.08 

Intersect Indicator for intersection presence (=1 if present; 0 if not 

present) 

0.486** 0.087 

Grade Absolute value of average grade on horizontal curve 

(percent) 

0.039* 0.028 

Lane_Wid Total width of combined lanes on horizontal curve (ft) -0.031* 0.020 

Should_Wid Total width of combined shoulders on horizontal curve (ft) -0.034** 0.010 

PAind Indicator for segment location (=1 if segment in 

Pennsylvania; 0 if segment in Indiana) 

-0.234** 0.094 

Constant Model constant -4.275** 0.722 

Alpha Dispersion parameter 0.805** 0.077 

Note: Alternative 1 (RwD-KABCO): Likelihood ratio chi-squared, 9df = 236.23 (p < 0.0001); 

Pseudo R2 = 0.075; Likelihood ratio of alpha chi-squared, 1df = 458.02 (p < 0.001; Pseudo R2 = 0.069; 

Likelihood ratio of alpha chi-squared, 1df = 65.85 (p < 0.001); ** statistically significant at 95 percent 

confidence level; * statistically significant at 80 percent confidence level; n/a not applicable. 

62 
Table 24. RwD-KABC for inverse radius and normal crown. 

Notation Variable Parameter 

Estimate 

S.E. 

LN(L*T) Natural logarithm of segment length multiplied by time 

period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.580** 0.099 

1/R Inverse of horizontal curve radius (ft-1) 405.32** 58.99 

Norm_Cn Indicator for normal crown (=1 if normal crown; 0 if 

superelevated) 

-0.496** 0.167 

Norm_Cn* 

1/R 

Interaction between indicator for normal crown and 

inverse radius 

512.07** 185.30 

Intersect Indicator for intersection presence (=1 if present; 0 if not 

present) 

0.310** 0.110 

Grade Absolute value of average grade on horizontal curve 

(percent) 

0.054* 0.033 

Lane_Wid Total width of combined lanes on horizontal curve (ft) -0.037* 0.027 

Should_Wid Total width of combined shoulders on horizontal curve (ft) -0.058** 0.014 

PAind Indicator for segment location (=1 if segment in 

Pennsylvania; 0 if segment in Indiana) 

0.416** 0.121 

Constant Model constant -4.960** 0.930 

Alpha Dispersion parameter 0.705** 0.129 

Note: Pseudo R2 = 0.075; Likelihood ratio of alpha chi-squared, 1df = 458.02 (p < 0.001); Alternative 2 

(RK-KABC): Likelihood ratio chi-squared, 9df = 134.42 (p < 0.0001); Pseudo R2 = 0.069; Likelihood 

ratio of alpha chi-squared, 1df = 65.85 (p < 0.001); ** statistically significant at 95 percent confidence 

level; * statistically significant at 80 percent confidence level; n/a not applicable. 

63 
Table 25. RwD-KABCO for friction demand. 

Notation Variable Parameter 

estimate 

S.E. 

LN(L*T) Natural logarithm of segment length multiplied by 

time period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.553** 0.079 

fd Side friction demand (assuming speed = speed limit) 4.101** 0.464 

Intersect Indicator for intersection presence (=1 if present; 0 if 

not present) 

0.508** 0.088 

Grade Absolute value of average grade on horizontal curve 

(percent) 

0.064** 0.028 

Lane_Wid Total width of combined lanes on horizontal curve 

(ft) 

-0.047** 0.020 

Should_Wid Total width of combined shoulders on horizontal 

curve (ft) 

-0.030** 0.010 

PAind Indicator for segment location (=1 if segment in 

Pennsylvania; 0 if segment in Indiana) 

-0.220** 0.096 

Constant Model constant -3.664** 0.723 

Alpha Dispersion parameter 0.859** 0.080 

Note: Alternative 1 (RwD-KABCO): Likelihood ratio chi-squared, 7df = 208.24 (p < 0.0001); Pseudo R2 

= 0.066; Likelihood ratio of alpha chi-squared, 1df = 503.21 (p < 0.001);; Pseudo R2 = 0.056; Likelihood 

ratio of alpha chi-squared, 1df = 80.79 (p < 0.001); ** statistically significant at 95 percent confidence 

level; * statistically significant at 80 percent confidence level; n/a not applicable. 

64 
Table 26. RwD-KABC for friction demand. 

Notation Variable Parameter 

Estimate 

S.E. 

LN(L*T) Natural logarithm of segment length 

multiplied by time period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.540** 0.101 

fd Side friction demand (assuming 

speed = speed limit) 

3.346** 0.496 

Intersect Indicator for intersection presence 

(=1 if present; 0 if not present) 

0.329** 0.113 

Grade Absolute value of average grade on 

horizontal curve (percent) 

0.083** 0.033 

Lane_Wid Total width of combined lanes on 

horizontal curve (ft) 

-0.049* 0.027 

Should_Wid Total width of combined shoulders 

on horizontal curve (ft) 

-0.052** 0.014 

PAind Indicator for segment location (=1 if 

segment in Pennsylvania; 0 if 

segment in Indiana) 

0.395** 0.123 

Constant Model constant -4.504** 0.936 

Alpha Dispersion parameter 0.801** 0.136 

Note: Pseudo R2 = 0.066; Likelihood ratio of alpha chi-squared, 1df = 503.21 (p < 0.001); Alternative 2 

(RK-KABC): Likelihood ratio chi-squared, 7df = 108.65 (p < 0.0001); Pseudo R2 = 0.056; Likelihood 

ratio of alpha chi-squared, 1df = 80.79 (p < 0.001); ** statistically significant at 95 percent confidence 

level; * statistically significant at 80 percent confidence level; n/a not applicable. 

65 
Table 27. RD models for design consistency. 

Notation Variable Parameter 

Estimate 

S.E. 

LN(L*T) Natural logarithm of segment length multiplied by 

time period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.429** 0.082 

CRR-M Modified change radius rate (ft/ft) 0.165** 0.039 

RTR Ratio of tangent length to radius (ft/ft) 0.018 0.024 

Intersect Indicator for intersection presence (=1 if present; 0 if 

not present) 

0.465** 0.093 

Grade Absolute value of average grade on horizontal curve 

(percent) 

0.076** 0.030 

Lane_Wid Total width of combined lanes on horizontal curve (ft) -0.056** 0.021 

Should_Wid Total width of combined shoulders on horizontal 

curve (ft) 

-0.043** 0.010 

PAind Indicator for segment location (=1 if segment in 

Pennsylvania; 0 if segment in Indiana) 

-0.308** 0.101 

Constant Model constant -2.224** 0.728 

Alpha Dispersion parameter 0.965** 0.088 

Note: Alternative 1 (RwD-KABCO): Likelihood ratio chi-squared, 8df = 144.06 (p < 0.0001); Pseudo R2 

= 0.047; Likelihood ratio of alpha chi-squared, 1df = 524.34 (p < 0.001); Likelihood ratio of alpha chisquared, 1df = 82.25 (p < 0.001); ** statistically significant at 95 percent confidence level; * statistically 

significant at 80 percent confidence level; n/a not applicable. 

66 
Table 28. RwD-KABC for design consistency. 

Notation Variable Parameter 

Estimate 

S.E. 

LN(L*T) Natural logarithm of segment 

length multiplied by time period 

1.0 (offset) n/a 

Ln(AADT) Natural logarithm of AADT 0.456** 0.104 

CRR-M Modified change radius rate (ft/ft) 0.136** 0.042 

RTR Ratio of tangent length to radius 

(ft/ft) 

0.008 0.018 

Intersect Indicator for intersection presence 

(=1 if present; 0 if not present) 

0.272** 0.116 

Grade Absolute value of average grade 

on horizontal curve (percent) 

0.091** 0.034 

Lane_Wid Total width of combined lanes on 

horizontal curve (ft) 

-0.054* 0.028 

Should_Wid Total width of combined 

shoulders on horizontal curve (ft) 

-0.063** 0.014 

PAind Indicator for segment location (=1 

if segment in Pennsylvania; 0 if 

segment in Indiana) 

0.338** 0.126 

Constant Model constant -3.533 0.941 

Alpha Dispersion parameter 0.875** 0.149 

Note: Alternative 2 (RK-KABC): Likelihood ratio chi-squared, 8df = 74.69 (p < 0.0001); Pseudo R2 = 

0.040; Likelihood ratio of alpha chi-squared, 1df = 82.25 (p < 0.001); ** statistically significant at 95 

percent confidence level; * statistically significant at 80 percent confidence level; n/a not applicable. 

Radius and Normal Crown Effects 

The estimated regression parameters for the safety effect of inverse horizontal curve radius were 

significant at the 95-percent confidence level and indicated that expected number of roadway 

departure and fatal and injury roadway departure crashes increases as horizontal curve radius 

decreases. The sensitivity between the expected number of roadway departure crashes and radius 

is highest for smaller radii and the sensitivity continually decreases as the radii get larger and 

larger. The main effects for the presence of a normal crown and for the interaction between a 

67 
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' ' ' ' ' \ .. \ ... '- ', ······· ' , ....... _ ····················· --- • ..::.- :-.:,:~ - ~ . ....... .;.:.;;.:;.:-.:..• :.u.r.:.:.::.;.w.w: ww.w.wMM.W.W.1 

normal crown and inverse horizontal curve radius are significant at the 95-percent confidence 

level. While the main effect is significant, it has no bearing on the CMF for the change in radius 

from an existing condition to a proposed alternative condition if a normal crown is carried 

through the curve in both conditions. However, it is used in the CMF if the proposed condition 

and existing result in a change from a normal crown to a superelevated cross section. The CMF 

for horizontal curvature, with or without a normal crown, is calculated using the following 

equation in figure 15. 

Figure 16 provides a plot of the CMF by curve radius for a normal crown and a superelevated 

condition for RwD-KABCO. The plots show that the CMF is more responsive to radius on a 

normal crown roadway, which is expected. Additionally, the plot compares the CMF to the 

horizontal curve radius CMF from the HSM. The HSM radius CMF used the average curve 

length from the curves in this study as an input. The CMF developed from this dataset is larger 

than the CMF from the HSM. The CMFs are not directly comparable, as the HSM CMF is for all 

crash types. 

Figure 16. Graph. CMF for changing radius (normal crown versus superelevated versus 

HSM CMF). 

68 
~' .. . ....._ • ······· ··:sra, 

The project team considered the coefficient for inverse horizontal curve radius for all curves, 

curves with a radius of 1,500 ft or smaller, and curves with a radius of 1,000 ft or smaller. Figure 

17 shows the CMFs for horizontal curve radius, assuming a base condition of a 1,000-ft radius, 

using the results of each model. The results show that when the average curve included in the 

analysis is larger, the estimated effect of horizontal curvature is larger. Therefore, the average 

effect of curvature is dependent upon the average of the sample being used. For the RID analysis, 

the average curve had a radius of over 2,000 ft, so it is possible that the analysis in table 23 and 

table 24 overestimates the safety effects of horizontal curve radius for tighter horizontal curves. 

Since smaller horizontal curve radii are typically of interest in safety analyses, a large sample of 

smaller radius curves should be explored in future analysis datasets. The overestimation 

challenge also appeared to be addressed by interacting curve radius with speed and 

superelevation as described in the next section. 

Figure 17. Graph. Comparison of CMFs by curves included in analysis. 

Friction Demand Effects 

The estimated regression parameter for friction demand is significant at the 95-percent 

confidence level. The results indicate that the expected number of roadway departure and fatal 

and injury roadway departure crashes increases as friction demand increases. Friction demand, as 

shown in figure 11, is calculated through the point-mass model, with speed limit substituting for 

design speed. Under this assumption, the expected number of roadway departure and fatal and 

injury roadway departure crashes increases as posted speed limit increases, curve radius 

decreases, and superelevation rate decreases. The sensitivity between the expected number of 

roadway departure crashes and radius is highest for smaller radii and the sensitivity continually 

decreases as the radii get larger and larger. Posted speed limit, superelevation rate, and curve 

radius are treated as an interaction term and impact the calculated CMF in tandem (e.g., the 

69 
 

2

݌ݔ݁ ൌ ܨܯܥ

ሺ4.101ൈሺ

݁݀ݏ݋݌݋ݎ݌ܸ

݁݀ݏ݋݌݋ݎ݌ܴൈ15

െ0.01ൈ݁ݏ݋݌݋ݎ݌݁݀ ሻሻ

݌ݔ݁

ሺ4.101ൈሺ

݅݊݃ݐݏ݅ݔܸ݁

15ൈܴ

2

݅݊݃ݐݏ݅ݔ݁

െ0.01ൈ݁݁ݔ݅ݐݏ݅݊݃ ሻሻ

I 

I 

I 

I 

I 

I 

' \ ' \ ' ·, . \ . ' ' ··· ... \ ' . ··• ... ' '· ······ ' ........ . ~ ·························· .......... - : ---~ ::....-:--:-·=--= ~•- -:-:.:"·•:·:·~~.- ·.- ·= :.;.·~·:···;.;:"·"·· .. 

safety effect of changing the horizontal curve radius is dependent upon the speed limit and 

superelevation). The CMF is calculated using the following equation in figure 18. 

Figure 18. Equation. CMF for a combination of posted speed limit, superelevation rate, and 

curve radius. 

Figure 19 graphically presents the CMF (for 20, 40, and 55 mph posted speed limits) for 

horizontal curve radius relative to the HSM CMF for horizontal curve radius. As the figure 

shows, the CMF increases as horizontal curve radius decreases at a given speed. Additionally, 

the CMF increases for a change in radius as the posted speed increases (e.g., the CMF for 

changing a radius at 20 mph is smaller than making the same change at 55 MPH). Figure 19 also 

includes the CMF for changing the horizontal curve radius from the HSM. For smaller radii, the 

HSM radius CMF is closer to the lower speed curves; as radius increases, the HSM radius CMF 

becomes closer to the higher speed curves. Figure 20 provides a graph of CMFs versus 

horizontal curve radius by speed limit, where the base condition is the minimum radius to 

maintain a normal crown (assuming the superelevation rate is 8 percent) from the AASHTO 

Green Book. The minimum radius provided for each curve is approximately 100 ft less than the 

minimum design radius from the AASHTO Green Book. 

Figure 19. Graph. CMF for total crashes by speed versus HSM. 

70 
--+-

,,..,.~_.,..,..,.,. ... .....,,.~ ................................... . 

CMF 

6 

5 

4 

3 

2 

1 

0 

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 

55 MPH 

50 MPH 

45 MPH 

40 MPH 

35 MPH 

30 MPH 

25 MPH 

20 MPH 

Radius 

Figure 20. Graph. CMF for RwD-KABCO crashes from North Carolina radius. 

The friction demand CMF has a broad range of applicability. While this document provides 

graphical representations for changing horizontal curve radius assuming a posted speed, the 

equation can be used for the following purposes: 

 Assessing the safety effect of changing horizontal curve radius while maintaining the 

same speed. 

 Assessing the safety effect of changing horizontal curve radius while changing the posted 

speed limit. 

 Assessing the safety effect of changing the superelevation rate. 

 Assessing the safety effect of increasing the posted speed limit on an existing curve 

(inputting information for existing horizontal curve radius and superelevation rate). 

 Assessing the safety effect of simultaneously increasing the superelevation rate and the 

posted speed limit on an existing horizontal curve. 

 Assessing the safety effect of simultaneously changing the posted speed limit, horizontal 

curve radius, and superelevation rate on an existing or proposed horizontal curve. 

71 
 

552

ܨܯܥ ൌ ݁݌ݔ ሺ4.101ൈሺ15ൈ1,000െ0.01ൈ8 .0ሻሻ

݁݌ݔ ሺ4.101ൈሺ 452

15ൈ550െ0.01ൈ8.0ሻሻ

 = 0.84 

 

452

ܨܯܥ ൌ ݁݌ݔ ሺ4.101 ൈሺ15ൈ1,000െ0.01ൈ8.0ሻሻ

݁݌ݔ ሺ4.101 ൈሺ 452

15ൈ550െ0.01ൈ8.0ሻሻ

 = 0.64 

ܨܯܥ ൌ ݁݌ݔ ሺ4.101 ൈሺ 552

15ൈ550െ0.01ൈ8.0ሻሻ

݁݌ݔ ሺ4.101 ൈሺ 452

15ൈ550െ0.01ൈ8.0ሻሻ

 = 1.64 

Example: 

An existing curve is posted at 45 mph, has a horizontal curve radius of 550 ft, and a 

superelevation rate of 8 percent. The safety impact of increasing the radius to 1,000 ft is to be 

calculated seen in figure 21. 

Figure 21. Equation. CMF for increasing radius to 1,000 ft. 

The CMF indicates an expected 36-percent reduction in the expected number of roadway 

departure crashes. If the posted speed limit were proposed to be increased to 55 mph in tandem 

with the increase in radius, the CMF would be calculated as shown in figure 22. 

Figure 22. Equation. CMF calculation based on increase in posted speed limit and increase 

in radius. 

The CMF indicates an expected 16-percent reduction in the expected number of roadway 

departure crashes. If the posted speed limit were proposed to be increased to 55 mph with no 

change in radius the CMF would be calculated as seen in figure 23. 

Figure 23. Equation. CMF calculation for increased speed with no change in radius. 

