Safety Evaluation of Horizontal Curve

Realignment on Rural, Two-Lane Roads

PUBLICATION NO. FHWA-HRT-17-066 APRIL 2018

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
FOREWORD

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

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

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

the safety improvements identified by the National Cooperative Highway Research Program

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

and Transportation Officials (AASHTO) Strategic Highway Safety Plan. The ELCSI-PFS studies 

provide a crash modification factor and benefit–cost (B/C) economic analysis for each of the 

targeted safety strategies identified as priorities by the pooled fund member States.

This study evaluates the safety effectiveness of horizontal curve realignment by increasing the 

radius of curved roadway segments on two-lane rural roads. One objective of this strategy is to 

reduce lane departure crashes, especially run-off-road crashes. The evaluation results showed 

substantial and significant reduction in crashes (total, injury and fatal crashes, run-off-road, and 

fixed object crashes, dark crashes, and wet-road crashes). The economic analysis revealed that 

increasing the radius of a horizontally curved roadway segment on two-lane, rural roads is a costeffective safety improvement for reducing all types of crashes. This document is intended for 

safety engineers, highway designers, planners, and practitioners at State and local agencies 

involved with AASHTO Strategic Highway Safety Plan implementation.

Monique R. Evans, P.E., CPM

Director, Office of Safety

Research and Development

Notice

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

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

the use of the information contained in this document.

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

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

objective of the document.

Quality Assurance Statement

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

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

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

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

ensure continuous quality improvement.
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-17-066

2. Government Accession 

No.

3. Recipient's Catalog No.

4. Title and Subtitle

Safety Evaluation of Horizontal Curve Realignment on Rural, Two-Lane 

Roads 

5. Report Date

April 2018

6. Performing Organization Code

7. Author(s) 

Raghavan Srinivasan, Daniel Carter, Craig Lyon, and Matthew Albee

8. Performing Organization Report No.

9. Performing Organization Name and Address

VHB Highway Safety Research Center

8300 Boone Blvd., Ste. 700 University of North Carolina

Vienna, VA 22182-2626 Chapel Hill, NC 27599-3430

10. Work Unit No.

11. Contract or Grant No.

DTFH61-13-D-0001

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; August 2013–

November 2016

14. Sponsoring Agency Code

HRDS-20

15. Supplementary Notes

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

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

Development Program and Task Manager was Roya Amjadi (HRDS-20).

16. Abstract

The Development of Crash Modification Factors program conducted safety evaluation of horizontal curve realignment on rural, 

two-lane roads for the Evaluation of Low Cost Safety Improvements Pooled Fund Study. The goal of this evaluation is to 

evaluate the safety effectiveness of this strategy. This strategy sought to reduce lane departure crashes, especially run-off-road 

crashes. This study determined the crash modification factors (CMFs) associated with curve realignment using the before–after 

empirical Bayes method and compared the results from published CMFs from cross-sectional studies. This evaluation used data 

from rural, two-lane roads in California, North Carolina, and Ohio. The evaluation revealed a 68-percent reduction in total 

crashes, a 74-percent reduction in injury and fatal crashes, a 78-percent reduction in run-off-road and fixed object crashes, a 42-

percent reduction in dark crashes, and an 80-percent reduction in wet crashes, all of which were statistically significant at the 

95-percent confidence level. The results pertain to a range of site characteristics, the most important of which is the range of the 

before and after degree of curve. The average degrees of curve in the before and after periods were 18.1 (with a minimum of 3.2 

and a maximum of 52.1) and 6.9 (with a minimum of 0.0 and a maximum of 16.3), respectively. The average central angle of 

the curves was approximately 42 degrees (with a minimum of 1 and a maximum of 117). The average annual average daily 

traffic at the treated sites was about 3,500 (with a minimum of 465 and a maximum of 11,917). The average length of the 

realigned segments was 0.15 mi (with a minimum of 0.03 and a maximum of 0.60). This study compared the total crash CMFs

with the results from previous cross-sectional studies. The CMFs from this before–after evaluation are lower compared to CMFs 

estimated from two previous cross-sectional studies. The economic analysis revealed a benefit–cost ratio of 3.17:1 with a range 

of 1.75:1 to 4.38:1. There is a need for further research with a larger sample of sites to assess the reliability of the CMFs 

obtained from this before–after evaluation.

17. Key Words

Horizontal curve, rural two-lane roads, realignment, radius, degree 

of curve, lane departure crashes, safety improvements, safety 

evaluations, empirical Bayesian, run-off-road, crash modification 

factors, crash modification functions, cross-sectional studies

18. Distribution Statement

No restrictions. This document is available 

through the National Technical Information 

Service, Springfield, VA 22161.

http://www.ntis.gov

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages:

54

22. Price

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

TABLE OF CONTENTS

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

CHAPTER 1. INTRODUCTION.................................................................................................3

BACKGROUND ON STRATEGY ......................................................................................... 3

BACKGROUND ON STUDY.................................................................................................. 3

LITERATURE REVIEW ........................................................................................................ 4

Summary of Literature Review ........................................................................................... 5

CHAPTER 2. OBJECTIVE..........................................................................................................7

CHAPTER 3. STUDY DESIGN...................................................................................................9

CASE 1: SAMPLE SIZE REQUIRED TO DETECT AN EXPECTED CHANGE

IN SAFETY ............................................................................................................................... 9

CASE 2: CHANGE IN SAFETY THAT CAN BE DETECTED WITH

AVAILABLE SAMPLE SIZES............................................................................................. 10

CHAPTER 4. METHODOLOGY..............................................................................................13

CHAPTER 5. DATA COLLECTION........................................................................................17

SITE IDENTIFICATION ...................................................................................................... 17

ROADWAY CHARACTERISTICS AND TRAFFIC VOLUME...................................... 18

CRASH DATA ........................................................................................................................ 21

CHAPTER 6. DEVELOPMENT OF SAFETY PERFORMANCE FUNCTIONS ...............23

CHAPTER 7. BEFORE–AFTER EVALUATION RESULTS................................................27

AGGREGATE ANALYSIS ................................................................................................... 27

DISAGGREGATE ANALYSIS............................................................................................. 28

CHAPTER 8. ECONOMIC ANALYSIS...................................................................................33

CHAPTER 9. SUMMARY AND CONCLUSIONS..................................................................35

LIMITATIONS....................................................................................................................... 35

APPENDIX A. SITE DATA........................................................................................................37

APPENDIX B. INVESTIGATION OF CRASH LOCATION ACCURACY ISSUES

USING NORTH CAROLINA DATA........................................................................................43

ACKNOWLEDGMENTS ...........................................................................................................45

REFERENCES.............................................................................................................................47
iv

LIST OF FIGURES

Figure 1. Equation. CMF for horizontal curvature on rural, two-lane roads from HSM................ 4

Figure 2. Equation. Bauer and Harwood CMFunction for injury and fatal crashes for safety 

effect of horizontal curve on straight grade........................................................................... 5

Figure 3. Equation. Estimated change in safety............................................................................ 13

Figure 4. Equation. EB estimate of expected crashes................................................................... 14

Figure 5. Equation. EB weight...................................................................................................... 14

Figure 6. Equation. Index of effectiveness ................................................................................... 14

Figure 7. Equation. Standard deviation of index of effectiveness................................................ 14

Figure 8. Photo. Example of horizontal curve realignment.......................................................... 17

Figure 9. Equation. Zegeer et al. model for crash prediction ....................................................... 24

Figure 10. Equation. Adjustment for tangent and curve difference.............................................. 24

Figure 11. Equation. Estimate of crashes for before-period conditions ....................................... 24

Figure 12. Equation. Form of SPF................................................................................................ 24

Figure 13. Equation. General form for CMFunction .................................................................... 29

Figure 14. Equation. Rewritten form of CMFunction .................................................................. 29

Figure 15. Equation. Another rewritten form of CMFunction...................................................... 29

Figure 16. Equation. Functional form for CMFunction................................................................ 30

Figure 17. Equation. Determining annual cost ............................................................................. 33

LIST OF TABLES

Table 1. Recommended CMFs ....................................................................................................... 1

Table 2. Before-period crash rate assumptions............................................................................... 9

Table 3. Minimum required before-period mi-yr ......................................................................... 10

Table 4. Sample analysis for crash effects.................................................................................... 11

Table 5. Before and after curve radii for treatment sites .............................................................. 20

Table 6. Site characteristics summary statistics............................................................................ 21

Table 7. Crash types and descriptions........................................................................................... 22

Table 8. Crash data summary statistics......................................................................................... 22

Table 9. SPF parameter estimates with standard errors................................................................ 25

Table 10. Aggregate CMF results................................................................................................. 27

Table 11. Option 2 CMFunction for total crashes ........................................................................ 30

Table 12. Recommended CMFs ................................................................................................... 35

Table 13. Descriptions and coding of data fields.......................................................................... 37

Table 14. Treatment site data by segment .................................................................................... 45

Table 15. Reference site data by segment..................................................................................... 47

Table 16. Naïve before–after evaluation for total crashes—North Carolina ................................ 43
v

LIST OF ABBREVIATIONS

AADT annual average daily traffic

B/C benefit–cost

CMF crash modification factor 

CMFunction crash modification function

DCMF Development of Crash Modification Factors (program)

EB empirical Bayes 

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

FHWA Federal Highway Administration 

GIS geographic information system

HSIS Highway Safety Information System

HSM Highway Safety Manual, first edition

NCDOT North Carolina Department of Transportation

PDO property-damage-only

RTM regression-to-the-mean

SPF safety performance function 

TAC technical advisory committee

USDOT U.S. Department of Transportation

1

EXECUTIVE SUMMARY

The Federal Highway Administration established the Development of Crash Modification Factors 

(DCMF) program in 2012 to address highway safety research needs for evaluating new and 

innovative safety strategies (improvements) by developing reliable quantitative estimates of their 

effectiveness in reducing crashes. The ultimate goal of the DCMF program is to save lives by 

identifying new safety strategies that effectively reduce crashes and promote those strategies for 

nationwide implementation by providing measures of their safety effectiveness and benefit–cost 

(B/C) ratios through research. State transportation departments and other transportation agencies 

need to have objective measures for safety effectiveness and B/C ratios before investing in new 

strategies for statewide safety improvements. Forty State transportation departments provided

technical feedback on safety improvements to the DCMF program and implemented new safety 

improvements to facilitate evaluations. These States are members of the Evaluation of Low-Cost 

Safety Improvements-Pooled Fund Study, which functions under the DCMF program. This study 

evaluated the effectiveness of horizontal curve realignment on rural, two-lane roads. One 

objective of this strategy is to reduce lane departure crashes, especially run-off-road crashes.

