Accident Analysis and Prevention 75 (2015) 35–42
Contents lists available at ScienceDirect
Accident Analysis and Prevention
journal homepage: www.elsevier.com/locate/aap
Potential crash reduction benefits of shoulder rumble strips in twolane rural highways
Mubassira Khan a, *, Ahmed Abdel-Rahim 1,b , Christopher J. Williams 2,c
a
The University of Texas at Austin, Dept of Civil, Architectural and Environmental Engineering, 301 E. Dean Keeton St. Stop C1761, ECJ Hall, Suite 6.9, Austin
TX 78712-1172, USA
b
The University of Idaho, Dept of Civil Engineering, 115 Engineering Physics Building, Moscow, ID 83844-0901, USA
c
The University of Idaho, Dept of Statistical Science, 875 Perimeter Dr. MS 1104, Moscow, ID 83844-1104, USA
A R T I C L E I N F O
A B S T R A C T
Article history:
Received 10 July 2014
Received in revised form 3 November 2014
Accepted 5 November 2014
Available online 20 November 2014
This paper reports the findings from a study aimed at examining the effectiveness of shoulder rumble
strips in reducing run-off-the-road (ROR) crashes on two-lane rural highways using the empirical Bayes
(EB) before-and-after analysis method. Specifically, the study analyzed the effects of traffic volume,
roadway geometry and paved right shoulder width on the effectiveness of shoulder rumble strips. The
results of this study demonstrate the safety benefits of shoulder rumble strips in reducing the ROR
crashes on two-lane rural highways using the state of Idaho 2001–2009 crash data. This study revealed a
14% reduction in all ROR crashes after the installation of shoulder rumble strips on 178.63 miles of
two-lane rural highways in Idaho. The results indicate that shoulder rumble strips were most effective on
roads with relatively moderate curvature and right paved shoulder width of 3 feet and more.
ã 2014 Elsevier Ltd. All rights reserved.
Keywords:
Run-off-the-road crashes
Shoulder rumble strips
EB before-and after analysis
Two-lane rural highways
1. Introduction
Run-off-the-road (ROR) crashes account for a large number of
severe crashes in the United States. In 2011, ROR crashes resulted in
16,948 fatalities – 51% of the total fatal crashes in the Unites States
(FHWA, 2013). The Federal Highway Administration (FHWA, 2004)
reports that up to 70% of ROR fatalities occur on rural highways
and, of these, about 90% occur on two-lane roads where the
geometry of the road often includes sharper curve and narrower
shoulder width, increasing the frequency and severity of these
crashes.
The majority of ROR crashes involve only a single vehicle and
are caused by driver performance errors, specifically distraction,
drowsiness, fatigue or inattention (Liu and Ye, 2011; Liu and
Subramanian, 2009). Rumble strips are a counter measure aimed at
reducing the frequency and severity of ROR crashes specific to
driver performance errors. Installed along the edge of a travel lane,
shoulder rumble strips produce noise and vibration that alert
drivers when their vehicles are drifting off the roadway.
* Corresponding author. Tel.: +1 512 471 4579; fax: +1 512 475 8744.
E-mail addresses: mubassira@utexas.edu (M. Khan), ahmed@uidaho.edu
(A. Abdel-Rahim), chrisw@uidaho.edu (C.J. Williams).
1
Tel.: +1 208 885 2957; fax: +1 208 885 2877.
2
Tel.: +1 208 885 2802; fax: +1 208 885 7959.
http://dx.doi.org/10.1016/j.aap.2014.11.007
0001-4575/ ã 2014 Elsevier Ltd. All rights reserved.
The safety benefit of shoulder rumble strips in reducing the
frequency and severity of ROR crashes have been emphasized in
many earlier studies (see, Torbic et al., 2009; Persaud et al., 2004;
Gårder and Davies, 2006; El-Basyouny and Sayed, 2012); however,
the research methodologies, target roadways, and the range of
results obtained in earlier studies are vary considerably. Most of
the studies in transportation safety research have used the beforeand-after analysis to evaluate the safety benefits of roadway
treatments such as shoulder rumble strips. The objective of the
before-and-after analysis is to compare the actual number of
crashes that occur after the installation of a safety measure with
the expected number of crashes that would have occurred during
the after period had the treatment not been installed. In this study,
before period crash counts refer crash counts before the
installation of the treatment and after period crash counts refer
crash counts after the treatment has installed. Four types of beforeand-after methods exist in the literature: (1) simple (Naïve)
before-and-after analysis, (2) comparison group (CG) analysis, (3)
empirical Bayes (EB) analysis and (4) full Bayes (FB) analysis.