The CMF indicates an expected 64-percent increase in the expected number of roadway 

departure crashes. 

Design Consistency Effects 

The estimated regression parameters for the CRR_M were positive and statistically significant at 

the 95-percent confidence level. The results indicate that the expected number of roadway 

departure crashes and fatal and injury roadway departure crashes on a horizontal curve not only 

increase as a function of that curve’s radius, but also as a function of the radii on the upstream 

and downstream curves. Flatter upstream and downstream radii result in a higher number of 

roadway departure crashes on the subject curve, likely because drivers enter the subject curve 

after becoming used to the flatter radii and higher operating speeds of the surrounding curves. 

Sharper upstream and downstream radii result in a lower number of roadway departure crashes 

on the subject curve, likely because drivers enter the subject curve after becoming used to the 

72 
sharper radii and lower operating speeds of the surrounding curves. The magnitudes of the CRRM effects were similar for both the total and fatal-plus-injury crash models. 

Estimated regression parameters for the RTR were positive, but were not statistically significant 

at any confidence level. As indicated in table 23 and 

table 24, the results for this variable were not consistent between States. Regression parameters 

for RTR were generally significant at the 95-percent level in Pennsylvania and were essentially 

zero in Indiana. In Pennsylvania, the results indicate that the expected number of roadway 

departure and fatal and injury roadway departure crashes increase as RTR increases. In other 

words, the expected number of roadway departure crashes on a horizontal curve not only 

increases as a function of that curve’s radius, but also as a function of the upstream and 

downstream tangent lengths. The sensitivity between the expected number of roadway departure 

crashes and radius is highest for smaller radii and the sensitivity continually decreases as the 

radii get larger and larger. Longer upstream and downstream tangents result in a higher number 

of roadway departure crashes on the study curve, likely because drivers enter the study curve 

after becoming used to the longer tangent section of alignment and higher operating speeds. 

Shorter upstream and downstream tangents result in a lower number of roadway departure 

crashes on the study curve, likely because drivers enter the study curve without enough time to 

increase their speed or get used to driving on the tangent section of alignment. The fact that RTR 

is more related to fatal-plus-injury crashes than total crashes makes intuitive sense, as it is likely 

the design consistency measure most related to curve entering speeds. Additional work is needed 

to uncover why the RTR effect was not present in Indiana. 

Other Effects 

The models demonstrate several other roadway departure safety effects in addition to those from 

the horizontal curve and design consistency measures: 

 Segment length and time period were included in the model as offset variables (i.e., 

setting those variables to unity provides an estimate of expected number of roadway 

departure crashes per mi per year). 

 The models include the presence of an intersection as a covariate. In all cases, the 

expected number of roadway departure and fatal and injury roadway departure crashes 

increases when an intersection is present. 

 Positive regression parameters were estimated for the absolute value of grade on the 

study curve. This indicates the expected number of roadway departure and fatal and 

injury roadway departure crashes increases when the absolute value of grade increases. 

 Negative regression parameters were estimated for total lane width and total shoulder 

width. This indicates the expected number of roadway departure and fatal and injury 

roadway departure crashes decreases when total lane width or total shoulder width 

increases. 

 Models included a State of Pennsylvania indicator variable to capture other unmeasured 

differences between Pennsylvania and Indiana. For all roadway departure crashes, the 

estimated parameter was always negative (indicating a lower number, on average, of 

73 
reported roadway departure crashes in Pennsylvania) and statistically significant at the 

95-percent level. For fatal and injury roadway departure crashes, the estimated parameter 

was always positive (indicating a higher number, on average, of fatal and reported injury 

roadway departure crashes in Pennsylvania) and statistically significant at the 95-percent 

level. These findings are intuitive for fatal and injury roadway departure crashes due to 

central Pennsylvania’s dynamic topography compared to Indiana’s flatter topography. 

Furthermore, it is intuitive that Indiana would have a higher number of reported PDO 

roadway departure crashes due to a lower reporting threshold. The reporting threshold is 

$1,000 in Indiana as opposed to a disabled vehicle in Pennsylvania. 

Comparison with Utah/Washington Analysis 

74 
75 
Table 29 provides a comparison between the results from the previous analysis 

(Utah/Washington) and the results from this analysis (RID). The comparison shows that the 

confidence intervals overlap for each characteristic for each crash severity. However, the 

coefficients for the inverse of horizontal curve radius (for both crash severities) and for RTR (for 

fatal and injury roadway departure crashes) differ substantially between the analyses. It appears 

that the incorporation of additional variables in the model reduced the magnitude of the 

estimated coefficients compared to the States with no additional information available. The RID 

provided what appeared to be higher quality data for curve radii and superelevation than the Utah 

and Washington datasets, as well as additional high-quality data for more variables, likely 

helping to identify more representative effects of the factors of interest. 

76 
Table 29. Results comparison. 

Notation RwDKABCO 

Utah 

RwDKABCO 

Washington 

RwDKABC 

Utah 

RwDKABC 

Washington 

RwDKABCO 

Indiana 

RwDKABCO 

Pennsylvania 

RwDKABC 

Indiana 

RwD

Penn

1/R 860.36 186.74 801.18 259.56 464.66 55.77 405.32 5

fd 4.292 1.474 4.573 2.047 4.101 0.464 3.346 0

CRR_M 0.253 0.118 0.249 0.169 0.165 0.039 0.136 0RTR 0.037 0.096 0.176 0.126 0.018 0.024 0.008 0

77 
CONCLUSIONS AND RECOMMENDATIONS 

This research explored and estimated relationships between elements of horizontal curvature and 

measures of design consistency, and the expected number of roadway departure crashes along 

horizontal curves on rural, two-lane, two-way roads. The research explored these relationships 

using a negative binomial (NB) regression modeling approach and observing the regression 

parameter estimates corresponding to the measures. Data used for model estimation were drawn 

from the SHRP 2 RID 2.0. The data were originally collected for use with the NDS data but were 

suitable for analysis with State-maintained traffic and crash data. A few points regarding the 

methodology are worth noting in this context: 

1. The study design was cross sectional. Whether estimated regression parameters from 

cross sectional studies can ever represent safety effects estimates is a matter of ongoing 

debate. More recent safety research has implemented cross sectional study designs 

intended to “mimic” randomized experiments and strengthen confidence in safety effects 

estimates, such as the propensity scores – potential outcomes framework. Road safety 

researchers have limited experience using the propensity scores – potential outcomes 

framework for treatments represented by continuous variables, such as alternative 

measures of design consistency. The scope of this effort did not support the use of the 

propensity scores – potential outcomes framework. 

2. The characteristics of the sample of horizontal curves, specifically related to the number 

or proportion of larger radii curves in the sample, appears to impact the estimated 

association between inverse curve radius and expected number of roadway departure 

crashes. Since the modeling technique is non-linear, including larger radii curves will 

impact the coefficient estimates, which can lead to larger CMFs for small radii curves 

upon application. This challenge appeared to be addressed by including an interaction 

between inverse curve radius, speed, and superelevation, represented by side friction 

demand. 

3. The crash data available for Indiana did not allow for elements of the RID data to be 

combined with the Washington and Utah data analyzed previously. The definitions of 

roadway departure crashes differ slightly between the two datasets. Information on 

harmful events was not available to fully differentiate crash types within non-collision 

crashes. However, non-collision crashes accounted for a very small proportion of 

roadway departure crashes. The Pennsylvania data could be combined with the 

Washington and Utah data in future analyses. 

The analysis results showed that the expected number of roadway departure crashes along a 

horizontal curve changes not only as a function of that curve’s radius, but also as a function of 

the radii on the upstream and downstream curves and, for Pennsylvania, the upstream and 

downstream tangent lengths. More specifically, for a subject curve with a given set of 

characteristics: 

 Flatter upstream and downstream radii result in a higher number of roadway departure 

crashes on the subject curve, likely because drivers enter the subject curve after becoming 

used to the flatter radii and higher operating speeds of the surrounding curves. 

78 
 Sharper upstream and downstream radii result in a lower number of roadway departure 

crashes on the subject curve, likely because drivers enter the subject curve after becoming 

used to the sharper radii and lower operating speeds of the surrounding curves. 

 Longer upstream and downstream tangents result in a higher number of roadway 

departure crashes on the subject curve in Pennsylvania, likely because drivers enter the 

subject curve after becoming used to the longer tangent section of alignment and higher 

operating speeds. This effect was not observed at a statistically significant level in 

Indiana. 

 Shorter upstream and downstream tangents result in a lower number of roadway 

departure crashes on the subject curve in Pennsylvania, likely because drivers enter the 

subject curve without enough time to increase their speed or get used to driving on the 

tangent section of alignment. This effect was not observed at a statistically significant 

level in Indiana. 

Such findings are intuitive given the concept of design consistency and represent a potential 

advancement to existing predictive methods in the HSM, which estimates the expected number 

of crashes on a segment as a function of the characteristics of only that segment. Future work 

should attempt to explore why the RTR effect did not seem to carry over to a State like Indiana, 

which has a much different roadside environment than Utah, Washington, or Pennsylvania. 

Additionally, the analysis results showed that the expected number of roadway departure crashes 

on a horizontal curve changes due to the combination of that curve’s radius and the presence of a 

normal crown. The project team attempted to further incorporate the main effect of actual 

superelevation rate (on superelevated curves), but did not find a statistically significant result. 

The results showed that the expected number of roadway departure crashes increase at a faster 

rate for smaller horizontal curve radii when the curve has a normal crown. Future research 

should further explore the direct effect of superelevation rate and should extend this analysis to 

analyze the safety impacts of superelevation deficiency (i.e., existing superelevation that is less 

than recommended by the AASHTO Green Book). 

The analysis results did, however, show that the expected number of roadway departure crashes 

on a horizontal curve increases as friction demand increases. Friction demand is calculated using 

the point-mass model, the posted speed limit as a substitute for design speed, the horizontal 

curve radius, and the superelevation rate. The results show an interaction between posted speed, 

curve radius, and the superelevation rate. 

The findings in the RID analysis are similar to those in the previous analysis of the Washington 

and Utah datasets. The safety effects of horizontal curve characteristics have a smaller effect in 

this analysis (however, the confidence intervals overlap), due to the ability to address potentially 

confounding characteristics with the RID dataset that was not possible with the Utah and 

Washington datasets. Additional safety treatments were available in the RID dataset (e.g., rumble 

strip presence, presence of warning signs), but these factors were more likely to be influenced by 

site selection bias (e.g., chevrons are typically placed on curves with a history of roadway 

departure crashes) or were not significant in models. Future research should expand the analysis 

to all applicable RID sites to bolster sample size and to allow for utilization of the propensity 

79 
scores – potential outcomes framework. Additionally, since the RID contains information on 

roadways most likely to be traveled by NDS participants, the curves in this database are often on 

arterials, which have much larger curve radii and more forgiving design characteristics than 

other, lesser traveled roadways. This analysis would benefit from including more curves with 

radii closer to the limiting radius from geometric design policies and from lower AADT 

roadways. Finally, the NDS itself could be used to try and verify the speed and lane keeping 

impacts of the horizontal curve and design consistency characteristics explored in this study to 

further support interpretations of the findings. 

80 
CHAPTER 6. SAFETY EVALUATION OF GUIDERAIL AND CURVE DELINEATORS 

ON HORIZONTAL CURVE ALONG TWO-LANE RURAL HIGHWAYS 

This chapter of the report considers the safety effects of several countermeasures that may be 

implemented along horizontal curves of two-lane rural highways. These include the following: 1) 

the presence of guiderail with delineators along the curve, 2) the presence of guiderail only, and 

3) the presence of only delineators along the curve. The first section of the chapter provides 

background information related to past research that reported on the safety effects of guiderail 

and delineators. The second section of the chapter describes the study sites, while the third 

section describes the data. The fourth section of the chapter summarizes the analysis 

methodology, and the fifth section explains the results. The final section offers conclusions from 

the evaluation. 

BACKGROUND 

According to the Manual on Uniform Traffic Control Devices (MUTCD) (2009), delineators can 

be used along the roadside when there are changes in horizontal alignment, thus providing 

guidance and information to users. Delineators should comprise of a retroreflective device whose 

minimum dimension is 3 inches for both width and height. The color of the delineators shall be 

consistent with color of the roadway edge lines. There is no specific information in the MUTCD 

concerning the use of delineators on two-lane rural highways; however, the following placement 

guidance is provided: 

 Delineators should be placed 2 to 8 ft outside of the roadway edge, unless an obstacle 

exists, where the placement should be converted to be in line with or inside the innermost 

edge of the obstacle. 

 The mounting height between the bottom of the retroreflective device and the elevation 

of roadway near edge should be approximately 4 ft. The MUTCD recommends minimum 

delineator spacing, ranging from 20 to 300 ft, depending upon radius of curve. The 

spacing should be adjusted along the curve so that drivers can recognize multiple 

delineators simultaneously when traversing horizontal curves. 

Delineators 

The effect of post-mounted delineators (PMDs) on vehicle operating speed, driver performance 

and crash risk has been reported by many researchers. This section of the literature review 

describes the findings from studies that reported on the relationship between PMDs and driving 

performance, with a focus on operating speed and crash risk along horizontal curves. 

Zador et al. (1987) evaluated the short-term and long-term effects of PMDs on the operating 

speed and lateral position of vehicles in the travel lane on horizontal curves. There were 46 study 

sites from Georgia and 5 study sites from New Mexico included in the field evaluation, all of 

which were on rural two-lane highways. A total of four independent variables were included in 

the evaluation. These included: treatment, direction of curve or turn, vertical alignment (grade < 

-2 percent or down, -2 percent ≤ grade ≤ 2 percent or level, and 2 percent < grade or up) and 

81 
sharpness of curve (less or more sharp within the grade and turn class). The delineators were 

installed on both sides of metal posts along the outside of the horizontal curves. The type, size, 

location and spacing requirements for the PMDs were consistent with the MUTCD. A traffic 

data recorder (TDR) was used to measure the operating speed and lateral position of vehicles in 

the lane as they traversed the curves. Two TDRs were set up for each observation period -- one 

was located 100 ft before the beginning of the curve and the other was 100 ft after the beginning 

of that curve. Data were collected during three different time periods to evaluate the short-term 

and long-term effects of the PMDs. These periods were shortly before and several weeks after 

the PMDs were installed, and 6 months after the installation. During each period, about 100 to 

150 vehicles were recorded during the daytime and nighttime travel periods separately. 

The results indicated that vehicle speed and lane position were significantly influenced by 

PMDs, compared to untreated sites. The short-term effect demonstrated an obvious speed 

increase before and after the application of PMDs for both daytime and nighttime period. Also, 

vehicles tended to travel towards the centerline when PMDs were installed along right-hand 

curves. While traveling along left-hand curves, they shifted away from the centerline before 

entering the curves and then towards the centerline as traversing the curves, regardless of the 

presence of PMDs. In addition, no evidence was found to validate significant variances over 

time. Overall, the authors concluded that the primary effect of PMDs was helping drivers better 

recognize horizontal curves ahead. 

Choi et al. (2015) developed crash modification factors (CMFs) of horizontal alignment 

elements, including PMDs. The study sites included 10 freeways in Korea. The PMDs were 

installed on 753 segments, and there were 2,170 segments in the reference group, with no 

vertical grade or horizontal curve. Safety performance functions (SPFs) were developed for each 

selected freeway, and an empirical Bayes (EB) method was applied to develop the CMFs. The 

CMF for PMDs was 1.190 with a standard error of 0.259. This suggests that PMDs are 

associated with an increase in the expected total crash frequency on freeway segments in Korea. 

Elvik and Vaa (2004) reported CMFs of implementing PMDs on two-lane rural roads using 

meta-analysis approach in 2004. The CMF for all crash type with serious injury, minor injury 

and possible injury severity level was 1.04 with an adjusted standard error of 0.1. The CMF for 

all crash type with property damage only was 1.05 with an adjusted standard error of 0.07. Both 

results indicate that PMDs installation is associated with a potentially increase in crash 

frequency. 

Chrysler et al. (2009) investigated the influence of PMDs on driver response to horizontal 

curves. The project consisted of a nighttime driving experiment on a closed course, a driver 

survey of curve perception, and a field evaluation of delineation treatments. Twenty volunteers 

participated in the nighttime driving test, which was intended to select delineation treatments 

used for the field observation. Two types of PMDs were selected -- one of the PMDs contained a 

single reflector at the top of the post (referred to as “dot” PMDs) and the other PMDs contained a 

retroreflective material over the full length of the post (referred to as “full” PMDs). Four sites on 

two-lane rural roads in Texas were selected to conduct the before-after field investigation, where 

no treatments were applied in the before period and one of the selected PMDs was installed in 

82 
the after period. For each approach of the selected curve, operating speed and lateral position of 

vehicles at the curve warning sign on the tangent segment, curve entry point, and curve midpoint 

were collected. The analysis showed that both “dot” PMDs and “full” PMDs significantly 

reduced the vehicle centerline encroachment rate. The “dot” PMDs reduced the rate by 78 

percent for a vehicle with 80-inch track width and 94 percent for a 61-inch width, while the 

“full” PMDs reduced the rate by 77 percent and 88 percent respectively. Also, both PMDs 

improved lane position. Drivers tended to drive about one foot closer to the edge line when 

compared to the baseline scenario. Finally, there was no statistically significant decrease in 

operating speed before and after the PMDs were installed along horizontal curves. 