This evaluation developed crash modification factors (CMFs) for curve realignment on rural,

two-lane roads using state-of-the-art before–after empirical Bayes methods and compared the 

results with previously developed CMFs from cross-sectional studies. The data included 39 

realigned locations from California, North Carolina, and Ohio, and 56 untreated reference curves.

Table 1 presents the recommended CMFs for curve realignment on rural, two-lane roads. The 

results pertain to a range of site characteristics, the most important of which is the range of before 

and after degree of curve. The average degrees of curve in the before and after periods were 18.1 

(with a minimum of 3.2 and a maximum of 52.1) and 6.9 (with a minimum of 0.0 and a 

maximum of 16.3), respectively. The average central angle of the curves was approximately 42 

degrees (with a minimum of 1 and a maximum of 117). The average annual average daily traffic 

at the treated sites was about 3,500 (with a minimum of 465 and a maximum of 11,917). The 

average length of the realigned segments was 0.15 mi (with a minimum of 0.03 and a maximum 

of 0.60).

Table 1. Recommended CMFs.

Metric Total Injury and Fatal

Run-Off-Road

Plus Fixed Object Dark Wet-Road

Estimate of CMF 0.315 0.259 0.216 0.584 0.204

Standard error of 

estimate of CMF 0.064 0.086 0.068 0.176 0.079

Note: Bold text indicates that CMFs are statistically significant at the 95-percent confidence level.

Crash modification functions (CMFunctions) that were estimated showed that safety benefits may 

be greater for curves with a larger central angle and where the difference in radius between the 

before- and after-period conditions is larger.

In addition to developing the CMFs through a before–after evaluation, this study also compared 

the total crash CMFs with the results from previous cross-sectional studies. The CMFs derived 

through this before–after evaluation are lower compared to CMFs estimated by two previous 
2

cross-sectional studies. The economic analysis revealed a B/C ratio of 3.17:1 with a range of 

1.75:1 to 4.38:1. There is a need for further research with a larger sample of sites to assess the 

reliability of the CMFs obtained from this before–after evaluation.
3

CHAPTER 1. INTRODUCTION

BACKGROUND ON STRATEGY

Horizontal curves have consistently been an area of concern for road safety practitioners, 

particularly for single-vehicle crashes. A 2010 report from the Bureau of Transportation Statistics 

showed that one-third of fatal single-vehicle crashes occur at curves.(1) Most crashes at curves 

involve a vehicle leaving the roadway and striking a fixed object or overturning.(2,3) To counter 

this problem, transportation departments employ many strategies ranging from low-cost 

improvements of enhanced signs, delineations, or high friction surfacing to higher-cost strategies 

such as realignment of the curve or improving the superelevation.

The American Association of State Highway and Transportation Officials Guide for Reducing 

Collisions on Horizontal Curves lists “increasing the radius of a horizontal curve” as one strategy 

for reducing the likelihood of a vehicle leaving its lane and either crossing the roadway centerline 

or leaving the roadway at a horizontal curve.(3) The guide acknowledges that modifying the 

horizontal alignment is the longest-term, highest-cost strategy because it involved reconstructing 

the roadway, as well as other considerations such as right-of-way acquisition and environmental 

review. However, many States employ this strategy. From 2013 to 2015, 23 States reported using 

Highway Safety Improvement Program funds to implement horizontal curve realignment via 83 

projects.(4)

BACKGROUND ON STUDY

The Federal Highway Administration (FHWA) established the Development of Crash 

Modification Factors (DCMF) program in 2012 to address highway safety research needs for 

evaluating new and innovative safety improvement strategies by developing reliable quantitative 

estimates of their effectiveness in reducing crashes. The ultimate goal of the DCMF program is to 

save lives by identifying new safety strategies that effectively reduce crashes and to promote 

those strategies for nationwide implementation by providing measures of their safety 

effectiveness and benefit–cost (B/C) ratios through research. State transportation departments and 

other transportation agencies need objective measures for safety effectiveness and B/C ratios 

before investing in broad applications of new strategies for safety improvements. Forty State 

transportation departments provide technical feedback on safety improvements to the DCMF 

program and implement new safety improvements to facilitate evaluations. These States are 

members of the Evaluation of Low-Cost Safety Improvements-Pooled Fund Study (ELCSI-PFS), 

which functions under the DCMF program.

Typically, researchers have based studies on the effect of horizontal curve radius on a crosssectional analysis, where they compare the safety performance of curves of different radii. This 

methodology allows for a larger potential sample of curves because there is not a need to know a 

conversion/installation date such as is needed in a before–after study. It allows the use of an 

entire State’s database of curved road sections, as was the case with Washington State data in the 

Bauer and Harwood and the Saleem and Persaud studies.(5,6)

However, before–after methodology is preferable to cross-sectional for evaluating the safety 

effect of an infrastructure modification.

(7) Before–after studies are conducted for many other 

evaluations of safety improvements and provide the best estimate of the effect of the 
4

improvement. Typically, the most difficult aspect of before–after studies is identifying where and 

when the safety improvement was implemented. 

The advantage to this study was the assistance provided by the Technical Advisory Committee 

(TAC) of the ELCSI-PFS. This committee consists of safety engineers and representatives from 

more than 40 States. The TAC served as a source of knowledge for projects where horizontal 

curves were realigned, making the before–after methodology possible. Using the information 

gained from the ELCSI-PFS TAC, this study sought to conduct a before–after study of curve 

realignments using an empirical Bayes (EB) methodology.

LITERATURE REVIEW

Several studies have produced crash modification factors (CMFs) and crash modification 

functions (CMFunctions) for curve radius on rural, two-lane roads. Several other studies, also 

listed, provide CMFs for curve radius for other roadway types.

The Highway Safety Manual (HSM), first edition, chapter for rural, two-lane roads includes a 

CMF for horizontal curvature (pp. 10–27).(8) The HSM based this CMF on regression analysis 

done by Zegeer et al.

(9) The base condition of the HSM predictive model for rural, two-lane roads 

is a tangent, and the CMF for a curve is calculated as shown in figure 1:

Figure 1. Equation. CMF for horizontal curvature on rural, two-lane roads from HSM.

Where:

L = length of horizontal curve in mi, including spiral transitions.

R = radius of curve in feet.

S = 1 if spiral transition present; 0 if not; 0.5 if present only on one end of curve.

A study by Bauer and Harwood focused on the interaction of horizontal curvature and vertical 

curvature and grade for rural, two-lane highways.(5) The authors conducted a cross-sectional 

analysis of roadway segments from Washington State. They used 3,457 mi of road and 6 yr of 

crash data to produce a series of CMFunctions that quantify the safety performance of various 

combinations of vertical and horizontal alignment. 

Their study classified horizontal alignment of roadway segments as follows:

• Tangent.

• Horizontal curve.

Their study classified vertical alignment of roadway segments as follows:
5

• Level.

• Straight grade (constant grade of 1 percent or more).

• Type 1 or 2 crest vertical curve.

• Type 1 or 2 sag vertical curve.

Figure 2 shows one of the CMFunctions produced by Bauer and Harwood. The function 

calculates a CMF for fatal and injury crashes for a horizontal curve that occurs on a straight grade 

(i.e., no vertical curvature). The study produced other CMFunctions for other conditions (e.g., 

horizontal curve on a type 1 vertical crest).

Figure 2. Equation. Bauer and Harwood CMFunction for injury and fatal crashes for safety 

effect of horizontal curve on straight grade.

(5)

Where:

G = absolute value of percent grade (0 percent for level tangents, 1 percent otherwise.

R = curve radius (ft) (missing for tangents).

Lc = horizontal curve length (mi) (not applicable for tangents).

Saleem and Persaud built on the work for two-lane highways to explore the development of a

CMFunction where they explored different designs to flatten an existing horizontal curve.

(6) They 

focused on horizontal curves only on level grade (less than 3 percent). They used 440 curves from 

Washington State with radii between 100 and 11,000 ft to conduct a cross-sectional analysis and 

develop CMFunctions. Their functions show that CMFs decreased (fewer crashes occured) for 

scenarios in which a larger radius is entertained. They furthermore found that the level of annual 

average daily traffic (AADT) on the subject segment did not influence the effect.