The Naïve before-and-after analysis assumes the crash data
follows a Poisson distribution and then compares the crash counts
for a location before and after a treatment to assess the safety
benefit attributed to a treatment. However, this method leads to
inaccurate and misleading (usually overestimated safety benefits)
conclusions because of its inherent limitations to address
regression to mean bias and external causal factors that change
with time (Shen and Gan, 2003).
36
M. Khan et al. / Accident Analysis and Prevention 75 (2015) 35–42
The CG analysis method was developed to take into account
different causal factors that change with time by using an
untreated comparison site or a group of sites that have similar
road geographic and traffic volume characteristics as the treatment
site. To estimate the crashes that would have occurred without the
treatment during the after period, the crash data of comparison
site(s) are used. The CG method can produce better estimates of the
after period crashes compared to Naïve before-and-after analysis;
however, the accuracy of the CG analysis results greatly depends on
the selection of comparison sites and cannot address the
regression to mean bias limitation.
The EB Method for estimating safety, developed by Hauer
(1997) and Hauer et al. (2002), increases the precision of
estimation to address the limitation of the Naïve and CG Methods
by accounting for the regression-to-the-mean effect (Shen and
Gan, 2003). The EB method also accounts for external causal factors
that change with time. Such factors can be weather, crash reporting
practices, and driving habits. This method is based on the
recognition that crash counts are not the only measure of safety
for an entity. To estimate the expected number of crashes in the
treatment site without treatment, the EB Method considers two
trends: (1) the crash trend at the treatment site prior to the
treatment installation, and (2) the safety performance or crash
trends at similar sites, referred as comparison sites that did not
have any treatment during the analysis period.
The FB analysis method is a generalized version of the EB
method, where instead of using crash trend information from
similar sites, a distribution of likely values is generated that is
combined with the treatment site specific crash trend to estimate
the expected crashes at the treatment sites without the treatment.
The FB analysis is a useful before-and-after method because it
better accounts for uncertainty in data used, however, is a complex
alternative to the EB approach (Persaud et al., 2010). The
complexity of the FB method makes it less attractive to use than
the EB method.
As a result, the EB method has been the standard for more than
a decade in road safety analysis aimed at evaluating the
effectiveness of different crash countermeasures. Examples of
some transportation safety research using the EB method for
evaluating the effectiveness of different crash countermeasures
include, but are not limited to, shoulder rumble strips (Torbic et al.,
2009; Sayed et al., 2010; Patel et al., 2007; Griffith, 1999);
centerline rumble strips (Torbic et al., 2009; Persaud et al., 2004),
curve delineation with signing enhancement (Srinivasan et al.,
2010); HAWK pedestrian cross-walk treatment (Fitzpatrick and
Park, 2010), actuated advance warning dilemma zone protection
system (Appiah et al., 2011); and high-visibility school crosswalks
(Feldman et al., 2010).
The evaluation of a crash countermeasure is very important to
allocate safety improvement program funds to maximize the
benefits of safety improvement projects. The result of the beforeand-after analysis is also used to develop crash modification
factors (CMF) aimed at estimating the potential changes in number
of crashes after the implementation of crash countermeasures. For
example, the Highway Safety Manual (AASHTO, 2010) provides
CMFs for various crash countermeasures.
Several states conducted studies to evaluate the safety benefit
of shoulder rumble strips and found that it is an effective crash
countermeasure to reduce single-vehicle ROR crashes (please see,
AASHTO, 2010; Park et al., 2014 for a detail review). For freeway
facilities and multi-lane rural facilities many different studies are
available that analyze the effectiveness of rumble strips, but for
two-lane rural highways, the availability of published research is
very limited (AASHTO, 2010). The CMFs supplied by the Highway
Safety Manual (HSM) only considered the daily traffic volume of
highways to evaluate the safety benefit of shoulder rumble strips.