Nygardhs et al. (2014) studied the effect of different PMD spacing on operating speeds at night. 

The study was conducted on a driving simulator, where a 9 m-wide and 6 km-long roadway 

segment was designed. The route comprised of six horizontal curves, each having different radii 

and turning directions. Researchers tested seven different PMD configurations, which included 

current standards in Norway, Sweden, Denmark, Finland, and suggestions from an expert panel, 

respectively. In general, the study was carried out in a way that each of the 14 participants would 

view every PMDs design combination in the experimental design. Throughout the simulation, 

the operating speed of each participant was collected at the same frequency of 10 Hz. The mean 

operating speed before the curve, within the curve and after the curve, as well as the whole route, 

was defined as the average of the mean speed of all participants. The speed data were analyzed 

using the univariate analyses of variance (ANOVA). The results demonstrated that if no 

distracted driving task was involved in the experimental run, the mean operating speed on the 

whole segment remained consistent between different PMDs spacing, as long as they were 

installed continuously along the route. Operating speed increased when PMDs were present, 

relative to the condition when no PMDs were present along the route. Moreover, if PMDs were 

installed continuously along the road, vehicle operating speeds were affected by the spacing. 

Finally, operating speeds appeared to be influenced more by PMDs on large radius curves than 

on flat radius curves. 

In summary, PMDs are intended to provide visual guidance to drivers about the presence and 

degree of horizontal curve. Based on published research, the CMFs associated with installing 

PMDs were slightly larger than one, indicating an expected increase in total crash frequency. In 

addition, PMDs have generally been associated with increased operating speeds when compared 

to horizontal curves without PMDs. 

Guardrail 

Guardrail has proven to be effective in reducing crash severity, especially for run-off-the-road 

(ROR) collisions. The focus of the review in this section is on the evaluation of guardrail 

effectiveness when applied along roadway shoulders. 

Park et al. (2016) estimated CMFs for guardrail and other roadside barriers using both the EB 

and full Bayes (FB) methods. In the study, 147 freeway segments in Florida were identified as a 

treatment group, including 127 sites where w-beam guardrail was installed and 20 sites where 

concrete barriers were installed. And there were 328 segments in the reference group. The results 

83 
showed that there were few differences in the CMFs developed using the EB and FB methods. If 

considering all severity levels (KABCO), the estimated CMFs were 1.09 for all crash types and 

1.01 for ROR crash type only, while if considering KAB severity levels only, the estimated 

CMFs were 0.85 for all crash types and 0.75 for ROR crashes. This indicates that guardrail 

increases the total crash frequency and ROR crash frequency when considering all severity 

levels. And guardrail installation appears to be associated with a reduction in severe crashes. 

Moreover, by estimating CMFs for ROR crash with respect to time, it was found that CMFs were 

1.05 for KABCO levels and 0.89 for KAB levels during the day, and CMFs were 0.98 and 0.53 

at night, respectively. This suggests that guardrail is more effective for ROR crashes during night 

time than day time. 

Choi et al. (2015) estimated CMFs of roadside barriers including guardrails in Korea. There were 

78 treated sites and 2,170 reference segments selected from 10 freeways. The statistical results 

showed that guardrails had a positive influence on crash reduction, where the CMF was 0.908 

with a standard error of 0.431. This indicates that guardrail installation is associated with a 

decrease in the expected total crash frequency on freeway segments in Korea. 

Elvik and Vaa (2004) reported CMFs of new guardrail along roadway embankment for ROR 

crashes. The estimated CMF was 0.56 with an adjusted standard error of 0.1 for fatal crash, 0.53 

with a standard error of 0.05 for injury crash, and 0.93 with a standard error of 0.31 for all 

crashes. This suggests that guardrail is effective in reducing crash severity, while it is not 

deterministic in total crash frequency reduction. 

Martin et al. (2013) conducted a long-term analysis of the impact of guardrail on motorway 

safety in France. Crash data used in the study included fatal, injury, and property damage only 

crashes occurring on a French motorway network from 1996 to 2010. Run-off crashes, including 

the type of barrier encountered, impact position, and vehicle behavior after collision, were also 

considered in the evaluation. The study results showed that guardrail significantly reduced injury 

rates in ROR crashes. The relative risk of at least one injury in a shoulder run-off-road crash was 

1.9 to 2.6 times higher for roadways without guardrail, compared with segments having roadside 

guardrails. Also, single-sided w-beam guardrail yielded the lowest injury rate in terms of 

vehicle-barrier collisions. 

Ben-Bassat et al. (2011) investigated the effect of guardrail, shoulder width, and roadway 

geometry on vehicle operating speeds and lane position in a driving simulator study. Twenty-two 

participants were included in the study, 11 male and 11 female. Each participant drove three 

different scenarios with various element combinations. These included: 0.5 m, 1.2 m and 3.0 m 

shoulder widths; presence or no presence of guardrail; and curve radius and direction. The results 

showed that vehicle speed was higher when guardrails were installed on straight roads or rightturning curves. Meanwhile, the operating speed was not necessarily higher on left-turning curves 

in the presence of guardrails. 

To summarize, guardrail is effective when applied along roadway shoulders. The CMFs from 

previous studies suggests a significant reduction in crash severity, as well as the ROR crash type. 

With regards to total crash frequency, confidence interval of the estimated CMFs usually contain 

84 
1.0, indicating that the presence of guardrail may not influence the expected total crash 

frequency when installed along roadway shoulders. 

STUDY SITES AND ROADWAY INVENTORY DATA 

The study sites for the present study are all horizontal curves on two-lane rural highways, in 

which 417 sites are located in Pennsylvania and 437 sites are located in Indiana. The analysis 

database was developed using the Strategic Highway Research Program (SHRP) 2 Roadway 

Information Database (RID). The RID database included a variety of features present along a 

horizontal curve on two-lane rural highways, such as: 

 Curve direction; 

 Curve radius, and curve length; 

 Superelevation and vertical grade (percent); 

 Posted speed limit (mph) and curve advisory speed (mph); 

 Presence of curve warning and chevron signs; 

 Curve lane width and shoulder width (ft); 

 Presence of rumble strips; 

 Roadside barrier types and barrier percentage within the horizontal curve (percent); 

 Presence of intersections; 

 Presence of lighting; and 

 Traffic volume (average annual daily traffic, veh/day). 

The treatments of interest, delineators and guiderail, were collected manually from a 

combination of Google Earth street view, Pennsylvania Department of Transportation 

(PennDOT) online video photologs, and the RID street view. It was assumed that the delineators 

and guiderail were present during the entire analysis period, so the evaluation methodology 

employed a cross-sectional study design. 

85 
Table 30. Summary of reference and treatment study sites. 

Category Pennsylvania Indiana Total 

Absence of both guiderail and delineators 

(Reference) 247 379 626 

Presence of guiderail (only) (treatment) 41 46 87 

Presence of delineator post (only) (treatment) 28 10 38 

Presence of guiderail with post-mounted 

delineators (treatment) 29 2 31 

Presence of guiderail with triangle delineators 

(treatment) 59 0 59 

Presence of guiderail with both post-mounted 

and triangle delineators (treatment) 13 0 13 

Presence of guiderail with sum of guiderail with 

delineators (treatment) 101 2 103 

Total 417 437 854 

Table 30 shows the number of horizontal curves with guiderail and delineators among the sample 

of curves in Pennsylvania and Indiana. There were 626 curves that did not contain either 

guiderail or delineators. There were 41 and 46 curves with only guiderail in the Pennsylvania and 

Indiana data files, respectively. There were a total of 38 horizontal curves in the sample with 

delineators only – this sample is not likely to yield reliable CMFs. There were 101 horizontal 

curves in Pennsylvania with both delineators and guiderail, but only 2 curves with both 

treatments in Indiana. Therefore, only Pennsylvania data were used to estimate CMFs for the 

dual application of delineators and guiderail. The effect of delineators only was inferred from the 

CMFs derived for the dual application of delineators and guiderail, relative to the CMF for 

guiderail only. A summary of the available sites used in the evaluation are shown in table 31. 

Table 31. Study sites of the safety evaluations. 

Safety Treatment Treatment Sites Reference Sites State 

Guiderail with delineators 101 247 Pennsylvania 

Guiderail 87 626 Pennsylvania, Indiana 

DESCRIPTION OF DATA 

This chapter describes the data used to estimate the safety effects of the delineator and guiderail 

countermeasures. Two datasets were developed to estimate the CMFs – one for guiderail with 

delineators and a second dataset for guiderail only. The dependent and independent variables 

available for the analysis are described separately for the treatment and reference group sites. 

Crash data for the years 2009 to 2013 (inclusive) in both Pennsylvania and Indiana were used in 

the evaluation. The following dependent variables were considered when developing the CMFs: 

86 
 Total crash frequency (all severities and all crash types). 

 Total number of fatal and injury (FI) crashes. 

 Total number of run-off-road related crashes (all severities). 

 Total number of night-time crashes (all severities). 

Traffic volume data were available from the year 2011 to 2013. AADT data for the years 2010 

and 2009 are extrapolated using a linear trend line between the years 2011 and 2013. The 

following independent variables were acquired from the RID: 

 Traffic volume (average annual daily traffic, veh/day); 

 Average curve length (mi); 

 Curve lane shoulder width (ft); 

 Horizontal curve radius, and degree of curvature; 

 Posted speed limit (mph); 

 Curve advisory speed (mph); 

 Presence of curve arrow; 

 Presence of chevron signs; and 

 Presence of intersections. 

During the analysis period, no treatments were installed, so the study design is a cross-sectional 

with-without comparison. Study sites with low traffic volumes (AADT < 100 veh/day), and 

roadways with posted speed limits lower than 35 mph were eliminated from the data analysis 

files, because nearly all of these sites were reference group locations in the guiderail with 

delineators dataset that were dissimilar with the treatment group sites in the same dataset. As 

shown in table 30, there were 101 treatment sites and 247 reference sites in the guiderail with 

delineators dataset. Over the 5-year analysis period, there were 505 treatment site observations 

and 1,235 reference site observations. Since there are very few sites with delineators present in 

the Indiana data, only Pennsylvania sites are included in the analysis for this evaluation. In the 

guiderail only dataset, there were 87 treatment sites (435 observations in 5 years) and 626 

reference sites (3,130 observations in 5 years) in the combined Pennsylvania and Indiana files. 

87 
 Table 32. Descriptive statistics of continuous variables in the guiderail with treatment 

delineators dataset. 

Continuous Variables Mean S.D. Minimum Maximum 

Total crashes per year 0.358 0.643 0 3

Total fatal and injury crashes per year 0.200 0.465 0 3

Total run-off-road crashes per year 0.242 0.520 0 2

Total night-time crashes per year 0.109 0.318 0 2

Average annual daily traffic (veh/day) 3,942 2,698 945 15,007 

Curve length (mi) 0.189 0.111 0.029 0.745 

Posted speed limit (mph) 47.228 8.553 35 55 

Curve advisory speed (mph) 45.000 9.960 15 55 

Difference between speed limit and advisory speed (mph) 2.327 5.703 0 25 

Curve lane shoulder width (ft) 3.534 1.667 0.351 8.256 

Degree of curvature 4.817 6.908 0.370 58.795 

Table 33. Descriptive statistics of continuous variables with reference delineators dataset. 

Continuous Variables Mean S.D. Minimum Maximum 

Total crashes per year 0.272 0.584 0 4 

Total fatal and injury crashes per year 0.139 0.386 0 3 

Total run-off-road crashes per year 0.169 0.441 0 3 

Total night-time crashes per year 0.101 0.335 0 3 

Average annual daily traffic (veh/day) 3,675 2,289 291 12,665 

Curve length (mi) 0.159 0.074 0.038 0.400 

Posted speed limit (mph) 45.972 7.955 35 55 

Curve advisory speed (mph) 44.595 8.822 20 55 

Difference between speed limit and advisory speed (mph) 1.457 4.039 0 20 

Curve lane shoulder width (ft) 2.743 1.829 0 10.595 

Degree of curvature 3.497 3.824 0.353 25.649 

88 
Table 34. Descriptive statistics of categorical variables with treatment delineators dataset. 

Categorical Variables Proportion for Yes 

Category 

Proportion for No 

Category 

Presence of curve arrow or chevron signs 7.92% 92.08% 

Presence of intersection in the curve 48.51% 51.49% 

Curve lane shoulder width under 4 ft 48.51% 51.49% 

Difference between speed limit and advisory 

speed is above 0 

17.82% 82.18%

Table 35. Descriptive statistics of categorical variables with reference delineators dataset. 

Categorical Variables Proportion for Yes 

Category 

Proportion for No 

Category 

Presence of curve arrow or chevron signs 5.67% 94.33% 

Presence of intersection in the curve 60.32% 39.68% 

Curve lane shoulder width under 4 ft 60.32% 39.68% 

Difference between speed limit and advisory 

speed is above 0 

13.77% 86.23% 

89 
Figure 24. Graph. Box plot of AADT in the delineator with guiderail dataset. 

Figure 25. Graph. Box plot of degree of curvature in the delineator with guiderail dataset.* 

Note: * represents box plot of degree of curvature excluding one outlier larger than 30. 

90 
60 

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Figure 26. Graph. Box plot of curve advisory speed in the delineator with guiderail dataset. 

Figure 27. Graph. Box plot of posted speed limit in the delineator with guiderail dataset. 

Table 32, table 33, table 34, and table 35 show summary statistics of the dependent and 

independent variables in the treatment and reference groups in the guiderail with delineator 

dataset. The average crash frequency of all crash types is higher in the treatment group than in 

the reference group. The mean nighttime crash frequencies are nearly identical between the two 

groups. Table 32, table 33, table 34, and table 35 also show that most of the roadway 

characteristics are similar between the treatment and reference groups. Figure 24, figure 25, 

figure 26, and figure 27 show box plots of AADT, degree of curvature, posted speed limit, and 

the curve advisory speed. With respect to the key features of the curve, the treatment sites and 

reference sites are comparable. 

91 
Table 36. Descriptive statistics of continuous variables in the guiderail only dataset. 

Continuous Variables Mean S.D. Minimum Maximum 

Total crashes per year (treatment) 0.349 0.835 0 9 

Total crashes per year (reference) 0.484 1.321 0 28 

Total fatal and injury crashes per year (treatment) 0.122 0.386 0 4 

Total fatal and injury crashes per year (reference) 0.153 0.438 0 4 

Total run-off-road crashes per year (treatment) 0.239 0.660 0 7 

Total run-off-road crashes per year (reference) 0.286 0.695 0 6 

Total nighttime crashes per year (treatment) 0.168 0.532 0 7 

Total nighttime crashes per year (reference) 0.189 0.543 0 6 

Average annual daily traffic (veh/day) (treatment) 4,757 2,801 703 16,808 

Average annual daily traffic (veh/day) (reference) 4,341 2,747 153 27,331 

Curve length (mi) (treatment) 0.199 0.110 0.045 0.844 

Curve length (mi) (reference) 0.188 0.099 0.031 0.768 

Posted speed limit (mph) (treatment) 50.632 6.564 35 55 

Posted speed limit (mph) (reference) 49.353 6.948 35 55 

Curve advisory speed (mph) (treatment) 48.736 8.459 15 55 

Curve advisory speed (mph) (reference) 47.764 8.746 15 55 

Difference between speed limit and advisory speed (mph) 

(treatment) 2.011 5.338 0 30 

Difference between speed limit and advisory speed (mph) 

(reference) 1.621 4.818 0 40 

Curve lane shoulder width (ft) (treatment) 4.313 2.629 0 11 

Curve lane shoulder width (ft) (reference) 2.858 2.529 0 11 

Degree of curvature (treatment) 4.098 4.049 0.442 27.828 

Degree of curvature (reference) 3.827 4.836 0.352 55.655 

92 
Table 37. Descriptive statistics of categorical variables in the guiderail only dataset. 

Categorical Variable Proportion Yes 

Category 

Proportion No 

Category 

Presence of curve arrow or chevron signs 

(treatment) 

6.90% 93.10% 

Presence of curve arrow or chevron signs 

(reference) 

6.07% 93.93% 

Presence of intersection in the curve (treatment) 52.87% 47.13% 

Presence of intersection in the curve (reference) 49.68% 50.32% 

Curve lane shoulder width under 4 ft (treatment) 48.28% 51.72% 

Curve lane shoulder width under 4 ft (reference) 81.79% 18.21% 

Difference between speed limit and advisory speed 

is above 0 (treatment) 

14.94% 85.06% 

Difference between speed limit and advisory speed 

is above 0 (reference) 

13.42% 86.58% 

Table 36 and table 37 show summary statistics for the dependent and independent variables of 

the treatment and reference groups in the guiderail only dataset. The average crash frequency for 

all crash types in the treatment group is lower than those in the reference group. Many roadway 

characteristics, such as AADT, curve length, posted speed limit, advisory speed, degree of 

curvature, presence of curve arrows or chevron signs, and the presence of intersections, are 

nearly identical between the two groups. The lane width and shoulder widths are higher in the 

treatment group than in the reference group. Figure 28, Figure 29, figure 30, and Figure 31 

shows box plots of AADT, degree of curvature, posted speed limit, and the curve advisory speed. 