The following studies have produced CMFs related to horizontal curve radius but focused on 

other types of crash or roadway conditions:

• Schneider et al. estimated CMFs for horizontal curvature on two-lane highways but 

focused on truck-involved crashes.(10)

• Banihashemi, Fitzpatrick et al., and Graham et al. produced CMFs involving horizontal 

curve radius but focused on rural, multilane highways.(11–13)

• Pratt et al. and Choi et al. produced CMFs for horizontal alignment but focused on 

freeways.(14,15)

Summary of Literature Review

Previous studies have generally shown that higher curve radius is associated with fewer crashes.

However, all the published studies that have examined the safety effect of horizontal curvature 

were based on cross-sectional studies that may not always provide reliable CMFs. This illustrates 

the need for before–after studies, even if researchers must base those studies on a small sample to 

verify the results that cross-sectional studies have obtained.

CMF = e

 0.044+0.19ln 2×

5730

R

 +4.52 

1

R

 

1

LC

 

7

CHAPTER 2. OBJECTIVE

The objective of this study was to develop a CMF for horizontal curve realignment, where

increasing the radius of a curved roadway segment served to flatten the curve. Most previous 

studies used cross-sectional models to develop CMFs, and this evaluation used the EB beforeevaluation method to develop CMFs and verify the results with the cross-sectional studies. The 

evaluation used data from California, Ohio, and North Carolina. The evaluation included the 

following crash types:

• Total.

• Injury and fatal.

• Run-off-road and fixed object.

• Crashes during dark.

• Wet crashes.

In addition to determining the overall safety effect of the treatment(s), a further objective was to 

address the following questions:

• Do effects vary by level of traffic volume?

• Do effects vary by the frequency of crashes before treatment?

• How do the effects vary based on a change in radius from the before to the after periods?

The evaluation of overall effectiveness included the consideration of the installation costs and 

crash savings in terms of the B/C ratio.

9

CHAPTER 3. STUDY DESIGN

When planning a before–after safety evaluation study, it is vital to ensure that enough data are 

included to statistically detect the expected change in safety. Even though those designing the 

study do not know the expected change in safety in the planning stage, it is still possible to make 

a rough determination of how many sites are required based on the best available information 

about the expected change in safety. Alternatively, one could estimate the statistically detectable 

change in safety for the number of available sites. For a detailed explanation of sample size 

considerations, as well as estimation methods, see chapter 9 of Hauer.

(16) The sample size 

analysis cases presented in this section address how large a sample is required to statistically 

detect an expected change in safety and the change in safety that can be detected with available 

sample sizes.

CASE 1: SAMPLE SIZE REQUIRED TO DETECT AN EXPECTED CHANGE IN

SAFETY

For this analysis, the project team assumed that the study used a conventional before–after study 

with comparison group design, because available sample size estimation methods are based on 

this assumption. The sample size estimates from this method would be conservative in that the 

EB methodology proposed would likely require fewer sites. To facilitate the analysis, the project 

team also assumed that the number of comparison sites is equal to the number of treatment sites, 

which again, is a conservative assumption.

Table 2 provides the crash rate assumptions used for total, injury and fatal, and run-off-road plus 

fixed-object crashes based on data from California, North Carolina, and Ohio. The project team 

obtained these rates by taking the before crash rate from the treated sites and reducing them by 25 

percent. This was based on the suggestion in Bahar to account for possible bias due to regressionto-the-mean (RTM).

(16) Because the sample of realignments is limited, the project team used an 

overall crash rate instead of individual rates from different States.

Table 2. Before-period crash rate assumptions.

Crash Type

Crash Rate 

per mi-yr

Total 4.47

Injury and Fatal 2.46

Run-off-road plus fixed-object 2.98

Table 3 provides estimates of the required number of before- and after-period mile-years (mi-yr)

for statistical significance at both a 90- and 95-percent confidence levels. Because the safety 

effects of realignment depend on many factors, including the specific change in the radius from 

the before to the after period, the expected reduction values in the table need to reflect the 

expected change in radius from the before to the after periods. Based on the initial data that the 

team obtained from the three States, the average radius in the before period was about 400 ft, the 

average radius in the after period was about 1,000 ft, and the average curve length was about 

0.15 mi. Using this information and results from Zegeer et al. and Bauer and Harwood, the CMF 

for total crashes for this change is expected to range from 0.65 to 0.75, i.e., a 25- to 35-percent
10

reduction in total crashes.(5,9) The reduction for injury and fatal crashes and run-off-road crashes 

could be higher.

Table 3. Minimum required before-period mi-yr.

Crash Type and Expected Percent 

Reduction in Crashes

95-Percent 

Confidence

90-Percent 

Confidence

All 20 58 41

All 30 21 15

All 40 9 6

Injury and fatal 20 106 75

Injury and fatal 30 38 27

Injury and fatal 40 17 12

Run-off-road plus fixed-object 20 87 62

Run-off-road plus fixed-object 30 31 22

Run-off-road plus fixed-object 40 14 10

Note: Assumes equal number of mi-yr for treatment and comparison sites and equal 

length of before and after periods. Bold text indicates recommended sample size.

The minimum sample indicates the level for which a study seems worthwhile; that is, it is 

feasible to detect with the level of confidence the largest effect that one may reasonably expect 

based on current knowledge about the strategy. The project team based these sample size 

calculations on the methodology in Hauer and on specific assumptions regarding the number of 

crashes per mile and years of available data.(15) Mi-yr are the number of miles where the strategy 

was implemented, multiplied by the number of years of data before or after implementation. For 

example, if a State implemented a strategy over 10 mi, and data are available for 4 yr since 

implementation, then there is a total of 40 mi-yr of after-period data available for the study.

In table 3, bold text indicates the sample size values recommended in this study. The project team 

recommends these values based on the likeliness of obtaining the estimated sample size as well 

as the anticipated effects of the treatment. As noted, the sample size estimates provided are 

conservative in that the state-of-the-art EB methodology proposed for the evaluations would 

require fewer sites than the less robust conventional before–after study with a comparison group

that had to be assumed for the calculations. Estimates may be predicted with greater confidence,

or a smaller reduction in crashes will be detectable, if there are more site-years of data available 

in the after period.

CASE 2: CHANGE IN SAFETY THAT CAN BE DETECTED WITH AVAILABLE 

SAMPLE SIZES

The standard deviations of the estimated percent change in safety describe the statistical accuracy 

attainable for a given sample size. From this, one can estimate p-values for various sample sizes 

and expected change in safety for a given crash history based on the method in Hauer.(16)

For the available data in the three States in this evaluation, the research team estimated the 

minimum percentage changes in crash frequency that could be statistically detectable at 90- and 

95-percent significance levels (see table 4). The results indicate that the data should be able to 

detect the recommended crash reduction values from table 3 if such an effect were present. Using 
11

these results, the authors decided to proceed with the evaluation using the data available at that 

time.

Table 4. Sample analysis for crash effects.

Crash Type

Mi-yr

in Before 

Period

Mi-yr

in After 

Period

Minimum Percent

Reduction

Detectable for 

Crash Rate

Assumption*

P = 0.10

Minimum Percent

Reduction

Detectable for 

Crash Rate

Assumption*

P = 0.05

Total 33 19 25 29

Injury and fatal 33 19 32 36

Run off road plus 

fixed object 33 19 30 34

Note: Results are to nearest 1 percent.

*Crash rate assumption is based on crash rates in table 3.

13

CHAPTER 4. METHODOLOGY

This methodology accounts for RTM using a reference group of similar but untreated sites, 

giving it a reputation for being especially rigorous. In the process, the project team uses safety 

performance functions (SPFs) to address the following issues:

• Overcoming the difficulties of using crash rates in normalizing for volume differences 

between the before and after periods.

• Accounting for time trends.

• Reducing the level of uncertainty in the estimates of safety effect.

• Properly accounting for differences in crash experience and reporting practice in 

amalgamating data and results from diverse jurisdictions.

The methodology also provides a foundation for developing guidelines for estimating the likely 

safety consequences of a contemplated strategy. Researchers can use the SPFs for roadways that 

have not undergone a curve realignment with observed crash histories to estimate the number of 

crashes without treatment. Researchers can then apply the CMFs developed to this number to 

estimate the number with treatment.

Figure 3 shows the equation used in the EB approach to find the estimated change in safety for a 

given crash type at a site.

Figure 3. Equation. Estimated change in safety. 

Where:

= expected number of crashes that would have occurred in the after period without the 

strategy.

= number of reported crashes in the after period. 

In estimating , the effects of RTM and changes in traffic volume are explicitly accounted for 

using SPFs, which relate crashes of different types to traffic flow and other relevant factors for 

each jurisdiction based on untreated sites (reference sites). Researchers can calibrate annual SPF 

multipliers to account for temporal effects on safety, such as variation in weather, demography, 

and crash reporting.

In the EB procedure, researchers first use the SPF to estimate the number of crashes that would 

be expected in each year of the before period at locations with traffic volumes and other 

characteristics similar to the one being analyzed (i.e., reference sites). The sum of these annual 

SPF estimates (P) is then combined with the count of crashes (x) in the before period at a strategy 

site to obtain an estimate of the expected number of crashes (m) before strategy. Researchers then 

calculate this estimate of m using the equation in figure 4.

 Safety = λ - π

λ

π

λ
14

Figure 4. Equation. EB estimate of expected crashes.

Where w is estimated from the mean and variance of the SPF estimate using the equation in 

figure 5.

,

Figure 5. Equation. EB weight.

Where k is the constant for a given model and is estimated from the SPF calibration. 

In estimating the SPF, a negative binomial distributed error structure is assumed with k being the 

overdispersion parameter of this distribution.