Because road geometries of two-lane rural highways vary
considerably, a need exists to study how road geometry affects
driver inattention, and how effective rumble strips are at reducing
ROR crashes caused by driver error. For example, a straight
segment of road increases the probability of falling asleep while
driving. Earlier research studies indicated that the effectiveness of
shoulder rumble strips can depend on the road geometry (Patel
et al., 2007); however, no earlier study was found to examine the
effect on different roadway geometry. Again, the shoulder width
can also affect the effectiveness of shoulder rumble strips. This
study contributes to the literature of transportation safety research
by evaluating the effectiveness of shoulder rumble strips in
reducing the number of ROR crashes in two-lane rural highways in
Idaho. Specifically, this study uses the EB analysis method to
investigate the effect of a roadway’s degree of curvature and
shoulder width on the crash reduction benefits of shoulder rumble
strips in two-lane rural highways.
The paper is structured as follows. The next section presents the
EB before-and-after analysis for count data. Section 3 presents
details of data used in the study followed by analysis results in
Section 4. The final section offers concluding thoughts and
directions for further research.
2. Methodology
The EB analysis method employs two sources of data to estimate
the expected number of crashes (A0 ) during the after period in the
treatment site without the treatment. The first source is the accident
trend of the treatment site before the treatment was installed (A01 );
and the second source is the safety performance or accident trends
of control site that do not have any treatment in the analyzed
period (A02 ). Let A be the observed number of reported crashes in
the after period. Then the change in safety for ROR crashes on a
road section with shoulder rumble strips installed is given by:
Changeinsafety ¼ A0 A
(1)
In the EB method, a safety performance function (SPF) for control
sites is used to estimate the annual number of crashes at control
sites that do not have any treatment in the analyzed period. The
SPF is a mathematical model that relates the dependent variable
crash frequency of a road entity to the independent variables such
as traffic volume and geometric characteristics of the entity.
Literature shows that the Poisson and negative binomial (NB)
regression models have been extensively studied and developed
for crash data analysis. However, the over dispersion characteristics of crash data suggests that the Poisson distribution is
inadequate for crash data. The NB distribution assumes that the
mean of the Poisson distribution is gamma distributed. The NB
regression model takes into account the over dispersion
parameter and thus it is now common to assume that accident
data comes from a negative binomial distribution. The sum of the
annual crashes estimated using SPF during the before periods
gives the estimate of A02 . Then the expected number of crashes (A0 )
before shoulder rumble strips installation can be estimated as:
A00 ¼ w1 A01 þ w2 A02 ; wherew1 þ w2 ¼ 1
(2)
where w1 and w2 are relative weights that determine the relative
significance of A01 andA02 .
These relative weights are estimated from the mean and
variance of the NB regression estimate as:
w1 ¼
A02
A02
andw2 ¼ 1 w1
þ 1=k
(3)
where k is the dispersion parameter estimated along with the NB
regression model parameters of SPF.
M. Khan et al. / Accident Analysis and Prevention 75 (2015) 35–42
3. Data description
A major assumption of EB Methodology is that the safety
performance model equation captures regularity on the time series
for a specific entity. To do so a factor is applied to A0 which is the
sum of the annual SPF predictions for the after period divided by
the sum of these predictions for the before period (A01 ). After taking
into account for the length of the after period and differences in
traffic volumes between the before and after periods, the estimate
of the expected number of crashes that would have occurred in the
after period without the shoulder rumble strips (A0 ) is obtained.
An unbiased estimate of the safety effectiveness index (u) of the
shoulder rumble strips installation can be obtained as follows:
u¼
Asum =A0sum
3.1. Data source
Four data sources were used in this research. The first data
source is a vehicle crash report (VCR) from Idaho Transportation
Department’s (ITD), Office of Highway Safety (OHS). All law
enforcement agencies in Idaho are required to send VCR forms to
the OHS, who maintains and archives the data. Therefore, crash
data for this study was obtained from the OHS crash database
using WebCARS, a web based crash analysis system developed
and maintained by the OHS. Crash data for a specific roadway
(such as US 12, US 30 and US 95) for a given number of years was
obtained in a single data file from the WEBCARS system. For each
reported crash for a given roadway the information obtained
included the number of units involved in the crash, the mile
point location selected of the crash, the date when the crash
occurred, and the first harmful event of the crash. All animal
related single vehicle ROR crashes are excluded from the
analysis.