With respect to the key features of the curve, the treatment sites and reference sites are 

comparable. 

93 
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Figure 28. Graph. Box plot of AADT in the guiderail dataset. 

Figure 29. Graph. Box plot of degree of curvature in the guiderail dataset.* 

Note: * represents box plot of degree of curvature excluding one outlier larger than 30. 

94 
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Figure 30. Graph. Box plot of posted speed limit in the guiderail dataset. 

Figure 31. Graph. Box plot of curve advisory speed in guiderail dataset. 

METHODOLOGY 

The propensity scores-potential outcomes framework was used in the present study to estimate 

the safety effects of guiderail with delineators and guiderail only. This section of the report 

provides an overview of the propensity score-potential outcome framework, including the basic 

structure of the counterfactual framework, estimation of propensity scores, matching algorithms, 

matching considerations, and methods to estimate treatment effects for safety countermeasures. 

Propensity Scores-Potential Outcomes Framework 

The propensity score-potential outcomes framework is a causal analysis method that incorporates 

propensity score matching into treatment effect estimation. It is an advanced quasi-experimental 

95 
ܻ݅݅ߨ ൌ ܻ݅

ܶ ൅ ሺ1 െ ߨ݅ሻܻܷ݅

study design methodology. The goal of this framework is to estimate the treatment effect using a 

subset in which the entities without the treatment are comparable to the treatment. This 

methodology is applicable to non-randomized observational data and removes several biases 

associated with cross-sectional methods (e.g. treatment selection bias, and bias due to 

confounding variables). The propensity scores are often estimated using a logit model. Then, the 

treated and untreated entities are matched according to the estimated propensity score. At last, 

non-parametric or parametric statistical methods can be used to estimate the treatment effect of a 

safety countermeasure. 

Counterfactual Framework 

The counterfactual framework emphasizes that an entity selected into either the treatment or notreatment group have potential outcomes in both States, including the observed and unobserved 

outcomes. (Rosenbaum 2002) The counterfactual framework is illustrated by the following 

equation seen in figure 32. 

Figure 32. Equation. Counterfactual framework. 

Where Yi is the outcome for entity i; Yi

T is the outcome for treated entity i; YiU is the outcome for 

untreated entity i; πi is the probability of entity i receiving a treatment. 

The core of the counterfactual framework is the potential outcomes. Considering that the 

potential outcome Y is associated with a range of causal states (treated T or untreated U), for 

each unit i actually experiencing the treatment, the treated outcome YTi is associated with causal 

state T. This outcome is actually observed. The potential outcome is the untreated outcome YUi of 

the same unit i and is associated with another causal state U and is thus hypothetical 

(counterfactual). The goal of causal analysis in the potential outcomes framework is to learn the 

difference in outcomes of a unit i while it experienced treatment and the same unit i while it did 

not experience the treatment (or experienced other treatments). This comparison is counterfactual 

by necessity because it involves the comparison between observable events YT

i and the 

unobservable events YUi. In the estimation of a treatment effect, given a unit i and a treatment 

action T, each action-unit pair is a potential outcome. The potential outcome framework is 

illustrated in table 38. 

96 
∑ ݉ ൫ܻ ܷหܶ ൌ 1ሻ ݅ൌ1 ݅ ݅

ݏ ݏ

݅ൌ1൫ܻ݅

ܷหܶ݅ ൌ 1ሻ ∆ܣܷܶൌ	 ൌ	

∑

∑݉

݅ൌ1൫ܻ݅

ܷหܶ݅ ൌ 0ሻ ∑ݏ

݅ൌ1൫ܻ݅

ܷหܶ݅ ൌ 0ሻ

ݏ

∑݉ ൫ܻܶหܶ ൌ 1ሻ ݅ൌ1 ݅ ݅ ݉

݉ ݅ൌ1൫ܻ݅

ܶหܶ݅ ൌ 1ሻ ∆ܣܶܶൌ	 ൌ	

∑

∑݉

݅ൌ1൫ܻ݅

ܶหܶ݅ ൌ 0ሻ ∑݉

݅ൌ1൫ܻ݅

ܶหܶ݅ ൌ 0ሻ

݉

Table 38. Potential outcomes framework. 

Status Treated Untreated 

Treated Observed (YT 

i | Ti = 1) Counterfactual (YT i | Ti = 0) 

Untreated Counterfactual (YU 

i | Ti = 1) Observed (YU i | Ti = 0) 

The treatment effect can be considered as either additive or multiplicative. In traffic safety 

research, since the variables in crash count models usually having multiplicative effects on the 

outcome (e.g., CMFs), the treatment effects are typically considered multiplicative. The 

multiplicative treatment effect is defined as the outcome of the treated divided by the outcome of 

the untreated. There are several treatment effect estimates of interest in transportation safety 

research such as the average treatment effect (ATE) and the average treatment effect for the 

treated (ATT). In traffic safety study, ATT is easier to identify and theoretically more 

informative since it describes the impact of treatment T for the units (horizontal curves) who 

were actually exposed to it. The parameters in the outcome model generally indicate the ATT. 

ATT is estimated as shown in the following equation seen in figure 33. 

Figure 33. Equation. Estimate of average treatment effect of treated. 

Where ∆ܣܶT is the average treatment effect for treated; Yi

T is the outcome for treated entity i; Ti is 

the treated state of entity i; m is the number of treated entities. 

The third estimate is the average treatment effect for the untreated (ATU). It estimates the 

average treatment effect for the untreated entities if they received treatment. It is useful when 

researchers would like to know what would have been the outcome for the untreated entities if 

the treatment had been applied. ATU is defined as seen in figure 34. 

Figure 34. Equation. Estimate of average treatment of untreated. 

Where ∆ܣܶU is the average treatment effect; Yi

U is the outcome for untreated entity i; Ti is the 

treated state of entity i; and s is the number of untreated entities. 

In traffic safety research, ∆ATE and ∆ATT are typically the two parameters of interest. ATT is 

usually preferred when evaluating the effect of a safety countermeasure since it is based on data 

from a sample of sites included in the evaluation. 

97 
 

----

݌ሺݔ݅ሻ ൌ ܲݎ ሺܶ݅ ൌ 1| ܺ݅ ൌ ݔ݅ሻ

݌ ൬ ݃݋݈ ൌ ሻ݌ሺ ݐ݃݅݋݈

0ߚ ൅ ݔ ݅ ݅ߚ ෍ ൌ ൰݌െ1

Estimating Propensity Scores 

Propensity scores for the treatment are often estimated using a binary logit regression model. 

(Shenyang Guo 2010). The binary logit model is specified in the following equation in figure 35. 

Figure 35. Equation. Propensity score logit model. 

Where p(xi) is the propensity of entity i being treated given the vector of covariates xi; p is the 

propensity score; xi is the vector of covariates; β0, and βi are the coefficients to be estimated in 

the logit model. 

Matching Algorithms 

There are several matching algorithms that could be used to match treated and untreated entities 

based on the propensity scores. The algorithms can be categorized into greedy and optimal 

matching. (Shenyang Guo 2010) Greedy matching is a linear matching algorithm. It works 

sequentially to find the best match (e.g., closest propensity score) for one treatment unit before 

creating a match for the second treatment unit. Once a match is created, the treatment unit is 

removed from further consideration. If replacement is allowed, a single control unit can be 

copied and matched to multiple treatment units. If matching is done without replacement, the 

control unit will be removed from further consideration. Greedy matching techniques include 

algorithms such as nearest-neighbor (NN) and Mahalanobis matching. Greedy matching divides 

large decision-making problems into a series of single decisions and processes them without 

reconsideration. Optimal matching algorithms create, break, and rearrange the matches in order 

to produce the minimum overall sum of match distances. They are basically optimization 

methods based on network flow theory. (Bertsekas 1991, Rosenbaum 2002, Shenyang Guo 

2010) Optimal matching can be done as full matching or pair matching. 

In this study, NN matching is used for several reasons. First, it is an effective algorithm to find 

good matches. It produces the best possible matches from a pair is chosen with the closest 

propensity scores. Second, NN matching is more efficient than optimal matching algorithms due 

to its linear decision path. Optimal matching usually requires higher computational time since the 

matched pairs are reconsidered in the optimization process (Holmes 2013). Finally, NN matching 

is a flexible algorithm to accommodate different sample sizes in the treatment or reference group 

by adjusting the matching ratio and replacement setting. 

98 
Matching Considerations 

Overlap and Common Support 

After estimating the propensity scores, an important step is to check the overlap and common 

support of the propensity score distributions between the treatment and control groups. Sufficient 

common support is necessary to process the matching; otherwise, a lack of common support 

indicates that the treatment and control groups are too dissimilar for comparison. 

Variable Selection 

The goal of the propensity score model is to balance the confounding covariates, thus variables 

should be carefully selected in the model. Rubin and Thomas (1996) and Brookhart et al. (2006) 

indicated that, in order to minimize the variance but not generate extra bias, the covariate set 

should include all of the variables related to both the treatment assignment and the outcome, as 

well as the variables that are not significantly associated with the treatment assignment but 

associated with the outcome. At the same time, variables that may have been affected by the 

treatment should not be included in the model. (Rosenbaum 1984) The judgement of variable 

selection requires careful consideration since excluding an important confounder will increase 

the bias. 

Matching ratio 

NN matching can be applied on a 1:1 or 1: k basis, and “with replacement” or “without 

replacement.” 1:1 matching discards a large number of observations but avoids poor matches, 

while 1: k matching produces higher precision, but sometimes does not decrease bias. When 

treatment and control groups have similar sample size, and better matches are preferred, 1:1 

matching is recommended. (Holmes 2013, Start 2010) 

Replacement 

Replacement is defined as allowing a control entity to be matched with multiple treatment 

entities. Matching with replacement allows a control entity to be reconsidered after pairing it 

with a treatment entity. Replacement is usually applied when the treatment entities significantly 

outnumber the control entities in the sample. In order to keep as many observations as possible, 

and reduce the bias and variance, it is necessary to allow replacement. On the other hand, when 

the sample size in the control group is large enough and there is enough common overlap, 

matching without replacement is preferred. (Caliendo and Kopeinig 2008, Shenyang Guo 2010, 

Stuart 2010) 

Caliper Width 

Caliper width is the level of tolerance for the maximum distance when matching the treatment 

entity with the control entity. Caliper width can be applied in the matching algorithms as a 

common support condition. It restrains the maximum distance of the propensity score (or other 

99 
 

distance measure) for all of the matched pairs, and thus will help avoid bad matches. There is a 

trade-off in specifying caliper width since larger caliper widths may lead to bias while smaller 

caliper widths reduce the number of observations to be used to estimate the potential outcomes. 

(Holmes 2013) In a large traffic safety dataset, it was recently shown that the treatment effect 

estimate does not change much as the caliper width changes. (Sasidharan and Donnell 2014) The 

recommended caliper size is about 0.20 ~ 0.25 times the standard deviation of the estimated 

propensity score. (Rosenbaum and Rubin 1985, Austin 2011) 

Assessing Covariate Balance 

Assessing covariate balance is necessary after matching. There are several ways to assess 

covariate balance. One method is to use the standardized bias (SB). (Rosenbaum and Rubin 

1985) When the absolute difference of SB is less than 20 (absolute standardized mean difference 

less than 0.2), it indicates that there is no statistical difference between the treatment and control 

groups. (Holmes 2013) Otherwise, the Kolmogorov-Smirnov (K-S) test, graphical checks such as 

box-plots or quantile-quantile (QQ) plots, can be used to check the balance of continuous 

variables. (Sekhon and Grieve 2008, Franklin et al. 2014, Garrido et al. 2014, Linden 2015) 

Estimating Treatment Effect 

The outcome model used to estimate the treatment effect is a negative binominal regression 

model (NB model). The model estimates expected crash frequency (number of crashes per year) 

on a roadway segment or intersection, as a function of the treatment variable and covariates. The 

negative binomial (NB) model is a common approach to model crash outcomes since it accounts 

for overdispersion that often exists in crash data. (Lord and Mannering 2010) The general 

functional form of a NB model is presented as follows in figure 36. 

Figure 36. Equation. NB regression model. 

Where λi is the expected crash frequency on roadway segment; βt is the parameter of estimable 

regression parameters of treatment; βi is the vector of estimable parameters of covariates; Xi is 

the vector of covariates; εi is the gamma-distributed error term. The mean-variance relationship 

for the negative binominal distribution is shown in figure 37. 

Figure 37. Equation. Variance of NB distribution. 

Where Var(yi) is the variance of crash outcome; E(yi) is the expected crash frequency on 

roadway segment i; α is the overdispersion parameter. Maximum likelihood estimation (MLE) is 

used to estimate the model parameters. 

100 
ANALYSIS RESULTS 

This section presents the propensity score matching analysis for the safety effect of two 

countermeasures: (1) guiderail with delineators (GD), and (2) guiderail only (G only). Each 

analysis includes propensity score estimation results, matching outcomes, covariate balance 

assessment, and CMF estimation. In addition, a disaggregate analysis using the degree of 

curvature is conducted for both countermeasures. Finally, CMFs for delineators only are 

estimated using the results of the guiderail with delineators and the guiderail only results. 

Safety Effects of Guiderail with Delineators (GD) 

A standard NB regression model is first estimated (see table 39, table 40, table 41, and table 42) 

for all the crash types using the data before matching. This model is estimated in order to reveal 

the factors that are statistically significant for each crash type. These factors are then considered 

as potential covariates in the matching process. The variables included in the model indicate the 

association between expected total crash frequency and the covariates in the model. Negative 

coefficients indicate a decrease in the expected crash frequency when those features are present 

along a horizontal curve. The model coefficients indicate that the presence of guiderail with 

delineators is expected to reduce total and nighttime crash frequency, but increase fatal and 

injury crashes and run-off-road-related crashes. However, those estimates are produced from the 

unbalanced raw data, which may introduce selection bias. 

Table 39. Statistical output of the cross-sectional NB regression for total crashes (GD). 

Variable Coef. S.E. 

Constant -4.851 0.709 

Natural logarithm of AADT 0.612 0.084 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

-0.003 0.104 

Degree of curvature 0.070 0.009 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.372 0.140 

Presence of intersection in the curve 

(1 if present; 0 otherwise) 

0.182 0.101 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a not applicable; * represents the treatment variable is not statistically significant. 

101 
Table 40. Statistical output of the cross-sectional NB regression for fatal and injury (GD). 

Variable Coef. S.E. 

Constant -5.705 0.928 

Natural logarithm of AADT 0.646 0.110 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

0.058 0.131 

Degree of curvature 0.061 0.011 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.641 0.168 

Presence of intersection in the curve 

(1 if present; 0 otherwise) -- -- 

Natural logarithm of length (offset) 1.000 n/a 

Note: --means the variable is not statistically significant; n/a not applicable; * represents the treatment 

variable is not statistically significant. 

Table 41. Statistical output of the cross-sectional NB regression for ROR crash (GD). 

Variable Coef. S.E. 

Constant -3.236 0.837 

Natural logarithm of AADT 0.368 0.100 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

0.022 0.128 

Degree of curvature 0.073 0.011 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.658 0.159 

Presence of intersection in the curve 

(1 if present; 0 otherwise) -- -- 

Natural logarithm of length (offset) 1.000 n/a 

Note: -- means the variable is not statistically significant; n/a not applicable; all other variables included 

are significant at 95-percent confidence level; * represents the treatment variable is not significant. 

102 
Table 42. Statistical output of the cross-sectional NB regression for nighttime crash (GD). 

Variable Coef. S.E. 

Constant -4.377 1.083 

Natural logarithm of AADT 0.454 0.129 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

-0.232 0.171 

Degree of curvature 0.075 0.012 

Presence of speed difference above 0 

(1 if present; 0 otherwise) -- -- 

Presence of intersection in the curve 

(1 if present; 0 otherwise) -- -- 

Natural logarithm of length (offset) 1.000 n/a 

Note: “--" means the variable is not significant thus excluded from the model; n/a not applicable; all other 

variables included are significant at 95-percent confidence level; * represents the treatment variable is not 

statistically significant. 

Propensity score matching 

Table 43 shows the propensity score matching configuration. The matching distance is defined 

by the propensity score, which is the probability of a horizontal curve receiving the treatment. In 

order to yield quality matches, 1:1 nearest neighbor matching is applied with a caliper width of 

0.2. Considering the relatively sample size in the treatment and reference group, matching with 

replacement is applied. The statistical output for the estimated propensity score model is 

presented in table 44. Covariates included in the model are the variables related to both the crash 

outcome and treatment assignment. 

Table 43. Propensity score matching configuration (GD). 

Matching configuration Matching configuration 

Distance Propensity score 

Algorithm Nearest neighbor matching 

Ratio 1:1 

Replacement Without replacement 

Caliper width 0.2 

103 
Table 44. Statistical output of propensity score model estimation (GD). 

Variable Coef. S.E. Z-statistic P-value 

Constant 0.674 0.796 0.850 0.397 

Natural logarithm of AADT 0.066 0.091 0.720 0.469 

Degree of curvature 0.153 0.019 7.860 <0.001 

Lane shoulder width under 4 ft 

(1 if present; 0 otherwise) 

-0.654 0.134 -4.880 <0.001 

Presence of chevron signs or curve arrow 

(1 if present; 0 otherwise) 

-0.888 0.305 -2.910 0.004 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.317 0.164 1.930 0.053 

Presence of intersection in the curve 

(1 if present; 0 otherwise) 

-0.578 0.113 -5.110 <0.001 

Natural logarithm of curve length 1.000 offset n/a n/a 

Note: Wald chi-square(6) = 148.60; Log-likelihood at convergence = -955.163; n/a not applicable. 