A factor is then applied to m to account for the length of the after period and differences 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 P, the sum of these predictions for the before period. 

The result, after applying this factor, is an estimate of . The procedure also produces an estimate 

of the variance of .

The estimate of is then summed over all sites in a strategy group of interest (to obtain sum) and 

compared with the count of crashes observed during the after period in that group ( sum). The 

variance of is also summed over all sites in the strategy group. 

The index of effectiveness ( ) is estimated using the equation in figure 6.

Figure 6. Equation. Index of effectiveness.

The standard deviation of is given by the equation in figure 7.

Figure 7. Equation. Standard deviation of index of effectiveness.

m = w(P)+(1-w)(x)

w =

1

1+ kP

λ

λ

λ λ

π

λ

θ

















2

( )

1

sum

sum

sum

sum

Var











θ

2

2

2 2

2

( )

1

( ) ( )

( )







































sum

sum

sum

sum

sum

sum

Var

Var Var

StDev
















15

The percent change in crashes is calculated as 100(1  ); thus, a value of  0.70 with a 

standard deviation of 0.12 indicates a 30-percent reduction in crashes with a standard deviation of 

12 percent.

θ θ

17

CHAPTER 5. DATA COLLECTION

SITE IDENTIFICATION

The initial list of potential treatment sites was assembled based on information obtained from the 

TAC. The State safety engineers provided lists of curve-related projects that were either changes 

in horizontal radius or changes in superelevation of the curve. Given the focus of this evaluation, 

the team pursued only those projects involving an increase to horizontal radius. The State 

personnel also provided a date when they realigned the curve, typically presented as the 

construction start date and construction end date.

The following five States initially provided lists of curves where they had increased the radius:

• California—4 sites (supplemented with others as described below).

• Kentucky—16 sites.

• North Carolina—11 sites.

• Ohio—15 sites.

• South Carolina—6 sites.

California staff provided a list of four sites of curve realignments. The project team used the State 

Safety Improvements Project Database developed by the Highway Safety Information System

(HSIS) to identify an additional 32 curve realignment projects in California. That database listed 

no additional curve realignment projects for North Carolina or Ohio.

Figure 8 presents an example of a horizontal curve that a State realigned. The solid red line on the 

aerial image illustrates the old alignment.

Source: Esri, DigitalGlobe, Earthstar Geographics, CNES/Airbus DS,

GeoEye, USDA FSA, USGS, Getmapping, Aerogrid, IGN, IGP, and the

GIS User Community.

Figure 8. Photo. Example of horizontal curve realignment.
18

The project team focused on sites in California, North Carolina, and Ohio, because these States 

represented some of the largest sample sizes, and all three of these States have data that are

available through HSIS. The use of HSIS data was an advantage not only because it facilitates the 

process of obtaining the crash and roadway data, but also because it enabled the team to obtain 

annual values for the traffic volume.

The project team identified reference sites by visually inspecting the roadway network at the area 

of each treatment curve and selecting one or two other curves nearby on the same route as 

reference curves. The team preferred curves with smaller radii in order to better match the 

“before” condition of the treatment sites. The team inspected a timeline of aerial imagery to 

ensure that no significant changes had taken place at these reference curves. The project team 

used the same timeline of imagery to verify (and occasionally correct) the installation year for the 

treatment sites.

ROADWAY CHARACTERISTICS AND TRAFFIC VOLUME

The project team used HSIS to obtain data on roadway characteristics and traffic volume. 

Although the States provided location data for the treated curves, it was often fairly general 

information, such as the milepost range for an entire roadway project, or simply a description 

(e.g., “SR 1100 from 0.4 mile to 0.2 mile west of US 13 Bypass, west of Windsor”). In order to 

request data from HSIS, the team had to determine the exact start and end mileposts of the 

treatment.

The team first located the treatment and reference sites in Google® EarthTM, then overlaid that 

file on a geographic information system (GIS)-based road network from each State. The project 

team used the GIS road file to identify the start and end mileposts of each curve, as well as verify 

or obtain other pieces of data that they needed to identify the road section, such as route number 

and county. This process was fairly straightforward for sites in Ohio and North Carolina. The 

process for the California sites proved to be more complicated, because California identifies route 

sections by a complex combination of district, route, route suffix, county, postmile prefix, and 

postmile. The main issue for this project was that the GIS road file did not contain all these 

required data. The team worked with several members of the California Department of 

Transportation (Caltrans) staff to resolve this issue and accurately identify the treatment and 

reference curves on the California network.

HSIS requested the following roadway characteristics:

• Right and left shoulder width.

• Right and left shoulder type.

• Number of lanes.

• Rural/urban designation.

• Annual average daily traffic.

Given the large range of installation dates of the curve realignments, the team requested these 

data for the following time spans:
19

• California—1997 to 2011.

• North Carolina—2003 to 2013.

• Ohio—2000 to 2013.

In addition to data from HSIS, the team also collected data from the GIS road files and aerial 

imagery (Google® EarthTM). These included the following:

• Curve radius before and after. The team used a GIS-based tool to measure the radius of 

the curve before and after realignment. Typically, the GIS linework represented either the 

before or after alignment (depending on how recently the realignment occurred and how 

up-to-date the GIS file was). The team used aerial imagery to obtain a measurement of the 

other period. 

• Distance to previous and next curve. The team noted the distance from the start of the 

study curve to the end point of the next curve and the distance from the end of the study 

curve to the start point of the next curve. They collected this to enable the analysis to 

distinguish isolated curves from grouped curves.

• Intersection in curve. Some curves had an intersection of a public road in the curve 

section or very near the endpoints of the curve. The team noted this intersection presence 

as a data variable.

Table 5 provides a list of all treatment sites (curves where radius was modified) with the before 

and after radius measurements. Table 6 provides a summary of characteristics for both treatment 

and reference sites. Appendix A provides a complete list of all site characteristics for treatment 

and reference sites. 
20

Table 5. Before and after curve radii for treatment sites.

Treatment 

Curve ID

Curve Radius 

Before (ft)

Curve Radius 

After (ft)

Amount of Radius 

Increase (ft)

Proportion of After 

to Before Radius

CA002A 110 362 252 3.29

CA018-A 157 1,588 1,431 10.11

CA002B 158 446 288 2.82

OH001 177 955 778 5.4

CA030-A 187 20,000* 19,813 106.95

CA018-B 190 1,079 889 5.68

CA018-C 190 1,657 1,467 8.72

CA018-D 200 441 241 2.21

NC008 206 351 145 1.7

CA022 228 446 218 1.96

CA011 229 1,640 1,411 7.16

OH011 259 700 441 2.7

OH012 282 800 518 2.84

NC006 307 512 205 1.67

CA003-A 335 500 165 1.49

NC004-A 337 433 96 1.28

NC004-B 380 415 35 1.09

OH004 387 1,069 682 2.76

CA013-D 390 809 419 2.07

NC002-C 398 698 300 1.75

CA026-D 405 1,902 1,497 4.7

CA013-2 419 684 265 1.63

CA013-C 429 602 173 1.4

CA013-A 440 742 302 1.69

NC003 445 842 397 1.89

NC002-A 470 20,000* 19,530 42.55

CA030-B 475 875 400 1.84

CA027 500 1,200 700 2.4

CA028-C 500 1,312 812 2.62

CA034-B 533 1,409 876 2.64

CA005 545 872 327 1.6

NC005 554 818 264 1.48

CA015-A 566 1,102 536 1.95

NC009 570 1,023 453 1.79

NC010 579 1,146 567 1.98

CA025-B 851 4,495 3,644 5.28

CA025-A 903 1,312 409 1.45

CA034-A 964 20,000* 19,036 20.75

CA003-D 1,781 10,000 8,219 5.61

*Locations with a radius of 20,000 in the after period are those where the curve was realigned to a straight segment.

Instead of showing a radius of infinity, the table shows a radius of 20,000.
21

Table 6. Site characteristics summary statistics.

Site Characteristic

Range of Values in Data for 

Treatment Sites

Range of Values in Data for 

Reference Sites

Curve radius (ft) before 

realignment Range: 110 to 1,780 Range: 75 to 2,900

Curve radius (ft) before 

realignment Average: 430 Average: 600

Curve radius (ft) after 

realignment

Range: 350 to 4,500 (and 

essentially straight tangent for 

four sites with radii over 

10,000)

N/A

Curve radius (ft) after 

realignment

Average (including radii over 

10,000): 2,700 N/A

Curve radius (ft) after 

realignment

Average (excluding radii over 

10,000): 1,000 N/A

Number of lanes Range: 2 to 3 Range: 2 to 3

Shoulder width Range: 1 to 8 Range: 1 to 9

Shoulder width Average: 3.9 Average: 3.7

AADT Range: 440 to 12,000 Range: 400 to 12,000

AADT Average: 3,480 Average: 2,600

N/A = not applicable.

CRASH DATA

The project team obtained crash data from HSIS for each year of the study period. HSIS provided 

individual crash records; the team aggregated these into counts by year for each curve. Table 7

provides a list of the types of crashes collected for this study. 

The project team assigned crashes to each segment according to the start and end mileposts of the 

curve (i.e., the point of curvature and point of tangency). In relying on mileposts, the authors

recognize the potential for data error, specifically crash locating, when working with 

sections/curves of small length. In addition, crash positions in rural areas especially can vary in 

accuracy because of fewer landmarks and intersections. Appendix B provides a further discussion 

of this issue.