The second data source used in this study is from ITD office of
Highway Operation and Safety (OHOS). OHOS provided all data
regarding the year and the location of the installation of shoulder
rumble strips examined in this study. Shoulder width, lane width
and advisory speed data for the highway sections were also
provided by ITD OHOS. The third data is the yearly vehicle exposure
data, in the form of average annual daily traffic (AADT), was
obtained from ITD automatic traffic recorders (ATRS) data
(4)
1 þ varðA0sum Þ=ðA0sum Þ2
where the estimate of A0 is then summed over all road sections in a
treatment group of interest to obtain A0sum and compared with the
observed number of crashes during the after period in that group
ðAsum Þ. The variance of A0 is also summed over all sections in the
treatment group to obtain varðA0sum Þ. The variance of the safety
effectiveness index can be obtained as:
varðuÞ ¼
u2 ½varðAsum Þ=ðAsum Þ2 þ varðA0sum Þ=ðA0sum Þ2 (5)
½1 þ varðA0sum Þ=ðA0sum Þ2 2
37
The percent change in crashes after the installation of shoulder
rumble strips is obtained as: (1 u) 100. The variance of the
change in crash is same as the variance of the safety effective index
(u) because of variance summation property.
Table 1
Treatment sites details for ROR crashes of two-lane highways.
Site ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
Length (mile)
4.03
5.00
5.00
5.00
5.00
5.00
3.64
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
2.45
6.60
5.00
5.00
2.99
2.63
4.22
4.57
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
2.51
Installation year
2006
2004
2004
2004
2004
2004
2004
2004
2004
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2005
2005
2005
2007
2007
2007
2007
2007
2007
2007
Number of years
Crash counts
AADT
Before
After
Before
After
Before
After
5
3
3
3
3
3
3
3
3
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
4
4
4
6
6
6
6
6
6
6
3
5
5
5
5
5
5
5
5
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
4
4
4
2
2
2
2
2
2
2
7
8
12
6
9
3
8
9
9
5
4
6
9
4
8
8
6
5
5
2
3
3
2
0
3
0
3
7
5
3
10
12
10
10
9
3
1
1
1
10
8
5
8
7
8
8
3
0
1
2
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
4
6
4
4
3
0
0
0
0
5875
3497
3497
3242
2124
2124
2124
3149
1005
638
638
638
638
638
638
638
677
677
677
677
3731
2778
2778
2778
2778
2224
1946
2918
2902
2842
2842
7135
7135
7135
7135
974
974
974
5470
3254
3254
3024
1981
1981
1981
3081
843
559
559
559
559
559
559
559
545
545
545
545
3894
2541
2541
2541
2541
1949
1888
2859
2910
2837
2837
7228
7228
7228
7228
1020
1020
1020
Road curvature type
Paved right shoulder width (feet)
2
3
3
2
3
2
3
3
3
2
3
3
3
3
3
3
3
3
2
3
1
1
1
2
2
2
3
3
3
3
3
2
2
1
2
2
3
2
7
1
3
3
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
5
4
5
5
4
5
6
4
5
5
5
6
3
4
6
1
1
3
38
M. Khan et al. / Accident Analysis and Prevention 75 (2015) 35–42
published. The fourth data source used in this study is the satellite
images from Google Earth for the roadway sections.
3.2. Data assembly
Road curvature data was obtained from two sources: satellite
images from Google Earth and speed advisory signs from ITD sign
inventory database. Three different roadway curvature types for
different road segments were used in the analysis: (1) straight road
segments or road segments with slight curvature, (2) moderate
curvature road segments with horizontal curves with relatively
large radius (roadway segments that have horizontal curves with a
design speed of 50 mph or more), and (3) sharp curvature
segments that require significant reduction in speed (roadway
sections that have sharp horizontal curves with a design speed of
45 mph or lower).