There are 419 out of 505 observations in the treatment group that are matched with 419 

observations in the control group. A total of 86 treatment observations were unmatched and 

discarded since there are no observations within the caliper width in the reference group. Table 

45 and table 46 show the summary statistics before and after matching in each group. Figure 38 

and figure 39 shows the distribution of the propensity scores in the treatment and reference 

groups before and after matching. The distribution of propensity scores before matching differs 

between the treatment and reference groups. Because there is large region of common support, 

most of the data could be matched using the propensity scores. 

104 
Table 45. Summary of variables before matching (GD). 

Variables Mean S.D. 

Propensity score (treatment) 0.373 0.186 

Propensity score (reference) 0.257 0.123 

ln(AADT) 8.066 0.658 

ln(AADT) 7.981 0.742 

ln(length) -1.819 0.551 

ln(length) -1.949 0.490 

Degree of curvature 4.817 6.908 

Degree of curvature 3.498 3.824 

Curve shoulder width larger than 4 ft 0.654 0.476 

Curve shoulder width larger than 4 ft 0.814 0.390 

Presence of chevron signs or curve arrows 0.079 0.270 

Presence of chevron signs or curve arrows 0.057 0.231 

Speed difference larger than 0 0.178 0.383 

Speed difference larger than 0 0.138 0.345 

Presence of intersection (treatment) 0.485 0.500 

Presence of intersection (reference) 0.603 0.489 

105 
Table 46. Summary of variables after matching (GD). 

Variables Mean S.D. 

Propensity score (treatment) 0.313 0.130 

Propensity score (reference) 0.312 0.130 

ln(AADT) (treatment) 8.049 0.647 

ln(AADT) (reference) 8.066 0.755 

Degree of curvature (treatment) 3.632 3.094 

Degree of curvature (reference) 3.361 3.820 

Curve shoulder width larger than 4 ft (treatment) 0.716 0.451 

Curve shoulder width larger than 4 ft (reference) 0.699 0.459 

Presence of chevron signs or curve arrows (treatment) 0.237 0.048 

Presence of chevron signs or curve arrows (reference) 0.048 0.214 

Speed difference larger than 0 (treatment) 0.136 0.343 

Speed difference larger than 0 (reference) 0.143 0.351 

Presence of intersection (treatment) 0.511 0.500 

Presence of intersection (reference) 0.530 0.500 

106 
4 

3 

~ 

• 2 

~ 

0 

0 

,, 

I \ I \ 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

01 

' ' ' ' ' ' ' ,, _____ , 

025 0~ 076 100 

propensityscore 

0.2 03 04 06 00 

ptOpenSilyscore 

group □ --CJ -

Figure 38. Graph. Propensity score distributions before matching (GD). 

Figure 39. Graph. Propensity score distributions after matching (GD). 

Covariate Balance Assessment 

Table 47 shows the mean and absolute standardized mean difference (ASMD) of the propensity 

scores and each covariate before and after matching. An ASMD value closer to 0 indicates better 

balance of the covariates between the treatment and control groups. An ASMD larger than 0.20 

indicates a statistically significant difference between the treatment and reference groups. As 

shown in table 47, the ASMD of the propensity score is reduced by 99.4 percent, from 0.738 to 

0.006. The average ASMD is reduced from 0.202 to 0.043 as a result of matching. With respect 

to the covariates, curve length, degree of curvature, and the indicator variable for intersection 

presence are unbalanced between the treatment and reference groups before matching (ASMD > 

0.20). However, matching produced well-balanced propensity scores. In addition, the last column 

of table 47 shows that all of the other covariates are improved significantly. The ASMD 

107 
I 

~ 

Treatment Variable 

I 

Mean 

Difference 

Before 

I 

Mean 

Difference 

After 

I 

ASMD 

Before 

'---

I 

ASMD 

After 

I 

Percent 

Change 

in 

Balance 

7

J

Propensity score* - 0.116 0.001 0.738 - 0.006 I 99.4% 

ln(AADT) 0.086 -0.017 0.122 0.024 I 80.2%

ln(length) - 0.130 -0.024 0.250 0.049 I 81.3%

Degree of curvature 1.319 0.271 0.236 0.078 I 79.4% 

Curve shoulder width larger than 4 ft -0.160 0.017 0.368 0.037 I 89.6%

Presence of chevron signs or curve 

arrows 

0.023 0.012 0.090 0.053 I 47.0%

Speed difference larger than 0 0.041 -0.007 0.111 0.021 I 82.4% 

Presence of intersection -0.118 -0.019 0.239 0.038 I 83.8% 

I Mean I n/a I n/a I 0.202 I 0.043 I n/a

• 

comparison of each covariate before and after matching is presented in Figure 40. Compared to 

the before-matching data, all of the ASMD values are close to zero after matching, indicating 

that the covariates in the treatment and reference groups are similar after matching. 

Table 47. Mean and ASMD before and after matching (GD). 

Note: * represents the probability of receiving the treatment. All other variables are covariates and n/a 

represents not applicable. 

Figure 40. Graph. ASMD before and after matching (GD). 

108 
CMF Estimates 

Table 48, table 49, note: n/a is not applicable; * represents the treatment variable is not statistically 

significant; all other variables included are significant at 95-percent confidence level. 

table 50, Table 51, and Table 52 show the statistical output from a cross-sectional NB model 

after matching, and the resulting CMF estimates of each crash type for the guiderail with 

delineator dataset. The total crash, fatal and injury crash, and night-time crash frequency CMF 

point estimates are smaller than 1.0, which indicates that guiderail with delineators offers a 

safety benefit along horizontal curves of two-lane rural highways. For the run-off-road-related 

crash type, the presence of guiderail with delineators has a negative safety effect (CMF > 1.0). 

However, considering the large standard error of the treatment variable coefficient in the crash 

type models, and the fact that all of the 95-percent confidence intervals for all CMFs contain the 

value 1.0, the safety effects of guiderail with delineators along horizontal curves should be 

evaluated further using a larger data sample. 

Table 48. Statistical output of NB model estimation after matching (GD). 

Variable Coef. S.E.

Constant -6.385 0.931

Natural logarithm of AADT 0.806 0.108 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

-0.030 0.124 

Degree of curvature 0.099 0.017 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.391 0.179 

Natural logarithm of length (offset) 1.000 n/a 

 

Note: n/a means not applicable; * represents the treatment variable is not statistically significant; all other 

variables included are statistically significant at 95-percent confidence level. 

109 
Table 49. Statistical output of NB model estimation for fatal and injury after matching 

(GD). 

Variables Coef. S.E. 

Constant -7.642 1.253 

Natural logarithm of AADT 0.873 0.145 

Presence of guiderail with delineators (1 if present; 0 otherwise)* -0.021 0.164 

Degree of curvature 0.098 0.022 

Presence of speed difference above 0 (1 if present; 0 otherwise) 0.735 0.214 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a is not applicable; * represents the treatment variable is not statistically significant; all other 

variables included are significant at 95-percent confidence level. 

Table 50. Statistical output of NB model estimation for ROR crash after matching (GD). 

Variables Coef. S.E. 

Constant -3.616 1.097 

Natural logarithm of AADT 0.396 0.129 

Presence of guiderail with delineators (1 if present; 0 otherwise)* 0.058 0.158 

Degree of curvature 0.111 0.020 

Presence of speed difference above 0 (1 if present; 0 otherwise) 0.596 0.205 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a is not applicable; * represents the treatment variable is not statistically significant; all other 

variables included are significant at 95-percent confidence level. 

110 
Safety Effect of Guiderail (G only) 

Table 51. Statistical output of NB model estimation for nighttime crash after matching 

(GD). 

Variables Coef. S.E. 

Constant -4.991 1.546 

Natural logarithm of AADT 0.522 0.180 

Presence of guiderail with delineators (1 if present; 0 otherwise)* -0.157 0.218 

Degree of curvature 0.070 0.033 

Presence of speed difference above 0 (1 if present; 0 otherwise) -- -- 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a means not applicable; — means the variable is not significant thus excluded from the model; * 

represents the treatment variable is not statistically significant; all other variables included are significant 

at 95-percent confidence level. 

Table 52. CMF estimates of guiderail with delineators (GD). 

Guiderail with Delineator Crash Type Estimate 95-percent CI 95-percent CI 

CMF Total crash 0.971 0.761 1.239 

CMF Fatal injury 0.979 0.711 1.350 

CMF ROR crash 1.059 0.776 1.445 

CMF Nighttime crash 0.855 0.558 1.309 

A standard NB regression model was estimated for all the crash types (see table 53, note: n/a is 

not applicable; * represents the treatment variable which is statistically significant; all other variables 

included are significant at 95-percent confidence level. 

table 54, table 55, and table 56) using the before matching data. The variables included in the 

models show the association between expected total crashes and the covariates in the model. 

Negative coefficients of the variables indicate a decrease in crash frequency when those features 

are present along horizontal curves. The model estimates indicate that the presence of guiderail 

in curves is expected to reduce all crash types. However, those estimates are produced from the 

unbalanced raw data, and may be influenced by selection bias. 

111 
Table 53. Statistical output of the cross-sectional NB regression for total crashes (G only). 

Variable Coef. S.E. 

Constant -5.789 0.544 

Natural logarithm of AADT 0.708 0.061 

Presence of guiderail 

(1 if present; 0 otherwise)* 

-0.310 0.116 

Degree of curvature 0.089 0.009 

Presence of curve shoulder width under 4 ft 

(1 if present; 0 otherwise) 

0.227 0.088 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.223 0.117 

Presence of intersection 

(1 if present; 0 otherwise) 

0.749 0.073 

Indicator of Pennsylvania 

(1 if Pennsylvania; 0 Indiana) 

-0.434 0.079 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a is not applicable; * represents the treatment variable which is statistically significant; all other 

variables included are significant at 95-percent confidence level. 

112 
Table 54. Statistical output of the cross-sectional NB regression for fatal and injury (G 

only). 

Variables Coef. S.E. 

Constant -5.870 0.779 

Natural logarithm of AADT 0.560 0.087 

Presence of guiderail (1 if present; 0 otherwise)* -0.240 0.163 

Degree of curvature 0.084 0.009 

Presence of curve shoulder width under 4 ft (1 if present; 0 otherwise) 0.362 0.123 

Presence of speed difference above 0 

(1 if present; 0 otherwise) -- -- 

Presence of intersection (1 if present; 0 otherwise) 0.612 0.103 

Indicator of Pennsylvania (1 if Pennsylvania; 0 Indiana) 0.201 0.103 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a not applicable; -- means the variable is not significant thus excluded from the model; * 

represents the treatment variable and is not statistically significant; all other variables included are 

significant at 95-percent confidence level; 

113 
Table 55. Statistical output of the cross-sectional NB regression for ROR crash (G only). 

Variables Coef. S.E. 

Constant -4.971 0.638 

Natural logarithm of AADT 0.528 0.072 

Presence of guiderail (1 if present; 0 otherwise)* -0.128 0.130 

Degree of curvature 0.096 0.009 

Presence of curve shoulder width under 4 ft (1 if present; 0 otherwise) 0.410 0.104 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.329 0.126 

Presence of intersection (1 if present; 0 otherwise) 0.738 0.084 

Indicator of Pennsylvania (1 if Pennsylvania; 0 Indiana) -0.435 0.091 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a is not applicable; * represents the treatment variable and is not statistically significant; all other 

variables included are significant at 95-percent confidence level. 

114 
Table 56. Statistical output of the cross-sectional NB regression for nighttime crash (G 

only). 

Variables Coef. S.E.

Constant -5.279 0.719

Natural logarithm of AADT 0.576 0.083 

Presence of guiderail (1 if present; 0 otherwise)* -0.166 0.147 

Degree of curvature 0.076 0.011 

Presence of curve shoulder width under 4 ft (1 if present; 0 otherwise) -- -- 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.344 0.157 

Presence of intersection (1 if present; 0 otherwise) 0.607 0.098 

Indicator of Pennsylvania (1 if Pennsylvania; 0 Indiana) -0.555 0.110 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a not applicable; -- means the variable is not significant thus excluded from the model; * 

represents the treatment variable and is not statistically significant; all other variables included are 

significant at 95-percent confidence level. 

Propensity Score Matching 

Table 57 shows the configuration of propensity score matching. The matching distance is defined 

by the propensity score, which is the probability of the curves receiving the treatment (G only). 

In order to yield quality matches, 1:1 NN matching is applied with a caliper width of 0.2. 

Considering the relatively small sample size in the treatment and reference group, matching with 

replacement is applied. The statistical output of estimated propensity score model is shown in 

table 58. The covariates included in the model are the variables related to both the crash outcome 

and treatment assignment. 

115 
Table 57. Propensity score matching configuration (G only). 

Matching configuration Matching configuration 

Distance Propensity score 

Algorithm Nearest neighbour matching 

Ratio 1:1 

Replacement Without replacement 

Caliper width 0.2 

Table 58. Statistical output of propensity score model estimation (G only). 

Variable Coef. S.E. z-statistic p-value 

Constant -0.434 0.783 -0.560 0.579 

Natural logarithm of AADT 0.064 0.090 0.720 0.474 

Degree of curvature 0.080 0.013 6.290 <0.001 

Curve shoulder width under 4 ft 

(1 if present; 0 otherwise) 

-1.485 0.115 -12.890 <0.001 

Presence of chevron signs or curve arrow 

(1 if present; 0 otherwise) 

0.076 0.288 0.260 0.792 

Presence of speed difference above 0 

(1 if present; 0 otherwise) 

0.582 0.171 3.400 0.001 

Presence of intersection in the curve 

(1 if present; 0 otherwise) 

-0.028 0.112 -0.250 0.802 

Indicator of Pennsylvania 

(1 if Pennsylvania; 0 Indiana) 

0.601 0.114 5.290 <0.001 

Natural logarithm of curve length 1.0000 Offset n/a n/a 

Note: Wald chi-square(7) = 260.35; Log-likelihood at convergence = -1216.4987; n/a not applicable. 

There were 425 out of 435 observations in the treatment group that were matched with 425 

observations in the control group. A total of 10 treatment observations were unmatched and 

discarded since there were no observations within the caliper width in the reference group. Table 

59 and table 60 show the summary statistics before and after matching in each group. Figure 41 

and figure 42 show the distribution of the propensity scores in the treatment and reference groups 

before and after matching. The distribution of propensity scores before matching indicates 

116 
significant differences between the treatment and reference groups. Most of the observations in 

the reference group have propensity scores between 0 and 0.1, indicating low probabilities to 

receive the treatment. On the other hand, the propensity scores in the treatment group are 

distributed between 0 and 0.4. Although the shapes of the distributions are quite different, there 

is enough common support to match the treatment and reference groups. 

Table 59. Summary of variables before matching (G only). 

Variables Treatment 

Mean 

Treatment 

S.D. 

Reference 

Mean 

Reference 

S.D. 

Propensity score 0.189 0.109 0.113 0.086 

ln(AADT) 8.298 0.597 8.173 0.684 

ln(length) -1.737 0.493 -1.801 0.520 

Degree of curvature 4.098 4.049 3.827 4.836 

Curve shoulder width larger than 4 

ft 0.483 0.500 0.818 0.386 

Presence of chevron signs or curve 

arrows 

0.069 0.254 0.061 0.239 

Speed difference larger than 0 0.149 0.357 0.134 0.341 

Presence of intersection 0.529 0.500 0.497 0.500 

Indicator of Pennsylvania 0.471 0.500 0.395 0.489 

Table 60. Summary of variables after matching (G only). 

Variables Treatment 

Mean 

Treatment 

S.D. 

Reference 

Mean 

Reference 

S.D. 

Propensity score 0.184 0.104 0.182 0.106 

ln(AADT) 8.283 0.594 8.286 0.667 

ln(length) -1.750 0.477 -1.749 0.527 

Degree of curvature 4.151 4.076 4.004 6.419 

Curve shoulder width larger than 4 

ft 0.494 0.501 0.504 0.501 

Presence of chevron signs or curve 

arrows 

0.071 0.256 0.068 0.252 

Speed difference larger than 0 0.137 0.344 0.139 0.346 

Presence of intersection 0.522 0.500 0.508 0.501 

Indicator of Pennsylvania 0.459 0.499 0.464 0.499 

117 
20 

l!I 

0 

.... __ _ 

01 D.2 03 0 4 

propensity score 

oroup □ ,___ CJ --

01 0.2 03 0 4 

propensity score 

group □ ....,._ CJ -

Figure 41. Graph. Propensity score distributions before matching (G only). 

Figure 42. Graph. Propensity score distributions after matching (G only). 