For treatment sites, the realignment of the curve from a sharp curve to a flatter curve resulted in a 

longer length. The team used mileposts from the after period for crash data. This means that 

crashes from the before period for the treatment site would include some amount of tangent 

section on either end of the curve. Another option would be to limit crashes in the before period 

to only those crashes occurring on the curve. However, that would mean a comparison from 

before to after periods of two different lengths—a shorter length in the before period and a longer 

length in the after period. The team felt this approach would have an inherent bias because of the 

length difference. Table 8 provides the summary statistics regarding the crash data.
22

Table 7. Crash types and descriptions.

Crash Type Description Coding Notes

Total Total crashes occurring within the 

curve.

Availability of certain years of 

crashes depended on the State data 

in HSIS.

Fatal and injury Fatal or injury crashes occurring 

within the curve.

Any injury level (A, B, and C) 

were included.

1

Run-off-road and 

fixed-object 

Run-off-road and fixed-object 

crashes occurring in the curve.

This crash count combined crashes 

coded as run-off-road, fixedobject, or hit object into one total.

Head-on 

Head-on crashes occurring in the 

curve.

N/A

Dark Dark crashes occurring in the 

curve.

Included any dark time crashes, 

lighted or unlighted roads.

Sideswipe Sideswipe crashes occurring in the 

curve.

Included sideswipes in the same or 

opposing directions.

Wet Wet crashes occurring in the curve. Included rain, sleet, snow, or ice.

1Measured on the KABCO scale, which is used to represent injury severity in crash reporting: K is fatal injury, A is 

serious injury, B is minor injury, C is possible injury, and O is property damage only.

N/A = not applicable.

Table 8. Crash data summary statistics.

Variables

Treatment 

Sites Before

Treatment 

Sites After

Reference

Sites

Number of sites 39 39 56

Years of data 220 130 610

Mi-yr 33.2 18.8 55.8

Total crashes per year 198 29 214

Injury and fatal per year 109 10 86

Run-off-road plus fixed-per-year 132 11 104

Head-on per year 10 0 5

Sideswipe per year 11 2 17

Dark per year 61 13 53

Wet per year 88 7 78
23

CHAPTER 6. DEVELOPMENT OF SAFETY PERFORMANCE FUNCTIONS

This section presents the single SPF developed. The project team used the SPF in the EB 

methodology to estimate the safety effectiveness of this strategy. The team used generalized 

linear modeling to estimate model coefficients, assuming a negative binomial error distribution.

This is consistent with the state of research in developing these models. In specifying a negative 

binomial error structure, the team iteratively estimated the dispersion parameter, k, from the 

model and the data. For a given dataset, smaller values of k indicate relatively better models.

The project team combined all States together to estimate the SPF with a separate intercept term 

estimated for each State. The team only calibrated the SPF for total crashes because the other 

crash type sample sizes were small. For other crash types, they applied the SPF for total crashes 

with a multiplier equal to the number of crashes of the type of interest divided by the number of 

total crashes at the reference sites. The project team developed the following multipliers for each 

crash type:

• Injury and fatal: 0.40.

• Run-off-road and fixed-object: 0.49.

• Head-on: 0.02.

• Sideswipe: 0.08.

• Dark: 0.25.

• Wet: 0.36.

Ideally, the project team would calibrate the SPF for each year to reflect time trends in crashes 

not related to the treatment of interest. However, the reference site data comprise only 214 

crashes in total, ranging from 2 to 28 in a single year. With such low yearly crash totals, it was 

not feasible to calibrate the SPF each year to reflect potential time trends.

To assess the entire impact on safety of curve realignment to a larger radius curve, it is necessary 

to consider a study area that extends beyond the limits of the smaller radii curve. When changing 

from a smaller to a larger radius, the reconstruction removes tangents on either side of the curve. 

The study area therefore needs to include the entire roadway travelled to get from the beginning 

to the ending of the largest curve radius under consideration.

Because the reference group consisted of only curved segments, the project team adjusted the 

SPF predictions in order to consider the expected crash frequencies on the tangent segments 

associated with the smaller radius curve in the before period that were subsequently removed. 

For this adjustment, the project team first applied the SPF calibrated from the reference group to 

the tangent segments as if the tangent segments removed had the same curvature as the curved 

segment to which they were adjacent. Then, they adjusted this estimate by an estimated ratio of 

expected crashes on a tangent to expected crashes on a curve.

The adjustment made use of the model developed by Zegeer et al., which is the basis of the CMF 

for horizontal curvature on two-lane roads in the HSM.

(8,9) Figure 9 shows the model prediction 

for the number of crashes per year.
24

Figure 9. Equation. Zegeer et al. model for crash prediction.

(9)

Where:

A = expected crash frequency per year.

L = length of the curve in mi.

D = degree of curvature.

S = one if spirals exist and zero otherwise.

V = AADT.

W = roadway width in ft.

The project team did not know if spiral transitions existed at the treated curves, so they assumed 

that spiral transitions are not present. Recognizing that the traffic volume and road width remain 

unchanged and the degree of curvature for a tangent is 0, they estimated the adjustment as shown 

in figure 10.

Figure 10. Equation. Adjustment for tangent and curve difference.

Where:

L = total tangent length.

D = degree of curve of the curved segment adjacent to the tangents.

The estimate of crashes for the before-period conditions, which include both the curved and 

tangent segments removed, is then shown in figure 11.

Figure 11. Equation. Estimate of crashes for before-period conditions.

The form of the SPF developed using the reference group sites, which is presented in table 9, is

shown in figure 12.

Figure 12. Equation. Form of SPF.
25

Where:

AADT = annual average daily traffic volume.

Length = length of horizontal curve in miles.

RAD = radius of horizontal curve in miles.

a, b, c, d, e = parameters estimated in the SPF calibration process (a is the intercept; b

represents a set of coefficients for each State).

Table 9. SPF parameter estimates with standard errors.

State Parameter Value Standard Error

All a –0.8951 1.6329

California b –1.2198 0.3352

North Carolina b –0.7103 0.3881

Ohio b 0.0000 N/A

All c 0.4424 0.1509

All d 0.9659 0.2943

All e –3.7331 1.6331

All k 0.4527 0.1555

N/A = not applicable.

27

CHAPTER 7. BEFORE–AFTER EVALUATION RESULTS

AGGREGATE ANALYSIS

Table 10 provides the estimates of expected crashes in the after period without treatment, the 

observed crashes in the after period, and the estimated CMF and its standard error for all crash 

types considered. Although all crash categories have low sample sizes of crashes, the project 

team did not analyze head-on and sideswipe crashes because of the very low number of crashes 

of these types at the study sites. The team based the CMFs reported in table 10 on all 39 locations 

that the States realigned. The project team also estimated the CMFs after removing the three 

locations that the States realigned to straight segments, and the resulting CMFs were almost 

identical to the ones reported in table 10.

Table 10. Aggregate CMF results.

Metric Total

Injury and 

Fatal

Run-OffRoad Plus 

FixedObject Dark Wet-Road

EB estimate of crashes 

expected in after period 

without strategy

91.43 38.11 50.29 21.90 33.88

Count of crashes observed in 

after period 29 10 11 13 7

Estimate of CMF 0.315 0.259 0.216 0.584 0.204

Standard error of estimate of 

CMF 0.064 0.086 0.068 0.176 0.079

Note: Bold text indicates that CMFs are statistically significant at the 95-percent confidence level.

The results indicate large reductions that are statistically significant at the 95-percent confidence 

level for all crash types analyzed. It is important to note, however, that the sample size of afterperiod crashes is small.

The results pertain to a range of site characteristics, the most important of which is the range of 

before and after curve radii. The average degrees of curve in the before and after periods were 

18.1 and 6.9, respectively (the degree of curve is mentioned here instead of radius because three

of the curves were realigned to straight segments, which have undefined radius values but have a 

degree of 0.0). The average central angle of the curves was approximately 42 degrees. As 

indicated earlier, the average AADT at these sites was about 3,500. The average length of the 

segments the States realigned was 0.1455 mi.

One of the intents of this evaluation was to compare the results of the before–after evaluations 

with published results from cross-sectional studies. The project team used two approaches to do 

this comparison. The team only did a comparison for the total crash CMF. The first approach

involved entering the average radii in the before and after periods along with the average segment 

length of the study sites to estimate the CMFs based on the equations given in Zegeer et al. (for 

total crashes) and Bauer and Harwood (for injury and fatal crashes).

(4,8) Based on the equation 

given in Zegeer et al., and assuming no spiral transition curves, the ratio of the CMF for a curve 

with a degree 6.9 to a curve with degree 18.1 is 0.672 for total crashes.

(8) For the same 
28

conditions, the CMFunction in Bauer and Harwood estimate a CMF of 0.784 for injury and fatal 

crashes.

(4)

The first approach is simplistic in that it does not specifically account for the fact that the 

relationship between the CMF and curve radius and segment length is non-linear in both Zegeer 

et al. and Bauer and Harwood.(4,8) To address this limitation, the project team identified a second 

approach. The second approach involved the following steps:

1. For each treated site, calculate the CMF based on Zegeer et al. and Bauer and 

Harwood.(4,8)

2. Multiply the EB expected crashes in the after period for each site (this is the expected 

crashes had the treatment not been implemented) with the CMFs from Zegeer et al., 

(1992) and Bauer and Harwood (2014). This product gives the expected crashes with the 

treatment for each site based on the CMFs from these two studies.

3. Calculate the sum of the expected crashes with the treatment for all sites based on the two 

studies.

4. The ratio of the expected crashes with the treatment to the EB expected crashes without 

the treatment provides an approximate CMF associated with the equations from the two 

studies.