Highways included in the analysis were divided into segments
with length ranging between 1 and 5 miles. Each highway
segment had consistent geometry (road curvature type, number
of lanes, lane and shoulder width), land use category (rural,
suburban, urban), and traffic flow levels. From the crash data file
all single vehicle ROR crashes that occurred in a given year at each
of the homogeneous highway segments are aggregated. The
roadway curvature type, AADT, right shoulder width, and length
of roadway segment data were appended to the aggregated yearly
crash data file.
3.3. Treatment sites
Treatment sites for the analysis were selected from three
highways in Idaho: US 12, US 30 and US 95. During 2004 through
2007, shoulder rumble strips were installed along 260.15-mile
two-lane highway segments in Idaho. Among the treatment
sections, 81.52-mile segments were not considered in the analysis
for two main reasons. First, some of these segments were very
close to city limits and thus have significant differential
operational speed limits. Second, some segments had major
geometric changes, such as change from two-lane to four-lane
segments or change in paved right shoulder width during the
period of the analysis.
After removing data for those roadway segments, 38 two-lane
highway treatment sites with a total length of 178.63 miles of
roadways were used to evaluate the safety effectiveness of
shoulder rumble strips. Lane width for all test sites was a standard
12 feet. The paved right shoulder width of the test sites ranges
between 1 and 7 feet. The AADT of the selected test sections
varied from 500 to 7500.
Detailed test site data of all ROR crashes are presented in
Table 1. Before and after average yearly crashes per 5-mile road
segments and the weighted average AADT are presented in Table 2.
The before and after average yearly crashes per 5-mile road
segments for the three roadway curvature types are presented in
Fig. 1. The average number of crashes for all treatment sites
dropped from 1.341 crashes to 0.721 crashes, which showed an
average 46% reduction in ROR crashes after the treatment. From
this simple comparison between the before and after period
crashes, the highest reduction in ROR crashes was found for road
segments with moderate to sharp horizontal curves. However, this
comparison does not take into account the causal factors that
change with time and cannot identify the reduction in ROR crashes
due to installation of shoulder rumble strips.
Because rumble strips are primarily designed to prevent
inattention, related ROR crashes and reduction in crashes
attributed to the treatment is expected to be the most where
drivers are more likely to be inattentive. Drivers are likely to be
more attentive while driving on road sections with sharp
Table 2
Before and after ROR crashes of two-lane highway treatment sites.
Road
curvature
type
1
2
3
Number
of sites
4
13
21
Length
(mile)
21.60
56.37
100.66
Average
Yearly crash/5 mile
AADT
Before After
Before After Change
(%)
Change
(%)
0.694
1.027
1.653
0.579 17%
0.570 45%
0.839 49%
4078
3483
1718
4039 1%
3390 3%
1627 5%
1.341
0.721
46%
2460
2373 4%
horizontal curve and less attentive when roadways are straight.
Therefore the reduction in number of crashes due to the treatment
is expected to be more for road sections with less horizontal curve
compared to the road sections with sharp horizontal curve. The
weighted average AADT at the treatment sites for all before periods
was 2460 vehicles, which decreased to 2373 vehicles for the after
period, about a 4% reduction. The highest reduction in AADT
between the before and after periods is observed for the road
sections with sharp horizontal curves. Though the crash rates
showed a reduction in ROR crashes after the treatment, it is likely
that some of this reduction may be attributed to the reduction in
traffic volume.
3.4. Control sites
Control sites were randomly selected from the same three US
highways (i.e., US 12, US 30 and US 95): a total of 53 sites were
selected for the two-lane highway before and after study. Yearly
crash data for the selected 53 control sections were assembled
from 2001 to 2009. These control site data were used to develop
the SPF of the EB analysis. Total length of the control sites was
256.2 miles with no shoulder rumble strips installed on any of
them during the analyzing period. Control sites had traffic volume
and geometric characteristics similar to the selected treatment
(test) sites. A total of 466 ROR crashes occurred in 9 years in
53 control sites, and the average yearly crashes per 5-mile road
segments were 1.01. The AADT of the 53 control sections was 2273.
Among 53 road sections a total of 6, 31 and 16 control sections
belonged to the group of straight, moderate and sharp horizontal
curvature categories. A total of 18 control sections had right paved
shoulder width less than 3 feet, 16 sites were available having right
shoulder width of 3 to 4 feet and 19 sites had right shoulder width
5 feet or more.