Covariate Balance Assessment 

Table 61 and table 62 show the mean and absolute standardized mean difference ASMD of the 

propensity score and each covariate before and after matching. An ASMD closer to zero 

indicates better balance of the covariates between the treatment and reference groups. An ASMD 

larger than 0.20 indicates a statistically significant difference between the treatment and 

reference groups. As shown in table 61, the ASMD of the propensity score is reduced by 98.4 

percent, from 0.778 to 0.012. The average ASMD is reduced from 0.176 to 0.014 as a result of 

matching. The last column in table 62 shows that matching significantly improved the balance 

among all covariates. The ASMD comparison of each covariate before and after matching is 

shown in figure 43. Compared to the before-matching data, all of the ASMD values are close to 

118 
zero after matching, indicating that the covariates are similar in the treatment and reference 

groups. 

Table 61. Mean and ASMD difference before and after matching (G only). 

Variable 

Mean 

Difference 

Before 

Mean 

Difference 

After 

ASMD 

Before 

ASMD 

After 

Percentage 

of Balance 

Improved 

Propensity 

score 

0.077 0.001 0.778 0.012 98.4% 

Table 62. Mean and ASMD covariates before and after matching (G only). 

Covariates 

Mean 

Difference 

Before 

Mean 

Difference 

After 

ASMD 

Before 

ASMD 

After 

Percentage 

of Balance 

Improved 

ln(AADT) 0.125 -0.003 0.194 0.005 97.4% 

ln(length) 0.063 -0.001 0.125 0.002 98.7% 

Degree of curvature 0.271 0.146 0.061 0.027 46.0% 

Curve shoulder width larger than 4 ft -0.335 -0.009 0.750 0.019 97.2% 

Presence of chevron signs or curve 

arrows 

0.008 0.002 0.034 0.009 71.5% 

Speed difference larger than 0 0.015 -0.002 0.044 0.007 84.6% 

Presence of intersection 0.032 0.014 0.064 0.028 55.8% 

Indicator of Pennsylvania 0.0767 -0.0047 0.155 0.009 93.9% 

Mean n/a n/a 0.176 0.014 n/a 

Note: n/a not applicable. 

119 
0 

0 

--•---•--

0 

0 

• 

0 

--·-- 0 

• 

0 

• 

0 

--•--

0.800 

ASMD 

0.700 

0.600 

0.500 

0.400 

0.300 

0.200 

0.100 

0.000 

ln(AADT) ln(length) Degreeo Curve 

curvature shoulder 

width larger 

than 4 ft 

Presence of 

chevron signs 

or curve 

arrows 

Speed 

difference 

larger than 0 

Presence of 

intersection 

Indicator of 

Pennsylvania 

Before matching After matching • 

Figure 43. Graph. ASMD before and after matching (G only). 

CMF Estimates 

Table 63, table 64, table 65, table 66, and table 67 show a NB regression model after matching, 

as well as the CMF estimates of each crash type. The CMF point estimates are all less than 1.0 

for total crashes and fatal and injury crashes, indicating that guiderail offers a safety benefit for 

these crash types along horizontal curves on two-lane roadways. For the ROR-related and nighttime crash frequency, the presence of only guiderail along horizontal curves has a CMF point 

estimate great than 1.0. However, all 95-percent confidence intervals for the CMFs contain 1.0, 

suggesting that additional research should be completed to compile a larger sample of study 

sites. 

120 
Table 63. Statistical output of NB model estimation for total crashes after matching (G 

only). 

Variable Coef. S.E. 

Constant -4.551 1.127 

Natural logarithm of AADT 0.539 0.129 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

-0.168 0.144 

Degree of curvature 0.097 0.015 

Presence of curve shoulder width under 4 ft 

(1 if present; 0 otherwise) -- -- 

Presence of intersection 

(1 if present; 0 otherwise) 

0.703 0.149 

Indicator of Pennsylvania 

(1 if Pennsylvania; 0 Indiana) -- -- 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a not applicable; -- means the variable is not significant thus excluded from the model; 

*represents the treatment variable and is not statistically significant; all other variables included are 

significant at 95-percent confidence level. 

121 
Table 64. Statistical output of NB model estimation for fatal and injury after matching (G 

only). 

Variable Coef. S.E. 

Constant -2.891 1.572 

Natural logarithm of AADT 0.226 0.179 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

-0.324 0.205 

Degree of curvature 0.090 0.018 

Presence of curve shoulder width under 4 ft 

(1 if present; 0 otherwise) -- -- 

Presence of intersection 

(1 if present; 0 otherwise) 

0.398 0.221 

Indicator of Pennsylvania 

(1 if Pennsylvania; 0 Indiana) 

0.398 0.221 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a not applicable; -- means the variable is not significant thus excluded from the model; 

*represents the treatment variable and is not statistically significant; all other variables included are 

significant at 95-percent confidence level. 

122 
Table 65. Statistical output of NB model estimation for ROR crash after matching (G only). 

Variable Coef. S.E. 

Constant -4.482 1.400 

Natural logarithm of AADT 0.445 0.159 

Presence of guiderail with delineators 

 (1 if present; 0 otherwise)* 

0.088 0.171 

Degree of curvature 0.096 0.016 

Presence of curve shoulder width under 4 ft 

(1 if present; 0 otherwise) 

0.400 0.183 

Presence of intersection 

(1 if present; 0 otherwise) 

0.833 0.185 

Indicator of Pennsylvania 

(1 if Pennsylvania; 0 Indiana) 

-0.459 0.187 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a not applicable; *represents the treatment variable and is not statistically significant; all other 

variables included are significant at 95-percent confidence level. 

123 
Table 66. Statistical output of NB model estimation for nighttime crash after matching (G 

only). 

Variable Coef. S.E. 

Constant -6.158 1.612 

Natural logarithm of AADT 0.625 0.181 

Presence of guiderail with delineators 

(1 if present; 0 otherwise)* 

0.026 0.196 

Degree of curvature 0.065 0.019 

Presence of curve shoulder width under 4 ft 

(1 if present; 0 otherwise) 

0.394 0.204 

Presence of intersection 

(1 if present; 0 otherwise) 

0.882 0.215 

Indicator of Pennsylvania 

(1 if Pennsylvania; 0 Indiana) 

-0.460 0.212 

Natural logarithm of length (offset) 1.000 n/a 

Note: n/a not applicable; *represents the treatment variable and is not statistically significant; all other 

variables included are significant at 95-percent confidence level. 

Table 67. CMF estimates of guiderail with delineators (G only). 

Guiderail Crash Type Estimate 95-percent CI 95-percent CI 

CMF Total crash 0.845 0.638 1.119 

CMF Fatal injury 0.723 0.484 1.080 

CMF ROR crash 1.092 0.781 1.528 

CMF Nighttime crash 1.026 0.699 1.507 

Disaggregate Analysis 

The objective of the disaggregate analysis was to verify if the safety effect estimates are 

consistent under differing application scenarios. In this study, the degree of curve was 

disaggregated into separate categories to determine if the CMFs for guiderail with delineators or 

guiderail only differed based on curve sharpness. The data were stratified at a degree of 

curvature threshold equal to four. The CMFs were estimated using the propensity score matching 

method for each degree of curvature category. 

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Guiderail with Delineators 

Base on the disaggregation, there were 101 sites (505 observations) included in the category 

when the degree of curve is greater than 4, including 37 treatment and 64 reference sites. There 

were 247 sites (1235 observations) assigned to the category with a degree of curve less than 4, 

including 64 treatment and 183 reference sites. Table 68 and table 69 show the summary 

statistics of each crash type and traffic volume for the disaggregate data. 

Table 68. Summary mean for each degree of curvature category (GD). 

Category Observation Total 

Crash 

Fatal 

and 

Injury 

ROR 

Crash 

Nighttime 

Crash AADT 

Degree of curvature ≥ 4 505 0.287 0.154 0.248 0.113 2757 

Degree of curvature < 4 1235 0.301 0.158 0.167 0.100 4159 

Table 69. Summary standard deviation for each degree of curvature category (GD). 

Category Observation Total 

Crash 

Fatal 

and 

Injury 

ROR 

Crash 

Nighttime 

Crash AADT 

Degree of curvature ≥ 4 505 0.583 0.408 0.538 0.341 2113 

Degree of curvature < 4 1235 0.611 0.413 0.431 0.326 2416 

Table 70 and table 71 show the disaggregate CMF estimates for each crash type. With the 

exception of the ROR crash type in the degree of curve greater than 4 category, all CMF point 

estimates are lower than 1.0. For sharper curves, with a degree of curvature equal to or greater 

than 4, the CMFs for each crash type (excluding total crashes) is lower relative to the flatter 

curve category. This suggests that guiderail with delineators may offer greater safety benefits on 

sharp horizontal curves relative to flat horizontal curves. However, the 95-percent confidence 

intervals include 1.0 for all CMFs, so additional research is recommended to increase the sample 

size of the guiderail with delineators treatment. 

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Table 70. Disaggregate analysis for CMF estimates using a degree of curvature greater 

than or equal to four, for crash type using propensity score matching (GD). 

Category Total Crash Fatal Injury ROR Crash Nighttime Crash 

CMF 0.976 0.871 0.845 0.622 

95-percent confidence interval 0.576 0.423 0.475 0.257 

95-percent confidence interval 1.654 1.791 1.503 1.500 

Table 71. Disaggregate analysis for CMF estimates using a degree of curvature less than 

four, for crash type using propensity score matching (GD). 

Category Total Crash Fatal Injury ROR Crash Nighttime Crash 

CMF 0.931 0.933 1.173 0.706 

95-percent confidence interval 0.702 0.646 0.804 0.435 

95-percent confidence interval 1.234 1.348 1.712 1.146 

Guiderail 

There were 192 sites (960 observations) assigned to the category of degree of curvature larger 

than 4, including 26 treatment sites and 166 reference sites. There were 521 sites (2,605 

observations) assigned to the degree of curvature smaller than 4 category, including 61 treatment 

sites and 460 reference sites. Table 72 and table 73 show the summary statistics of each crash 

type and traffic volume for the disaggregate data. 

Table 72. Summary mean for each degree of curvature category (G only). 

Category Observations Total 

Crash 

Fatal 

Injury 

ROR 

Crash 

Nighttime 

Crash AADT 

Degree of curvature ≥ 4 960 0.443 0.152 0.325 0.191 3273 

Degree of curvature < 4 2605 0.477 0.148 0.264 0.185 4804 

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Table 73. Summary standard deviation for each degree of curvature category (G only). 

Category Observations Total 

Crash 

Fatal 

Injury 

ROR 

Crash 

Nighttime 

Crash AADT 

Degree of curvature ≥ 4 960 0.966 0.426 0.747 0.544 2114 

Degree of curvature < 4 2605 1.368 0.434 0.669 0.540 2850 

Table 74 and table 75 show the disaggregate CMF point estimates for each crash type. All CMFs 

for flatter curves (degree of curve smaller than 4) were lower than the CMFs for the sharper 

curves. This suggests that installing guiderail on flat the horizontal curves on two-lane rural 

highways may offer greater safety benefits relative to installing guiderail on sharper horizontal 

curves. The CMFs for ROR and nighttime crashes on sharp horizontal curves have point 

estimates that exceed 1.0. 

Table 74. Disaggregate analysis for CMF estimates degree of curvature greater than or 

equal to four, for crash types using propensity score matching (G only). 

Category Total Crash Fatal Injury ROR Crash Nighttime Crash 

CMF 0.954 0.943 1.159 1.082 

95-percent confidence interval 0.576 0.493 0.665 0.564 

95-percent confidence interval 1.581 1.802 2.021 2.074 

Table 75. Disaggregate analysis for CMF estimates for degree of curvature less than four, 

for crash types using propensity score matching (G only). 

Category Total Crash Fatal Injury ROR Crash Nighttime Crash 

CMF 0.805 0.647 0.868 1.001 

95-percent confidence interval 0.551 0.377 0.536 0.584 

95-percent confidence interval 1.178 1.108 1.406 1.714 

Summary of Results 

Table 76 shows the expected CMF effect sizes for each crash type based on the literature review 

and engineering intuition. An up-arrow indicates a negative safety effect, or a CMF larger than 

1.0, while a down-arrow indicates a positive safety effect, or a CMF smaller than 1.0. A twosided horizontal arrow indicates both safety benefits and dis-benefits are possible. As shown in 

table 32, table 33, table 34, table 35, table 36, and table 37, guiderail with delineators, and 

delineators only were expected to increase total crash frequency but reduce the fatal and injury 

crash frequency. According to the literature review, the presence of guiderail has been shown to 

both positively and negatively affect total crash frequency but has positive safety effects on fatal 

and injury crashes. For ROR crashes, the presence of guiderail (whether it is with delineators or 

not) is expected to increase the expected crash frequency, which was also indicated in the 

literature. The presence of delineators was expected to be an effective safety countermeasure 

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with regards to nighttime crashes, which has also been verified in the literature. However, the 

presence of guiderail only is expected to increase nighttime crash frequency. 

Table 76. Expected CMFs of the countermeasures for each crash type. 

Treatment Total Crash Fatal Injury ROR Crash Dark Crash 

Guiderail with delineator ↑ ↓ ↑ ↓

Guiderail ↔ ↓ ↑ ↑

Delineator ↑ ↓ ↓ ↓

Table 77. Summary of CMF estimates for all sites of guiderail with delineator, guiderail 

only, and delineators. 

Safety Effect Total Crash Fatal Injury ROR Crash Nighttime Crash 

CMFgd 0.971 0.979 1.059 0.855 

CMFg 0.845 0.723 1.092 1.026

 CMFd* 1.149 1.354 0.970 0.833 

Note: * the safety effect of delineators (CMFd) is estimated by taking the ratio of CMFgd and CMFg. 

Table 78. Summary of CMF estimates for degree of curvature greater than or equal to four 

of guiderail with delineator, guiderail only, and delineators. 

Safety Effect Total Crash Fatal Injury ROR Crash Nighttime Crash 

CMFgd 0.976 0.871 0.845 0.622 

CMFg 0.954 0.943 1.159 1.082 

CMFd* 1.023 0.924 0.729 0.575

 Note: * the safety effect of delineators (CMFd) is estimated by taking the ratio of CMFgd and CMFg. 

Table 79. Summary of CMF estimates for degree of curvature less than four of 

guiderail with delineator, guiderail only, and delineators. 

Safety Effect Total Crash Fatal Injury ROR Crash Nighttime Crash 

CMFgd 0.931 0.933 1.173 0.706 

CMFg 0.805 0.647 0.868 1.001 

CMFd* 1.156 1.443 1.351 0.706

 Note: * the safety effect of delineators (CMFd) is estimated by taking the ratio of CMFgd and CMFg. 

As shown in table 77, table 78, and table 79 the CMF point estimates from the present study 

were often consistent with expectations. The CMF estimates of guiderail with delineators 

(CMFgd), and guiderail only (CMFg) were used to derive CMF estimates for delineators only 

(CMFd). Regarding the safety effect of the only presence of guiderail, the results show that it has 

safety benefits for total crashes, as well as fatal and injury crashes. The estimates are consistent 

with expectations. However, for ROR and nighttime crashes, is the CMFs for guiderail exceed 

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1.0 in all conditions, except for the ROR crash type in mild curves. These results are also 

consistent with engineering expectations. 

The CMF for delineators (CMFd) are inferred from the ratio of CMFgd relative to CMFg. The 

results indicate that all the CMFd for total crashes are larger than 1.0, which is consistent with 

engineering expectation. However, for sharp curves, the CMF for delineators is closer to 1.0 

when compared to the CMF for mild curves. Regarding fatal and injury crashes, the CMF for 

delineators is less than 1.0 for sharp curves, but greater than 1.0 for mild curves. Similar findings 

resulted for ROR crashes. For nighttime crashes, the CMF for delineators was less than 1.0 for 

both sharp and flat horizontal curves. The CMFs were generally consistent with engineering 

expectations for sharper horizontal curves. 

DISCUSSION AND CONCLUSIONS 

This study used the RID to evaluate the safety effects of guiderail only, guiderail with 

delineators, and delineators along horizontal curves on two-lane rural highways in Pennsylvania. 

A propensity scores-potential outcomes framework was used to compare segments of roadway 

with the treatment of interest to similar roadways without the treatment. The results show that 

guiderail with delineators have safety benefits for total crashes, fatal and injury crashes, ROR, 

and nighttime crashes on horizontal curves that are four degrees or sharper. On flatter horizontal 

curves, the safety effects are also positive for total, fatal and injury, and nighttime crashes, but 

the present dataset does not show a ROR crash safety benefit for guiderail with delineators on 

horizontal curves that are flatter than four degrees. 

For guiderail only, safety benefits were found for total and fatal and injury crashes on sharp 

horizontal curves, while the CMFs exceeded 1.0 for ROR and nighttime crashes on sharp curves. 

Adding guiderail to the roadside introduces a fixed object, so an increase in ROR crashes on 

sharp horizontal curves is consistent with expectations. Similarly, at night, guiderail without 

delineators will have limited visibility, so it was expected that expected crash frequencies at 

night may increase when guiderail is present along horizontal curves. Based on the present study, 

the presence of guiderail appears to offer total crash, fatal and injury crash, and ROR crash 

benefits on flat horizontal curves. This may be the result of the decreased likelihood that vehicles 

will leave the roadway on flat horizontal curves. 