Based on the second approach, the CMF from Zegeer et al. was 0.699 (for total crashes), and the 

CMF from the Bauer and Harwood was 0.736 (for injury and fatal crashes).(4,8)

The CMFs from the previous studies are higher than the CMFs of 0.315 and 0.259 that were 

estimated using the before and after EB evaluation for total and injury and fatal crashes, 

respectively. However, as mentioned earlier, the project team based this before–after evaluation 

on a limited sample, and readers should consider it with caution.

DISAGGREGATE ANALYSIS

The expected CMF value for a specific site could vary significantly based on its characteristics. 

This is the object of the disaggregate analysis. The focus of the disaggregate analysis was on total 

crashes due to the small number of after-period crashes. Since the CMF could be a function of the 

site characteristics (e.g., change in the radius or degree of curvature due to realignment), an 

attempt was made to further analyze the data to develop a CMFunction for the purposes of 

estimating a site-specific CMF.

The traditional approach for estimating CMFunctions includes the use of the CMF value as the 

dependent variable and site/treatment characteristics as independent variables. Figure 13 presents 

one way to express this.
29

Figure 13. Equation. General form for CMFunction.

Where f represents a generic function.

This CMFunction could then be estimated as a regression equation. Elvik recommended that the 

variance of the CMF needs to be considered in this estimation.(17) The inverse of the variance is 

typically introduced as a weight in a weighted regression model. In other words, for an 

observation (or site) whose CMF is CMFi with a variance of Var(CMFi), the weight will be 

1/Var(CMFi). For linear regression, this would be appropriate.

Some recent studies have recommended the use of a different model form such as a lognormal 

model that would ensure the predicted CMF from a CMFunction would always be greater than 

zero. In the case of the log-normal model, Bonneson showed that the appropriate weight for a 

weighted log-normal regression model would instead be [CMFi/Var(CMFi)].

(18) This is because, 

based on figure 7, the Var(CMFi) is not independent of CMFi, i.e., lower CMFs values would 

tend to have lower variances as well. 

For either the normal regression or lognormal regression models with weights, reliable estimates 

of CMFs and their variances are necessary. In order to have reliable estimates of these 

parameters, researchers often combine sites with similar characteristics, especially if there are 

sites where the reported crashes in the after period are zero. However, this aggregation can lead 

to loss of useful information. In this study, the project team proposed a different approach to 

overcome the disadvantage of losing information due to aggregation. This approach involves 

rewriting figure 13 as follows in figure 14.

Figure 14. Equation. Rewritten form of CMFunction.

Where:

= expected number of crashes that would have occurred in the after period without the 

strategy.

= number of reported crashes in the after period.

Figure 14 can again be rewritten as follows in figure 15.

Figure 15. Equation. Another rewritten form of CMFunction.

Written in this form, it is possible to estimate this equation as a count data model (such as 

Poisson or negative binomial model) with as the dependent variable and as the offset. This 

approach is similar to estimating an SPF with the goal of predicting the number of crashes per 

mile, where crash frequency is included as the dependent variable and section length is included 
30

as the offset. One limitation with this approach is that the offset is an estimated value from the 

EB procedure with a variance. There has been some limited research in traffic safety on the 

implications of errors/variance in the independent variables, but further research is necessary, 

possibly using simulation.

The independent variables for the CMFunction included the following:

• AADT.

• Difference/ratio between the after and before radius/degree of curvature.

• Central angle of the curve.

Figure 16 is the functional form for the CMFunction that was estimated using negative binomial 

regression.

Figure 16. Equation. Functional form for CMFunction.

Where a0 represents the intercept, and a1 through an represent the coefficients for independent 

variables X1 through Xn.

In three locations, States aligned the curved sections to be a straight segment, indicating a radius 

of infinity in the after period. However, expressing the curvature as a degree of the curve 

(5,730/radius in ft) instead of radius would allow this study to include these sites the States

realigned to a straight segment, since the degree of curvature for a straight segment is 0. To 

address this issue, the project team explored the following two options:

• Option 1: Include all 39 sites.

• Option 2: Exclude the three sections that the States realigned to a straight segment (i.e., 

include data from 36 sites).

Multiple CMFunctions were considered, including the consideration of the ratio of degree of 

curvature instead of the difference in degree of curvature from the before to the after periods (in 

Option 1), and the ratio the radius (and/or curvature) instead of the difference in radius (and/or 

curvature) from the before and after periods (in Option 2). The best CMFunction was from 

Option 2, which is presented in table 11.

Table 11. Option 2 CMFunction for total crashes.

Variable

Estimate (Standard 

Error)

Intercept –3.4775 (3.7253)

ln(AADT) 0.5299 (0.4219)

Central Angle –0.0342 (0.0162)

Radius after – radius before (mi) –1.6628 (1.5026)

Overdispersion parameter (k) 0.3951 (0.5239)
31

The estimated parameters indicate that the CMF increases as AADT increases but decreases as 

the difference between the radii of the two curves increases and as the central angle increases. 

Many of the parameters have a high standard error including the overdispersion parameter. If the 

true value of the overdispersion parameter were zero, then a Poisson model would be appropriate. 

The project team calibrated the same model with a Poisson error distribution but showed little 

change in the parameter estimates.

Readers should not consider the CMFunction robust because the project team based it on a small 

sample of sites. In checking the predicted CMFs for individual sites, some illogical predictions do 

result, such as predicting a large increase in crashes at high AADT sites. For these reasons, the 

project team does not recommend applying the CMFunction developed. However, the general 

indications of the CMFunction may be useful in a contemplated curve realignment, in particular 

that safety benefits may be greater for curves with a larger central angle and where the difference 

in radius between the before- and after-period conditions is larger. This is consistent with 

previous cross-sectional studies (e.g., Zegeer et al., Bauer and Harwood) that indicate that the 

safety benefits due to realignment would be greater with a larger increase in radius from the 

before to the after periods.(4,8)

33

CHAPTER 8. ECONOMIC ANALYSIS

The project team undertook the following steps for the economic analysis:

1. The research team estimated the change in property-damage-only (PDO) crashes using the 

EB predicted crashes in the after period and the actual crashes in the after period for total 

and injury and fatal crashes.

2. Using the number of mi-yr in the after period, the research team determined the change in 

PDO crashes per mi-yr and the change in injury and fatal crashes per mi-yr. The team 

estimated the expected benefit due to the realignment as 1.495 injury and fatal crashes per 

mi per yr and 1.826 PDO crashes per mi per yr.

3. For the benefit calculations, the project team used the most recent FHWA mean 

comprehensive crash costs disaggregated by crash severity and location type as a base.

(19)

They developed these costs based on 2001 crash costs and the unit cost (in 2001 U.S. 

dollars) for injury and fatal crashes and PDO crashes in rural areas was $206,015 and 

$7,800, respectively. The team updated this to 2015 dollars by applying the ratio of the 

U.S. Department of Transportation (USDOT) 2015 value of a statistical life of $9.4 

million to the 2001 value of $3.8 million (USDOT 2015).

(20) Applying this factor of 2.48

to the unit costs resulted in an aggregate 2015 unit cost of $510,446 for injury and fatal 

crashes and $19,326 for PDO crashes. The expected annual benefit due to the fewer 

crashes after realignment was $510,446 * 1.495 + $19,326 * 1.826, which totals 

approximately $798,507. Based on the suggestions from USDOT, the team conducted 

sensitivity analyses to obtain a low and high value for the benefits, and consequently a 

low and high value for the B/C ratios.

4. The research team estimated the annualized cost of the treatment, as shown in figure 17.

Figure 17. Equation. Determining annual cost.

Where:

C = treatment cost; based on information from North Carolina, the average realignment 

cost per mi was $3,121,599.

R = discount rate (as a decimal) and assumed to be 0.07. 

N = expected service life (years) of 30 yr.

The annualized cost per year for realignment was $251,558.

5. The project team calculated the B/C ratio of the annual crash savings to the annualized 

treatment cost. The B/C ratio was 3.17:1, with a low of 1.75:1 to a high of 4.38:1.

Annual Cost =

C ∗ R

1 − 1 + R −N

35

CHAPTER 9. SUMMARY AND CONCLUSIONS

This evaluation used the EB before–after method in order to evaluate the safety aspects of curve 

realignment on rural, two-lane roads. Not surprisingly, the sample size in this evaluation was 

limited because realignments are expensive. However, previous studies used cross-sectional 

regression methods that may not always provide reliable CMFs.

Table 12 presents the recommended CMFs for curve realignment on rural, two-lane roads. The 

results pertain to a range of site characteristics, the most important of which is the range of before 

and after degree of curve. The average degrees of curve in the before and after periods were 18.1 

(with a minimum of 3.2 and a maximum of 52.1) and 6.9 (with a minimum of 0.0 and a 

maximum of 16.3), respectively. The average central angle of the curves was approximately 42 

degrees (with a minimum of 1 and a maximum of 117). The average AADT at the treated sites 

was about 3,500 (with a minimum of 465 and a maximum of 11,917). The average length of the 

realigned segments was 0.15 mi (with a minimum of 0.03 and a maximum of 0.60).

Table 12. Recommended CMFs.

Metric Total

Injury and 

Fatal

Run-Off-Road

Plus Fixed-Object Dark Wet-Road

Estimate of CMF 0.315 0.259 0.216 0.584 0.204

Standard error of 

estimate of CMF 0.064 0.086 0.068 0.176 0.079

Note: Bold text indicates that CMF is statistically significant at the 95-percent confidence level.