4. Analysis and results
4.1. Development of the SPF
The SPF developed for the study using the control site data is
assumed to follow an NB regression model. Generalized linear
model methods were used to perform the regression analyses,
using with a log link function. A log linear relationship between the
mean number of crashes and the independent variables is specified
by the log link function. The log link function ensures that the
dependent variable of this model, which is the mean number of
crashes per year per segment of a given length for the fitted model,
is positive. Maximum likelihood estimates (MLE) of all model
parameters were estimated using the GENMOD generalized linear
model procedure in the SAS software package.
The independent variables considered for the model are AADT,
length of road segment, right shoulder width, road curvature
type, and year. Among these variables, AADT was introduced as a
continuous variable, and the roadway segment length was
M. Khan et al. / Accident Analysis and Prevention 75 (2015) 35–42
[(Fig._1)TD$IG]
39
Fig. 1. Before and after ROR crashes of two-lane highway treatment sites.
introduced as an offset variable for which no regression
parameter was estimated. The year variable was introduced to
consider various unobserved factors such as demographic
changes that took place throughout the duration of the study
period. Road curvature type and the year variables were
introduced as class (categorical) variables. For the right paved
shoulder width variable, we tested two alternative functional
forms that included a linear form and dummy variables for
different width ranges. After extensive testing, the paved right
shoulder width was introduced as a set of dummy variables –
“less than or equal to 2 feet”, “3 to 4 feet” and “greater than or
equal to 5 feet”, with the “greater than or equal to 5 feet” as the
base category. Interactions among the variables were also
considered, however, did not come out to be significant.
Diagnostic tests applicable for GLMs were performed for the
developed SPF. To identify outliers which have a large effect on
the outcome of the fitting regression model, the leverage of the
observations were calculated using their hat values. Hat-values,
Table 3
Negative binomial regression model results.
Parameter
Estimate
Standard error
Intercept
7.269
0.999
<.0001
0.13
<.0001
Roadway traffic characteristics
Log (AADT)
0.684
p-value
Roadway environment characteristics
Right shoulder width(width 5 feet is the base)
Right shoulder width 2 feet
0.575
Right shoulder width = 3–4 feet
0.512
Roadway curvature type (type 3 is the base)
Roadway curvature type = 1
0.433
Roadway curvature type = 2
0.180
0.14
0.13
<.0001
<0.001
0.22
0.12
0.041
0.112
Time effect
Year (year 2009 is the base)
Year = 2001
Year = 2002
Year = 2003
Year = 2004
Year = 2005
Year = 2006
Year = 2007
Year = 2008
0.21
0.22
0.21
0.23
0.24
0.23
0.21
0.23
0.079
0.164
0.025
0.070
0.810
0.643
0.092
0.971
Dispersion parameter
Dispersion
Final log-likelihood
0.376
0.302
0.469
0.385
0.056
0.110
0.361
0.008
0.127
432.341
0.07
<.0001
standardized residuals, and Cook’s distances were calculated from
the NB regression model and found no observation with a very
large hat value to select as an outlier. The parameter estimates of
the NB regression model using the control site data are presented
in Table 3.
The sign of the coefficient of the AADT variable is positive and
in-line with earlier research studies (see Patel et al., 2007 and
Bamzai et al., 2011 for similar results). The positive coefficient
value represents that the probability of ROR crash frequency
increases with increasing AADT. The coefficients of the road
curvature variables are estimated where road curvature type 3 is
the base category. As expected, sharper horizontal roadway
curvature increases the likelihood of the higher number of ROR
crashes in two-lane rural highways. Right shoulder width 5 feet is
the base category for the right shoulder width variable. The risk of
higher number of ROR crash is lowest for the base category.
Compared to the base category, the signs of the coefficients of right
shoulder width less than 5 feet are positive. The positive signs for
right shoulder width less than 5 feet indicate that the narrower
shoulder width (width <5 feet) increases the risk of higher number
of ROR crashes. The magnitude of the right shoulder width variable
indicate that narrower right shoulder width increases the
likelihood of the higher number of ROR crashes in two-lane rural
highways. The model result shows that the risk associated with
shoulder width are not linear in nature. This non-linearity may
cause due to the small number of available control sites used in
each of the category and also unobserved factors associated with
the data.