The CMFs for delineators were derived from the guiderail with delineators and guiderail only 

CMFs. On curves sharper than four degrees, delineators offered a safety benefit relative to fatal 

and injury, ROR, and nighttime crashes, presumably because the added guidance to drivers is 

helping to define sharp curves and subsequently lowering travel speeds and reducing severe 

crash types at night. On flatter horizontal curves, the CMFs for delineators exceed 1.0 for total, 

fatal and injury, and ROR crashes. The delineators may be promoting higher speeds on these 

curves because the delineators make the curve appear flat, thus promoting high-speed roadway 

departure events. 

The data in this study were acquired from Indiana and Pennsylvania. It is recommended that 

additional two-lane rural highway curves be identified in other States to confirm the results 

presented herein. In particular, this study was unable to consider guiderail or delineator 

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effectiveness in States with significantly different geographic or climatic conditions. Further, 

information related to the offset of the roadside barrier was not available in the RID data, and the 

offset may affect the frequency and severity of crashes on horizontal curves. 

130 
CHAPTER 7. HORIZONTAL CURVE WARNING PAVEMENT MARKINGS 

Horizontal curve warning pavement markings are a safety treatment that includes an arrow in the 

direction of the curve with the word “slow” under the arrow, painted on the road located near the 

beginning of the horizontal curve in the direction of travel. An alternative version of this 

treatment includes the curve direction arrow or a speed advisory in place of the word “slow.” 

Figure 44 shows the curve-slow version of the treatment. The objective of this treatment is to 

warn drivers of an upcoming, sharp horizontal curve. The intended purpose of the pavement 

marking is to reduce operating speeds when entering a curve, thereby reducing roadway 

departure crashes. No previous studies have investigated the safety effects of this treatment. 

The objective of this evaluation is to analyze the safety effectiveness of the horizontal curve 

warning pavement marking and to develop crash modification factors (CMFs) for its use. 

Figure 44. Photo. Horizontal curve warning pavement marking (Retting and Farmer, 

1998). 

BACKGROUND 

Published research on the horizontal curve warning pavement marking has focused on 

operational evaluations. A speed evaluation of this treatment by Retting and Farmer (1998) 

involved an arrow curved to the left with the word “slow” painted beneath it at a location 

approximately 220 ft before the point of curvature (PC) of a left-hand horizontal curve. A single 

curve on a two-lane suburban highway in northern Virginia with a paved roadway width of 20 ft 

received the treatment. A separate curve on the same highway was used as a control site; only 

this curve did not contain the horizontal curve pavement marking warning. The posted speed 

limit was 35 mph, while an advisory speed of 15 mph was posted approximately 500 ft before 

the curve with the treatment. 

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Vehicle operating speeds were collected at locations 90-ft prior to the PC as well as at a location 

650 ft prior to the PC of the treated curve. Speeds at the control curve were collected 100 ft prior 

to the PC. Operating speed data were collected five months prior to installation of the pavement 

marking and two weeks after installation. Logistic regression was used to model the effect of the 

pavement marking on vehicle operating speeds. The results indicated a statistically significant 

decrease in mean operating speeds at the location before the PC, based on a comparison of 

operating speeds at the treatment and the control sites, before and after the pavement marking 

sign was deployed. The magnitude of the speed reduction was 7 percent (2.4 mph) after the 

horizontal curve warning pavement marking was implemented. 

The on-pavement curve warning pavement markings were also evaluated by Hallmark et al. 

(2012) This study included markings at two horizontal curve locations on two-lane rural 

highways in Iowa. No comparison locations were used in the evaluation. Operating speed data at 

each of the curves were collected one month before installation, one month after installation, and 

12 months after installation of the treatments. Vehicle speeds were collected at the PC, midpoint 

of the horizontal curve, and point of tangency (PT) at each curve location. Changes in mean 

speed for each of the locations were then analyzed using t-tests. The percentage of vehicles 

exceeding the posted speed limit was also analyzed using a test of proportions. 

When aggregated, the results indicated that the curve warning pavement markings were not 

effective in reducing either the mean or 85th-percentile operating speeds in the short- or longterm after periods at both curve locations. When considering each curve separately, the results 

indicated increased speeds at one curve and decreased speeds at the second curve location. 

In summary, the safety effects of horizontal curve pavement marking warning signs have not be 

evaluated. The operational effects, based solely on operating speed measures, are not clear. 

Research has found that the horizontal curve pavement markings reduce operating speeds when 

approaching the curve, while other research has found that operating speed within the limits of 

the curve are not affected by the markings. 

ANALYSIS METHOD 

An observational before-after safety study is considered a robust evaluation method for assessing 

the effectiveness of safety countermeasures. This method requires that data be available from 

both before and after the implementation of the countermeasure. An overview of the empirical 

Bayes (EB) method is provided below: (Hauer 1997, Persaud and Lyon 2007, Park et al. 2012) 

 Step 1: Predict what the safety performance would have been in the after period had the 

countermeasure not been implemented. 

 Step 2: Estimate what the actual safety performance was in the after period with the 

countermeasure. 

 Step 3: Compare the results of Step 1 and Step 2. 

In Step 1, a reference group is used to account for the effects of traffic volume and temporal 

effects on safety due to the variation in weather, demographics, and crash reporting. This is done 

132 
by estimating a safety performance function (SPF) relating crash frequency to traffic flow and 

other safety-influencing features present at the study sites. The development of the SPF in this 

evaluation is based on a reference group of horizontal curve sites which were not treated with 

any safety countermeasures during the analysis period. 

Variables considered for SPF estimation included crash, traffic volume, and roadway and 

roadside features. Standard negative binomial (NB) regression methods were used to estimate the 

SPFs using the STATA statistical software. 

The method described below is consistent with Persaud and Lyon (2007). In the EB method, the 

expected number of crashes had no treatment been applied (for the after period – N ) is EB , After 

based on the SPF, which is first used to estimate the number of crashes expected in each year of 

the before period at locations with traffic volumes and other site characteristics similar to the 

treatment site being analyzed. The sum of the annual SPF estimates N pred ,before  are combined 

with the count of crashes N in the before period at the treatment site to obtain an Observed ,before 

estimate of the expected number of crashes N EB ,before  before the treatment was applied. This 

estimate of N was developed as seen in figure 45. EB ,before 

Figure 45. Equation. Expected number of crashes in the before period EB analysis. 

Given that the SPF was specified using the standard negative binomial, the weight w is estimated 

as follows in figure 46. 

Figure 46. Equation. EB weighting factor. 

A factor is then applied to N to account for the length of the after period and differences EB ,before 

in traffic volumes between the before and after periods. This factor is the sum of the annual SPF 

predictions for the after period divided by N , the sum of the predictions in the before pred ,before 

period. After applying this factor, an estimate of N results. Additionally, an estimate of EB , After 

the variance of the expected number of crashes that would have occurred in the after period 

without the treatment was computed following the method described by Persaud and Lyon 

(2007). 

The estimate of N EB , After is summed over all sites in a treatment group of interest  N EB,after 

and compared with the count of crashes during the after period in that group  N Obs ,after . The 

variance of N is also summed over all sections in the group of interest (i.e., EB , After 

VARNEB,after ). 

The index of safety effectiveness () is determined using the following in figure 47. 

133 
 

 

 

 

 

Figure 47. Equation. Index of effectiveness. 

The standard deviation of  is determined using the following in figure 48. 

 

 

 

 

 

Figure 48. Equation. Standard deviation of index of effectiveness. 

The 95-percent confidence interval for  was found by adding and subtracting 1.96 times 

stdev   from . 

SPF Estimation 

The general functional form of the SPF to be estimated is shown below in figure 49 and is the 

same for all crash types considered (e.g., SVROR or total crashes). The expected crash frequency 

(per mi per year) was the dependent variable and the traffic volume (AADT), and other sitecharacteristic data (X1,..., Xn) were entered into the model as predictor (independent) variables. 

Only data from the reference group were used to estimate the SPFs (i.e., horizontal curves 

without the treatment). The segment length variable (L) is the horizontal curve length. The 0 

term is the regression constant, while the remaining  (Length, AADT, 1, ..., n) were estimated 

from the data sample using NB regression. 

 

Figure 49. Equation. SPF. 

DATA 

Data for this project were collected and compiled using several existing databases maintained by 

Penn State and the Pennsylvania Department of Transportation (PennDOT). The roadway 

inventory database (RID) was developed at Penn State using PennDOT roadway inventory data, 

on-line video photologs, and Google Earth, and included all two-lane rural highways owned and 

134 
operated by PennDOT. It should be noted that PennDOT codifies the State roadway network 

using four digits (e.g., State route 2024), but this study only considers roadways with three or 

fewer digits (e.g., State route 0823, 0016, or 0006). This is because traffic volume data on the 

four-digit State routes are often missing because these roadways are often low-speed, lowvolume roadways that traverse short lengths. The online video photologs are maintained by 

PennDOT and were used to collect roadside hazard rating (based on the 1 to 7 scale proposed by 

Zegeer et al., 1987), the presence of centerline and shoulder rumble strips, and other pertinent 

roadway and roadside features. Google Earth was used to collect curve radius and length data. 

These variables were combined with existing variables in the PennDOT roadway inventory data, 

implementation dates and locations of the on-pavement curve markings, and crash data files to 

create the database used for this evaluation. Crash data were available for the years 2005-2013 

(inclusive). 

Horizontal curves with the on-pavement curve warning pavement markings in Pennsylvania twolane highways with installation dates between 2000 and 2015 were obtained from PennDOT. 

However, since crash data were only available for the years 2005-2013, only horizontal curves 

with treatment installations between the years 2006 and 2012 could be used in the analysis (i.e., 

that have at least one year of crash data in both the before period (i.e., treated in 2006) or at least 

one year in the after period (i.e., treated in 2012)). Thus, in the analysis, a total of 263 treated 

horizontal curves were included. This included 93 curves with installation dates in 2006, 23 in 

2007, 4 in 2008, 16 in 2009, 42 in 2010, 41 in 2011, and 44 in 2012. These curves were used as 

the treatment group. Other horizontal curves with installation dates prior to 2006 or in 2013 were 

removed from the database prior to analysis. The reference group included 21,902 horizontal 

curves on two-lane highways in Pennsylvania that did not receive the horizontal curve warning 

pavement marking at any time prior to 2014. These horizontal curves were used to estimate the 

SPFs. 

Variable definitions in the analysis database are provided in table 80. Descriptive statistics for 

the reference group are provided in table 81 and table 82. Descriptive statistics for the treated 

curves in the before period are provided in table 83 and table 84. Descriptive statistics for the 

treated curves in the after period are provided in table 85 and table 86. 

The horizontal curves with on-pavement curve warning pavement markings that were treated 

between 2006 and 2012 each only had 8 years of data in the final analysis database due to 

removing data for the year the markings were implemented (to reduce the potential bias 

associated with knowing the specific day when the markings were painted, and associated work 

zone locations around the treatment sites). All locations in the reference group contained up to 9 

years of data. There were a few curves in the reference group that traffic volumes and other data 

were missing for some years. Due to the large size of the database, the observations with missing 

values were removed from the analysis files prior to analysis. 

RESULTS 

The EB method was applied using the 263 treated curves. The target crash types were run-offroad, nighttime, nighttime run-off-road (ROR), and nighttime fatal and injury crashes. Total 

135 
crashes, as well as total fatal and injury crashes (for both day and night combined), were also 

evaluated. The estimated SPFs for each of the crash types evaluated are shown in table 87, table 

88, table 89, table 90, table 91, and table 92. As shown, the same variables were included in the 

SPFs for all crash types with the exception of not including roadside hazard rating indicator 

variables in the SPFs for nighttime, nighttime ROR, and nighttime fatal + injury crashes. The 

roadside hazard rating variables were not included in these SPFs due to high t-statistics and pvalues (e.g., p-values > 0.625) and unexpected signs and magnitudes of the estimated 

coefficients (i.e., higher ratings were associated with fewer crash frequencies). 

Table 80. Variable descriptions. 

Variable Description 

AADT Annual average daily traffic 

Length (mi) Curve length in mi 

Shoulder width (ft) Shoulder width in ft 

Degree of curve The degree of curvature 

Total crashes The total number of crashes 

Fatal + injury crashes The total number of fatal and injury crashes 

ROR crashes The total number of crashes 

Nighttime crashes The total number of crashes 

Nighttime ROR crashes The total number of crashes 

Nighttime fatal + injury crashes The total number of crashes 

Posted speed 50-55 mph If the posted speed is 50-55 mph = 1, 0 = otherwise 

Year = 2005 If the year is 2005 = , 0 = otherwise 

Year = 2006 If the year is 2006 = , 0 = otherwise 

Year = 2007 If the year is 2007 = , 0 = otherwise 

Year = 2008 If the year is 2008 = , 0 = otherwise 

Year = 2009 If the year is 2009 = , 0 = otherwise 

Year = 2010 If the year is 20010 = , 0 = otherwise 

Year = 2011 If the year is 2011 = , 0 = otherwise 

Year = 2012 If the year is 2012 = , 0 = otherwise 

Passing zone present If a passing zone is present = 1, 0 = otherwise 

Centerline rumble strips If a centerline rumble strips are present = 1, 0 = otherwise 

Shoulder rumble strips If a shoulder rumble strips are present = 1, 0 = otherwise 

Roadside hazard rating = 4 or 5 If roadside hazard rating is 4 or 5 = 1, 0 = otherwise 

Roadside hazard rating = 6 or 7 If roadside hazard rating is 6 or 7 = 1, 0 = otherwise 

136 
Table 81. Descriptive statistics for reference group (21, 902 curves). 

Variable Mean S.D. Min Max 

AADT 2597 2395 100 15,998 

Length (mi) 0.082 0.066 0 0.567 

Shoulder width (ft) 3.571 1.890 0 12 

Degree of curve 7.724 8.416 0.852 94.307 

Total crashes 0.104 0.389 0 12 

Fatal + injury crashes 0.057 0.267 0 7 

ROR crashes 0.069 0.293 0 7 

Nighttime crashes 0.040 0.214 0 6 

Nighttime ROR crashes 0.031 0.185 0 4 

Nighttime fatal + injury crashes 0.021 0.150 0 3 

Table 82. Descriptive statistics for reference group indicator variables (21, 902 curves). 

Variable Proportion in Sample 

Posted speed 50-55 mph 0.393 

Year = 2005 0.111 

Year = 2006 0.111 

Year = 2007 0.111 

Year = 2008 0.111 

Year = 2009 0.111 

Year = 2010 0.111 

Year = 2011 0.111 

Year = 2012 0.111 

Passing zone present 0.164 

Centerline rumble strips 0.215 

Shoulder rumble strips 0.069 

Roadside hazard rating = 4 or 5 0.720 

Roadside hazard rating = 6 or 7 0.244 

137 
Table 83. Descriptive statistics for treated group in the before period (263 curves). 

Variable Mean S.D. Min Max 

AADT 2802 2491 100 15,998 

Length (mi) 0.075 0.063 0.010 0.471 

Shoulder Width (ft) 3.600 1.972 0 12 

Degree of curve 10.017 13.163 0.854 94.558 

Total crashes 0.044 0.242 0 3 

Fatal + injury crashes 0.019 0.152 0 2 

ROR crashes 0.020 0.142 0 1 

Nighttime crashes 0.017 0.131 0 1 

Nighttime ROR crashes 0.012 0.110 0 1 

Nighttime fatal + injury crashes 0.008 0.090 0 1 

Table 84. Descriptive statistics for treated group in the before period indicator variables 

(263 curves). 

Variable Proportion in Sample 

Posted Speed 50-55 mph 0.416 

Year = 2005 0.269 

Year = 2006 0.174 

Year = 2007 0.150 

Year = 2008 0.146 

Year = 2009 0.130 

Year = 2010 0.087 

Year = 2011 0.045 

Year = 2012 0.000 

Passing zone present 0.182 

Centerline rumble strips 0.205 

Shoulder rumble strips 0.079 

Roadside hazard rating = 4 or 5 0.739 

Roadside hazard rating = 6 or 7 0.186 

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Table 85. Descriptive statistics for treated group in the after period (263 curves). 

Variable Mean S.D. Min Max 

AADT 2584 2258 103 14,493 

Length (mi) 0.075 0.065 0.0099 0.471 

Shoulder width (ft) 3.666 2.072 0 12 

Degree of curve 8.964 9.553 0.854 94.558 

Total crashes 0.055 0.240 0 2 

Fatal + injury crashes 0.034 0.181 0 1 

ROR crashes 0.046 0.218 0 2 

Nighttime crashes 0.026 0.159 0 1 

Nighttime ROR crashes 0.021 0.145 0 1 

Nighttime fatal + injury crashes 0.015 0.122 0 1 

Table 86. Descriptive statistics for treated group in the after period indicator variables (263 

curves). 