Estimated CMFunctions showed that safety benefits may be greater for curves with a larger 

central angle and where the difference in radius between the before- and after-period conditions 

is larger.

In addition to developing the CMFs using before–after evaluation, this study also compared the 

total crash CMF with the results from previous cross-sectional studies. The CMFs from this 

before–after evaluation are much lower than CMFs estimated by two previous cross-sectional 

studies. The CMFs from the cross-sectional studies were between 0.600 and 0.750 compared to 

the CMF of 0.315 derived from this before–after evaluation. The economic analysis revealed a 

B/C ratio of 3.17:1 with a range of 1.75:1 to 4.38:1.

LIMITATIONS

There are several recognized limitations to these findings, which are as follows:

• The sample size is limited. The project team recommends further studies with a larger set 

of sites.

• Typically, before–after evaluations using the EB method include annual calibration 

factors to account for time trends. However, the limited sample of sites and crashes in the 

reference group did not allow for the use of annual calibration factors. Given the 

substantial effects estimated for all crash types, it is unlikely that accounting for time 

trends would have materially affected the conclusions. 
36

• This evaluation did not explicitly consider other changes that may have occurred at the 

same time that the States realigned the curves (e.g., changes to the roadside, including the 

clear zone). It is important to note that at least one of the previous cross-sectional studies 

did not account for changes to roadside or the shoulder.(4)

• The project team did not collect grade and vertical curvature of the subject segments. The 

team recognizes that, as shown in the work by Bauer and Harwood, the presence of a 

grade or vertical curve can affect the CMF of the change in horizontal curve radius.(4)

• The project team did not explicitly know of the presence of a spiral transition for each 

curve, though the total curve length and crash data would have included any spiral portion 

of road. The work by Zegeer et al. and presented in the HSM includes a factor for spiral 

presence.(8)

• This evaluation did not include information about chevrons or other types of delineation 

at the horizontal curves that States realigned. However, other previous cross-sectional

studies also did not account for delineation of the curves.

(4)

• The authors recognize the potential for data error, specifically crash locating, when 

working with sections/curves of small length. In addition, crash positions in rural areas 

especially can vary in accuracy. Appendix B provides a further discussion of this issue.
37

APPENDIX A. SITE DATA

The tables in this appendix provide the full characteristics and volume data on the sites used in 

the study. Table 13 provides a description of each data field and notes on how the project team 

coded each field. Table 14 provides the data for the treatment sites, and table 15 provides the data 

for the reference sites.

Table 13. Descriptions and coding of data fields.

Data Field Description Coding Notes

DCMF StudyID Unique ID for each curve.

Concluding letter R mostly indicates reference 

site, but not always. Trust the "Treatment or 

Reference" column.

Segment length (mi) Length of curve. Distances are in miles.

State State of origin. There were three States—CA, NC, and OH. 

Treatment or 

reference

Indicator of treatment or 

reference site.

Curve radius before

(ft)

Radius of curve before 

realignment.

Measurement was taken from estimated point of 

curve (PC) to estimated point of tangent (PT).

Curve radius after

(ft)

Radius of curve after 

realignment.

Measurement was taken from estimated PC to 

estimated PT.

Last year of before

period

Use all years up to and 

including this year for the 

before period (treatment 

sites).

This was determined based on the project 

construction start date.

First year of after

period

Use all years after and 

including this year for the 

after period (treatment sites).

This was determined based on the project 

construction end date.

Distance to end 

milepost of previous 

curve (mi)

Distance in miles to previous 

curve (upstream according to 

mileposting).

This can be used to categorize curves as isolated 

or grouped. If the distance was over 0.5 mi, the 

exact distance was not always measured but 

listed as “>0.5.”

Distance to begin 

milepost of next 

curve (mi)

Distance in mi to next curve 

(downstream according to 

mileposting).

This can be used to categorize curves as isolated 

or grouped.

At or near 

intersection 

Indicates whether an 

intersection occurred in or 

near the ends of the curve.

Unknown means the data was not collected for 

that site.

Speed limit Speed limit in mph. Only available for NC.

Right shoulder 

width Right shoulder width in feet. Only available for NC and CA.

Left shoulder width Left shoulder width in feet. Only available for NC and CA.

Number of lanes

Number of though lanes in 

curve.

Note that CA had some sections that were 3-

lane.

AADT

AADT in vehicles per day 

(vpd) for the curve. Provided 

annually.

Availability of certain years of AADT depended 

on the State data in HSIS.
Table 14. Treatment site data by segment.

DCMF 

StudyID

Length 

(mi)

Curve 

Radius 

Before

(ft)

Curve 

Radius 

After

(ft)

Last 

Year 

of 

Before

Period

First 

Year 

of 

After

Period

Distance to 

End 

Milepost

of 

Previous 

Curve (mi)

Distance to 

Begin 

Milepost 

of Next 

Curve (mi)

At or Near 

Intersection

Speed 

Limit

Right 

Shoulder 

Width (ft)

Left 

Shoulder 

Width (ft) Lanes

Average 

AADT

NC002-A 0.1710 470 20,000 2004 2007 0.384 0.261 N 55 4 3 2 4,167

NC002-C 0.1430 398 698 2004 2007 0 0.667 N 55 4 4 2 2,608

NC003 0.1950 445 842 2009 2012 0.05 0.268 N 55 4 4 2 4,500

NC004-A 0.0600 337 433 2011 2013 0.064 0.147 N 45 3 3 2 11,917

NC004-B 0.0830 380 415 2011 2013 0.392 0.064 N 45 3 3 2 11,917

NC005 0.3150 554 818 2011 2014 0.55 0.363 N 55 6 6 2 3,042

NC006 0.1700 307 512 2011 2014 0.009 0.016 Y 55 4 4 2 1,942

NC008 0.0830 206 351 2007 2010 0.199 0.072 N 55 4 4 2 445

NC009 0.1090 570 1,023 2010 2013 0.063 0.258 Y 55 2 2 2 6,008

NC010 0.0800 579 1,146 2011 2013 >0.5 0.34 N 45 5 5 2 4,150

CA002A 0.0668 110 362 2009 2012 0.000 0.000 Unknown – 2 2 2 2,720

CA002B 0.0250 158 445.5 2009 2012 0.000 0.041 Unknown – 2 2 2 2,720

CA003-A 0.1095 335 500 2008 2012 0.054 0.000 N – 2 2 2 2,246

CA003-D 0.3189 1,781 10,000 2008 2012 0.000 0.068 N – 2 2 2 2,246

CA005 0.1290 545 872 2006 2010 0.372 0.074 Unknown – 6 6 2 988

CA011 0.1303 229 1,640 2003 2006 0.345 0.577 N – 6 2 2 3,400

CA013-2 0.1223 419 684 2004 2007 0.063 0.022 Unknown – 4 4 3 6,004

CA013-A 0.0867 440 742 2005 2009 0.163 0.061 Unknown – 4 4 3 6,145

CA013-C 0.1077 429 601.5 2005 2009 0.000 0.135 Unknown – 4 4 3 6,145

CA013-D 0.1200 390 809 2005 2009 0.000 0.052 Unknown – 4 4 3 6,145

CA015-A 0.1095 566 1,102 2005 2008 0.206 0.000 N – 2 2 2 466

CA018-A 0.0600 157 1,588 2008 2012 0.040 0.000 Unknown – 8 4 2 3,800

CA018-B 0.0700 190 1,079 2008 2012 0.017 0.000 Unknown – 8 4 3 3,800

CA018-C 0.0700 190 1,657 2008 2012 0.000 0.000 Unknown – 8 4 3 3,800

38
DCMF 

StudyID

Length 

(mi)

Curve 

Radius 

Before

(ft)

Curve 

Radius 

After

(ft)

Last 

Year 

of 

Before

Period

First 

Year 

of 

After

Period

Distance to 

End 

Milepost

of 

Previous 

Curve (mi)

Distance to 

Begin 

Milepost 

of Next 

Curve (mi)

At or Near 

Intersection

Speed 

Limit

Right 

Shoulder 

Width (ft)

Left 

Shoulder 

Width (ft) Lanes

Average 

AADT

CA018-D 0.0700 200 441 2008 2012 0.000 0.000 Unknown – 8 4 3 3,800

CA022 0.0752 227.5 446 2008 2011 0.000 0.000 Unknown – 4 2 2 3,975

CA025-A 0.1754 902.5 1,312 2005 2009 0.517 0.124 N – 8 8 2 1,669

CA025-B 0.3341 850.5 4,495 2005 2009 0.124 0.092 Y – 8 8 2 1,669

CA026-D 0.1100 405 1,902 2006 2010 0.000 0.000 Y – 6 6 2 753

CA027 0.1246 500 1,200 2004 2008 0.100 0.150 N – 2 2 2 1,055

CA028-C 0.0455 500 1,312 2006 2010 0.000 0.180 Unknown – 1 1 2 2,535

CA030-A 0.0432 187 20,000 2005 2010 0.000 0.000 Unknown – 2 2 2 466

CA030-B 0.0703 475 875 2005 2010 0.000 0.000 Unknown – 2 2 2 466

CA034-A 0.6000 964 20,000 2008 2011 0.030 0.000 N – 2 2 2 1,181

CA034-B 0.4500 532.5 1,409 2008 2011 0.000 0.265 N – 8 2 3 1,181

OH001 0.2080 177.12 954.93 2004 2006 1.329 0.347 Y – – – 2 6,143

OH004 0.1540 387.04 1,069.28 2009 2012 2.69 0.357 N – – – 2 3,396

OH011 0.1080 259.12 700 2003 2005 0.32 >.5 Y – – – 2 3,579

OH012 0.1700 282.08 800 2007 2009 0.695 0.52 N – – – 2 2,368

–No data.