Variable Proportion in Sample 

Posted Speed 50-55 mph 0.371 

Year = 2005 0.000 

Year = 2006 0.000 

Year = 2007 0.083 

Year = 2008 0.103 

Year = 2009 0.107 

Year = 2010 0.121 

Year = 2011 0.158 

Year = 2012 0.195 

Passing zone present 0.169 

Centerline rumble strips 0.248 

Shoulder rumble strips 0.102 

Roadside hazard rating = 4 or 5 0.765 

Roadside hazard rating = 6 or 7 0.194 

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Table 87. Estimated SPFs for total crashes.* 

Variable Coef. S.E. P-Value 

Natural log of AADT 0.762 0.010 <0.001 

Natural log of length 0.823 0.013 <0.001 

Posted speed 50-55 mph -0.047 0.018 0.008 

Year = 2005 -0.841 0.039 <0.001 

Year = 2006 -0.214 0.033 <0.001 

Year = 2007 -0.195 0.033 <0.001 

Year = 2008 -0.028 0.032 0.375 

Year = 2009 -0.058 0.032 0.071 

Year = 2010 -0.053 0.032 0.099 

Year = 2011 -0.013 0.032 0.684 

Year = 2012 -0.449 0.035 <0.001 

Degree of curve 0.039 0.001 <0.001 

Shoulder width (ft) -0.058 0.005 <0.001 

Passing zone present -0.085 0.022 <0.001 

Centerline rumble strips 0.084 0.020 <0.001 

Shoulder rumble strips -0.024 0.031 0.435 

Roadside hazard rating = 4 or 5 0.014 0.044 0.749 

Roadside hazard rating = 6 or 7 0.035 0.047 0.452 

Constant -5.981 0.100 <0.001 

Overdispersion parameter (α) 1.724 0.048 <0.001 

Note: * represents pseudo r-square = 0.0880. 

140 
Table 88. Estimated SPFs for fatal and injury crashes.* 

Variable Coef. S.E. P-Value 

Natural log of AADT 0.727 0.013 <0.001 

Natural log of length 0.817 0.016 <0.001 

Posted Speed 50-55 mph -0.040 0.023 0.077 

Year = 2005 -0.761 0.050 <0.001 

Year = 2006 -0.139 0.042 0.001 

Year = 2007 -0.186 0.043 <0.001 

Year = 2008 -0.025 0.041 0.539 

Year = 2009 -0.023 0.042 0.575 

Year = 2010 0.012 0.041 0.773 

Year = 2011 -0.056 0.042 0.178 

Year = 2012 -0.391 0.045 <0.001 

Degree of curve 0.038 0.001 <0.001 

Shoulder width (ft) -0.051 0.006 <0.001 

Passing zone present -0.085 0.028 0.003 

Centerline rumble strips 0.094 0.025 <0.001 

Shoulder rumble strips -0.042 0.040 0.287 

Roadside hazard rating = 4 or 5 0.003 0.057 0.955 

Roadside hazard rating = 6 or 7 0.024 0.060 0.687 

Constant -6.361 0.128 <0.001 

Overdispersion Parameter (α) 1.885 0.083 <0.001

 Note: * represents pseudo r-square = 0.0785. 

141 
Table 89. Estimated SPFs for ROR crashes.* 

Variable Coef. S.E. P-Value 

Natural log of AADT 0.574 0.012 <0.001 

Natural log of length 0.835 0.015 <0.001 

Posted speed 50-55 mph -0.005 0.020 0.801 

Year = 2005 -0.959 0.047 <0.001 

Year = 2006 -0.214 0.039 <0.001 

Year = 2007 -0.247 0.039 <0.001 

Year = 2008 -0.014 0.037 0.707 

Year = 2009 -0.059 0.037 0.111 

Year = 2010 -0.049 0.037 0.188 

Year = 2011 -0.023 0.037 0.540 

Year = 2012 -0.455 0.041 <0.001 

Degree of curve 0.039 0.001 <0.001 

Shoulder width (ft) -0.068 0.006 <0.001 

Passing zone present -0.112 0.026 <0.001 

Centerline rumble strips 0.146 0.023 <0.001 

Shoulder rumble strips -0.027 0.036 0.453 

Roadside hazard rating = 4 or 5 0.022 0.052 0.681 

Roadside hazard rating = 6 or 7 0.096 0.055 0.083 

Constant -4.865 0.114 <0.001 

Overdispersion parameter (α) 0.516 0.041 <0.001 

Note: * represents pseudo r-square = 0.0699. 

142 
Table 90. Estimated SPFs for nighttime crashes.* 

Variable Coef. S.E. P-Value 

Natural log of AADT 0.730 0.016 <0.001 

Natural log of length 0.778 0.019 <0.001 

Posted speed 50-55 mph -0.035 0.026 0.182 

Year = 2005 -0.864 0.059 <0.001 

Year = 2006 -0.124 0.048 0.010 

Year = 2007 -0.224 0.049 <0.001 

Year = 2008 -0.033 0.047 0.490 

Year = 2009 -0.161 0.049 0.001 

Year = 2010 -0.090 0.048 0.060 

Year = 2011 0.006 0.047 0.894 

Year = 2012 -0.491 0.053 <0.001 

Degree of curve 0.037 0.001 <0.001 

Shoulder width (ft) -0.062 0.007 <0.001 

Passing zone present -0.045 0.032 0.163 

Centerline rumble strips 0.108 0.029 <0.001 

Shoulder rumble strips -0.058 0.046 0.204 

Constant -6.746 0.133 <0.001 

Overdispersion parameter (α) 1.690 0.110 <0.001

 Note: * represents pseudo r-square = 0.0747. 

143 
Table 91. Estimated SPFs for nighttime ROR crashes.* 

Variable Coef. S.E. P-Value 

Natural log of AADT 0.621 0.017 <0.001 

Natural log of length 0.784 0.021 <0.001 

Posted speed 50-55 mph -0.050 0.029 0.090 

Year = 2005 -0.925 0.068 <0.001 

Year = 2006 -0.095 0.054 0.077 

Year = 2007 -0.224 0.055 <0.001 

Year = 2008 -0.003 0.053 0.949 

Year = 2009 -0.159 0.055 0.004 

Year = 2010 -0.044 0.053 0.406 

Year = 2011 -0.011 0.053 0.842 

Year = 2012 -0.488 0.060 <0.001 

Degree of curve 0.038 0.001 <0.001 

Shoulder width (ft) -0.068 0.008 <0.001 

Passing zone present -0.084 0.037 0.024 

Centerline rumble strips 0.124 0.033 <0.001 

Shoulder rumble strips -0.086 0.053 0.104 

Constant -6.101 0.145 <0.001 

Overdispersion parameter (α) 1.787 0.146 <0.001 

Note: * represents pseudo r-square = 0.0634. 

144 
Table 92. Estimated SPFs for nighttime fatal and injury crashes.* 

Variable Coef. S.E. P-Value 

Natural log of AADT 0.707 0.021 <0.001 

Natural log of length 0.777 0.025 <0.001 

Posted Speed 50-55 mph -0.037 0.035 0.294 

Year = 2005 -0.791 0.079 <0.001 

Year = 2006 -0.038 0.064 0.548 

Year = 2007 -0.269 0.067 <0.001 

Year = 2008 -0.044 0.064 0.488 

Year = 2009 -0.175 0.066 0.008 

Year = 2010 -0.049 0.064 0.449 

Year = 2011 -0.053 0.064 0.409 

Year = 2012 -0.468 0.072 <0.001 

Degree of Curve 0.036 0.002 <0.001 

Shoulder width (ft) -0.055 0.009 <0.001 

Passing zone present -0.023 0.044 0.601 

Centerline rumble strips 0.144 0.039 <0.001 

Shoulder rumble strips -0.120 0.063 0.056 

Constant -7.249 0.179 <0.001 

Overdispersion parameter (α) 1.948 0.212 <0.001 

Note: * represents pseudo r-square = 0.0659. 

The results of the estimates in each of the SPFs are consistent with engineering intuition. The 

estimates for both the natural logarithm of average annual daily traffic (AADT) and natural 

logarithm of curve length are consistent with values that have been found in previous research 

and that are included in the first edition of the American Association of State Highway and 

Transportation Officials’ (AASHTO) Highway Safety Manual (HSM). (AASHTO 2010) Posted 

speed limits of 50-55 mph were found to be associated with lower crash frequencies, consistent 

with previous research (Wood and Porter 2013, Wood et al. 2015, Wood et al. 2016) and likely 

145 
due to application of more forgiving geometric design criteria on high-speed roads relative to 

low-speed roads. The SPFs also indicate that, as the degree of curve increases (curve radius 

decreases), expected crash frequency is expected to increase. As shoulder width increases, the 

expected number of crashes decreases (consistent with the HSM). Horizontal curves with passing 

zones were found to be associated with fewer crashes, likely due to having longer available sight 

distances. The findings for passing zones are also consistent with the HSM. Centerline rumble 

strips were associated with an increase in expected crash frequency along horizontal curves, 

which is consistent with previous research. (Torbic et al. 2009) Shoulder rumble strips were 

associated with a decrease in expected crashes, which is also consistent with previous research. 

(Pitale et al. 2009) The effects of the year indicator variables accounted for differences in factors 

that change over time, such as differences in weather, crash reporting, and the driving 

population. The baseline year for all models was 2013. 

The SPFs shown table 87, table 88, table 89, table 90, table 91, and table 92 were used in the 

empirical Bayes estimation procedure to develop CMFs. The values from the analysis (i.e., 

∑NObs,after, ∑NEB,after, ∑VAR(NEB,after)), as well as the estimated CMFs and 95-percent confidence 

intervals for each crash type and severity are provided in table 93 and table 94. As shown, the 

CMFs for total crashes and fatal plus injury crashes are statistically significant at the 95-percent 

confidence level while the other crash types and severities are not. However, all CMFs indicate a 

decrease in crashes due to the installation of horizontal curve warning pavement markings. The 

magnitudes of these reductions are 34.8 percent for total crashes, 30.7 percent for fatal and injury 

crashes, 23.1 percent for ROR crashes, 29.2 percent for nighttime crashes, 25.5 percent for 

nighttime ROR crashes, and 22.9 percent for nighttime fatal and injury crashes. As a result, 

horizontal curve pavement marking warnings appear to be a low-cost treatment that is effective 

in reducing crashes at horizontal curves. 

Table 93. EB analysis results. 

Crash Type Total Crashes Fatal + Injury Crashes ROR Crashes 

 0.652 0.693 0.769 

Stdev() 0.115 0.144 0.140 

 95% lower bound 0.426 0.411 0.495 

 95% upper bound 0.877 0.975 1.044 

∑NObs,after 62 38 52 

∑NEB,after 93.652 53.848 66.578 

∑VAR(NEB,after) 141.138 53.527 66.513 

146 
Table 94. EB analysis results cont. 

Crash Type Nighttime 

Crashes 

Nighttime ROR 

Crashes 

Nighttime Fatal 

+ Injury Crashes 

 0.708 0.745 0.771 

Stdev() 0.157 0.176 0.211 

 95% lower bound 0.400 0.399 0.358 

 95% upper bound 1.015 1.090 1.185 

∑NObs,after 29 24 17 

∑NEB,after 40.309 31.714 21.632 

∑VAR(NEB,after) 26.418 16.270 8.721 

CONCLUSIONS 

This chapter of the report assessed the efficacy of installing horizontal curve warning pavement 

markings in reducing crashes along horizontal curves. For the analysis, 263 treated curves from 

Pennsylvania on two-lane rural highways were used in an EB observational before-after study to 

develop CMFs. Nine years of data were used, covering the period from 2005 to 2013. The 

reference group used to develop SPFs included 21,902 curves on two-lane rural roads in 

Pennsylvania. CMFs were developed for total crashes, fatal and injury crashes, ROR crashes, 

nighttime crashes, nighttime ROR crashes, and nighttime fatal and injury crashes. 

The results of the CMFs indicated that horizontal curve warning pavement markings are 

associated with reductions of 34.8 percent for total crashes, 30.7 percent for fatal and injury 

crashes, 23.1 percent for ROR crashes, 29.2 percent for nighttime crashes, 25.5 percent for 

nighttime ROR crashes, and 22.9 percent for nighttime fatal and injury crashes. The results were 

statistically significant at the 95-percent confidence level for the total crashes as well as for the 

fatal and injury crashes. Thus, the horizontal curve pavement warning markings are effective at 

reducing total crashes along horizontal curves and should be considered a low-cost safety 

improvement for horizontal curves on two-lane rural roadways. A limitation of the present study 

is that horizontal curve pavement markings will deteriorate over time. This analysis assumes that 

the pavement markings retain their visibility once applied at the treatment locations. Future 

research should consider how the pavement marking visibility changes over time when 

estimating the SPFs and CMFs in a before-after evaluation. 

147 
148 
CHAPTER 8. CONCLUSIONS AND FUTURE RESEARCH NEEDS 

Three evaluations were performed in the present study in order to supplement the existing 

published literature on roadway departure crashes along horizontal curves of two-lane rural 

highways. The findings from these evaluations are as follows: 

1. The expected number of roadway departure crashes along a horizontal curve changes as a 

function of curve radius, radii of adjacent curves, and the upstream and downstream 

tangent lengths. Sharper upstream and downstream horizontal curves are associated with 

fewer expected roadway departure crashes based on the design consistency evaluations in 

the present study. Longer approach tangents are associated with a higher expected 

frequency of roadway departure crashes, while shorter upstream and downstream are 

associated with fewer expected roadway departure crashes. 

2. The expected number of roadway departure crashes on horizontal curves increase as the 

friction demand increases. While the posted speed limit was used as a substitute for the 

design speed in the point-mass model for this evaluation, the findings suggest that, when 

the superelevation of a horizontal curve is fixed, higher operating speeds are associated 

with higher expected roadway departure crash frequencies. 

3. Guiderail with delineators are expected to reduce total, fatal plus injury, run-off-road 

(ROR), and nighttime crashes along horizontal curves that are four degrees or sharper. 

On horizontal curves that are flatter than four degrees, guiderail with delineators are 

expected to reduce total, fatal plus injury, and nighttime crashes, but the present study did 

not find a benefit for ROR crashes on flatter curves with guiderail and delineators. 

4. When applying guiderail only to horizontal curves on two-lane rural highways, the 

expected number of total and fatal plus injury crashes decreased in the present study on 

sharp curves, while the expected number of ROR and nighttime crashes increased on 

sharp curves. The presence of guiderail on flatter curves is expected to reduce total, fatal 

plus injury, and ROR crashes based on the results of the present study. 

5. While an adequate sample of curves with delineators only could not be found from the 

roadway inventory database (RID), a crash modification factor (CMF) for delineators was 

derived based on the ratio of CMFs for guiderail with delineators (GD) and guiderail only 

(G only). On horizontal curves sharper than four degrees, delineators were found to 

reduce the expected number of fatal plus injury, ROR, and nighttime crashes. On flatter 

horizontal curves, however, delineators were associated with higher expected total, fatal 

plus injury, and ROR crashes. 

6. Horizontal curve warning pavement markings are associated with fewer expected total, 

fatal plus injury, ROR, nighttime, nighttime ROR, and nighttime fatal plus injury crashes 

on two-lane rural highways. 

There are several opportunities for future research in relation to roadway departure crashes along 

two-lane rural highways. These include, but are not limited to the following: 

1. The relationship between superelevation deficiency and safety did not reveal a 

statistically significant finding in the present study. Future research should explore the 

effects of superelevation on roadway departure crashes. 

149 
2. This research did not include operating speeds or lane position data in the safety 

evaluations using the SHRP 2 RID data. Adding speed and lane position data to the 

design consistency-safety models estimated in the present study may further uncover 

relationships between the driver, roadway infrastructure, and safety. 

3. The horizontal curves found in the RID data used in the present study did not identify an 

adequate sample of curves with only post-mounted delineators. Future research is 

recommended to identity curves that use only this treatment to offer guidance to 

motorists at night, and to perform a safety evaluation of this treatment. 

4. Develop statistical models or crash frequency for pavement marking treatments that 

consider the visibility (i.e., retroflectivity) of the markings. The visibility of pavement 

marking countermeasures changes over time, and these trends should be integrated into 

future countermeasure evaluations. 

5. The relationship between operating speed and crash frequency is not well-established. 

Efforts to better understand this may be uncovered in the Federal Highway 

Administration (FHWA) Rural Road Safety Initiative, but most transportation data 

analytics platforms (e.g., INRIX, iPEMS, etc.) collect data from probe vehicles, and may 

not reflect the entire traffic stream. 

6. The relationship between safety and several geometric design features along horizontal 

curves are not yet well established. While there are CMFs in the first edition of the 

Highway Safety Manual (HSM) for lane width, shoulder width, horizontal curve radius, 

superelevation, vertical grade, driveway density, and roadside hazard rating, the 

interaction effects are not addressed through empirical research. 

7. The in-service performance of roadside hardware is an emerging field, which offers 

opportunity to study the relationship between roadway departure events and longitudinal 

barrier systems. 

8. While the FHWA has developed minimum retroreflectivity levels for signs and pavement 

markings based on driver visibility needs, the correlation between visibility levels and 

roadway departure crashes is not fully-developed. 

150 
ACKNOWLEDGEMENTS 

This report was prepared for the FHWA Office of Safety Research and Development under 

Contract DTFH61-12-C-00032. The FHWA Technical Representative for this project was 

Joseph Cheung. 

The research team gratefully acknowledges the participation of Center of Transportation 

Research and Education at Iowa State University, Indiana Department of Transportation, North 

Carolina Department of Transportation, Pennsylvania Department of Transportation, Utah 

Department of Transportation, and Washington Department of Transportation for their assistance 

in this study. 

151 
152 
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FHWA, Offce of Safety 

Joseph Cheung 

202-366-6994

joseph.cheung@dot.gov

FHWA-SA-19-005