39
Table 15. Reference site data by segment.

DCMF 

StudyID

Length 

(mi)

Curve 

Radius 

(ft)

Distance to 

End Milepost

of Previous 

Curve (mi)

Distance to 

Begin 

Milepost

of Next 

Curve (mi)

At or Near 

Intersection

Speed 

Limit

Right 

Shoulder 

Width 

(ft)

Left 

Shoulder 

Width 

(ft) Lanes

Average 

AADT

NC002-R 0.0650 304 0.458 0.31 Y 55 4 4 2 2,608

NC004-R 0.0940 538 0.496 0.392 N 45 8 8 2 11,917

NC005-R 0.1300 1,141 0.363 NA N 55 6 6 2 3,042

NC007-R 0.0870 673 0.088 0.196 N 55 6 6 2 2,142

NC008-R1 0.0610 168 0.05 0.061 N 55 4 4 2 442

NC008-R2 0.0650 170 0.068 0.052 N 55 4 4 2 428

NC009-R 0.1010 967 0.087 0.074 N 55 2 2 2 6,008

NC010-R 0.0450 730 0.405 0.637 N 45 5 5 2 4,150

NC001-R 0.0540 248 0.29 >0.5 N 55 4 4 2 917

NC003-R 0.1890 741 0.332 0.209 Y 55 4 4 2 3,808

NC006-R 0.0590 918 0.059 0.341 N 55 4 4 2 1,121

CA002R1 0.0470 144 0.034 0.034 Unknown – 2 2 2 2,720

CA002R2 0.0532 75 0.022 0.030 Unknown – 8 8 2 2,663

CA003R1 0.0598 324 0.075 0.000 Unknown – 2 2 2 2,246

CA003R2 0.0744 516 0.053 0.100 Unknown – 4 2 2 1,808

CA005R1 0.0824 503 0.097 0.384 Unknown – 6 6 2 988

CA005R2 0.0496 404 0.102 0.131 Unknown – 6 6 2 988

CA006 0.1900 2,938 0.542 4.600 Y – 4 4 2 2,878

CA006R 0.1400 2,181 0.660 0.542 Unknown – 4 4 2 3,257

CA011R 0.1015 1,341 0.113 0.340 Unknown – 6 2 2 3,400

CA013R1 0.1000 430 0.000 0.140 Unknown – 4 4 3 6,209

CA013R3 0.0621 420 0.028 0.108 Unknown – 4 4 3 6,145

CA015R1 0.0907 940 0.179 0.284 Unknown – 2 2 2 466

CA015R2 0.0483 427 0.056 0.021 Unknown – 2 2 2 466

CA018R1 0.0811 234 0.027 0.072 Unknown – 4 4 2 3,975

40
DCMF 

StudyID

Length 

(mi)

Curve 

Radius 

(ft)

Distance to 

End Milepost

of Previous 

Curve (mi)

Distance to 

Begin 

Milepost

of Next 

Curve (mi)

At or Near 

Intersection

Speed 

Limit

Right 

Shoulder 

Width 

(ft)

Left 

Shoulder 

Width 

(ft) Lanes

Average 

AADT

CA018R2 0.0650 298 0.010 0.009 Unknown – 4 4 2 3,975

CA018R3 0.0981 210 0.000 0.000 Unknown – 4 4 2 3,975

CA018R4 0.0697 137 0.000 0.000 Unknown – 4 4 3 3,975

CA022R 0.0360 309 0.000 0.026 Unknown – 4 2 2 3,975

CA025R2 0.2000 1,443.5 0.070 0.180 Unknown – 9 9 2 1,669

CA026R1 0.0636 332 0.052 0.000 Unknown – 2 2 2 401

CA026R2 0.0508 179 0.000 0.020 Unknown – 2 2 2 401

CA026R3 0.0754 345 0.000 0.086 Unknown – 2 2 2 401

CA027R 0.4379 1,993 0.100 0.192 Unknown – 2 2 2 1,037

CA028R1 0.0811 592 0.087 0.000 Unknown – 2 2 2 3,200

CA028R2 0.0900 1,270 0.302 0.036 Unknown – 1 1 2 2,618

CA028R3 0.0498 580 0.170 0.150 Unknown – 3 3 2 1,871

CA029 0.2155 340 3.083 1.467 N – 4 4 2 7,068

CA029R1 0.0854 336 0.082 0.032 Unknown – 4 4 2 4,938

CA029R2 0.1076 441 0.000 0.000 Unknown – 2 2 2 4,938

CA030R1 0.0473 197 0.000 0.000 Unknown – 2 2 2 466

CA030R2 0.0960 335 0.152 0.000 Unknown – 2 2 2 466

CA032R1 0.0445 253 0.000 0.000 Unknown – 3 3 2 719

CA032R2 0.0300 241 0.022 0.009 Unknown – 6 6 2 719

CA034R1 0.1300 480 0.050 0.120 Unknown – 2 2 2 1,181

CA034R2 0.1200 467 0.080 0.000 Unknown – 2 2 2 1,181

CA034R3 0.2000 925 0.060 0.400 Unknown – 2 2 2 1,181

CA035R1 0.1028 350 0.028 0.099 Unknown – 4 4 2 589

CA035R2 0.0769 292 0.100 0.033 Unknown – 4 4 2 589

OH002R 0.0350 331.28 0.084 0.915 Y – – – 2 4,055

OH002R1 0.0520 764.24 0.186 0.177 N – – – 2 4,055

41
DCMF 

StudyID

Length 

(mi)

Curve 

Radius 

(ft)

Distance to 

End Milepost

of Previous 

Curve (mi)

Distance to 

Begin 

Milepost

of Next 

Curve (mi)

At or Near 

Intersection

Speed 

Limit

Right 

Shoulder 

Width 

(ft)

Left 

Shoulder 

Width 

(ft) Lanes

Average 

AADT

OH002R2 0.0620 295.2 0.919 0.806 Y – – – 2 4,055

OH003R 0.0860 541.2 0.145 0.272 Y – – – 2 1,733

OH003R1 0.1090 596.96 0.157 0.189 N – – – 2 2,396

OH012R 0.0510 403.44 0.268 0.695 N – – – 2 2,368

OH013R1 0.0920 583.84 0.168 0.633 N – – – 2 1,879

–No data.

42
43

APPENDIX B. INVESTIGATION OF CRASH LOCATION ACCURACY ISSUES USING 

NORTH CAROLINA DATA

One of the issues with crash studies involving horizontal curves, particularly in rural areas, is the 

potential error in locating crashes on short sections. In order to investigate the potential impact of

crash location errors, North Carolina Department of Transportation (NCDOT) conducted a 

detailed manual review of each crash that occurred at and/or near the treated sections in North 

Carolina. NCDOT staff assigned a crash to the treated sections based on a manual review of each 

crash report, including the crash diagram and the narrative, even if the crash was not originally 

assigned to the section based on the milepost. The authors conducted a naïve before–after 

evaluation of the treatment using both the NCDOT results and the results based on the crashes 

assigned to the sections solely based on the mileposts. The results of the naïve before–after 

evaluation for total crashes are available in table 16.

Table 16. Naïve before–after evaluation for total crashes—North Carolina. 

Source of Crash Data

Crashes in 

the Before 

Period

Crashes in 

the After 

Period

Expected 

Crashes in the 

After Period 

Without 

Treatment

CMF (S.E.) 

Based on Naïve 

Before–After 

Evaluation

Mileposted crashes only 68 12 32.6 0.34 (0.13)

NCDOT manual review 

of individual crashes 184 18 80.2 0.22 (0.06)

As evidenced in the table, the number of crashes in the before period is about three times higher 

for NCDOT’s manual review of individual crash reports compared to crashes that were assigned 

solely based on milepost information. A large portion of this difference is from one site where 

there were 7 crashes assigned to that section based on the milepost, but NCDOT determined that 

there were 65 crashes in that section. However, even after excluding this potential outlier, the 

number of crashes in the before period was about two times higher based on NCDOT’s review.

This led to the question of whether the accuracy of crash counts on short sections affected the 

CMF results. The results from this investigation by NCDOT show that the curve realignment 

may be more effective than originally thought (i.e., calculated from mileposted crashes). 

However, a homogeneity test conducted using the CMFs from these two methods revealed that 

the difference between the CMFs was not statistically significant at the 0.05 level.

This analysis presents considerations for future research efforts. Most studies solely rely on 

mileposts to assign a crash to a section. This limited study by NCDOT has revealed that relying 

solely on mileposts could potentially lead to significant errors, as the crashes may be largely 

undercounted. For this study, the effect of this undercounting on the CMF result was not 

significant. Further research is needed to investigate this issue. 

45

ACKNOWLEDGMENTS 

This report was prepared for the FHWA Office of Safety Research and Development under 

Contract DTFH61-13-D-0001. The FHWA Program and Task Manager for this project was Roya 

Amjadi.

The team gratefully acknowledges that this research would not have been possible without the 

assistance provided by the following agencies:

• Caltrans.

• NCDOT.

• Ohio DOT.

The authors would like to especially thank NCDOT staff for their detailed review of the crash 

data from North Carolina and for educating the research team about the importance of crash 

location errors in short sections. The authors would also like to thank HSIS staff for providing 

data for this research.

47

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