To test the statistical significance for the independent variables,
likelihood ratio (LR) tests were performed and are presented in
Table 4. The LR statistics for the selected independent variables and
their corresponding p-values indicate that AADT, right shoulder
width, and year variables are significant at the 0.05 level in
determining the number of ROR crash for two-lane rural highways.
The road curvature type variable is statistically significant at the
0.10-significance level.
Table 4
Statistical significance test for the independent variables.
Parameter
DF
Chi-square statistics
Pr > ChiSq
Log (AADT)
Right shoulder width
Roadway curvature
Year
1
2
2
8
28.73
20.86
4.95
17.81
<.0001
<.0001
0.0842
0.0227
40
M. Khan et al. / Accident Analysis and Prevention 75 (2015) 35–42
4.2. EB analysis results
The results of EB analysis for all ROR crashes in two-lane rural
highways are presented in Table 5. The observed number of ROR
crashes after the installation of shoulder rumble strips was
92.0 and the EB estimates of the expected crashes without any
treatment was 106.2. The unbiased estimate of safety effectiveness
index and its variance was calculated for each test sites using the
EB procedures. The unbiased estimate of the safety effectiveness
index and its variance were calculated over all road sections.
It was estimated that the installation of rumble strips resulted
in an overall 13.7% reduction for all ROR crashes. The corresponding standard deviation was estimated as 10.5%. The result is
consistent with earlier research on the expected total reduction in
ROR crashes due to shoulder rumble strips on two-lane rural
roads (please see Torbic et al., 2009 and Patel et al., 2007); the
first report estimated a 15% reduction and the second one
estimated a 13% reduction in ROR crashes after shoulder rumble
strips installation). It is important to note that the 95th-percentile
confidence intervals for this CMF would be 13.7% + 20.6%, that
includes zero (that is the estimate is not statistically significant at
the 0.05 level).
Table 5
EB analysis results for two-lane highway treatment sites.
Site ID Observed crashes during the after period Expected crashes during
after period without
treatment
Actual count
1
1
2
10
3
8
4
5
5
8
6
7
7
8
8
8
9
3
10
0
11
1
12
2
13
2
14
0
15
0
16
1
17
0
18
2
19
0
20
1
21
1
22
0
23
1
24
0
25
0
26
1
27
0
28
1
29
0
30
4
31
6
32
4
33
4
34
3
35
0
36
0
37
0
38
0
Actual crash counts
EB estimated crash counts
Percent reduction
EB estimates
Standard
deviation
3.09
1.16
8.70
2.04
10.53
2.21
6.47
1.62
7.65
1.74
4.41
1.25
5.87
1.37
9.14
2.05
5.07
1.19
0.89
0.51
1.08
0.50
1.09
0.60
1.32
0.67
0.93
0.56
1.25
0.65
1.25
0.65
1.06
0.60
0.98
0.58
0.87
0.51
0.45
0.30
1.30
0.76
1.20
0.74
0.80
0.52
0.49
0.41
0.96
0.59
0.59
0.43
0.98
0.59
2.17
1.11
2.99
1.06
3.59
1.16
5.39
1.64
2.86
1.26
3.14
1.45
2.87
1.33
2.43
1.16
1.04
0.61
0.84
0.58
0.50
0.32
92.00
106.23
14% (p-value = 0.19)
Although the installation of rumble strips resulted an overall
improvement in the reduction of ROR crashes, the examination of
each treatment site shows a variability among the effect between
treatment sites. This variability can be attributed to a number of
unobserved factors including environmental factors (such as light
condition, weather condition, and pavement condition), and driver
specific factors. The safety effect of shoulder rumble strips on
different AADT range, road geometry type, and shoulder width are
summarized in Table 6. Although results are not statistically
significant because of the small number of available treatment
sites and the variability within each treatment group, they are
presented here to provide a blueprint to investigate each of the
variable effects.
4.2.1. Treatment evaluation in context of AADT
The EB estimated index of effectiveness shows that shoulder
rumble strips were the most effective in reducing ROR crashes in
low-volume road sections. Road sections with an average AADT
less than 1000, estimated 37% reduction in ROR crashes after the
installation of shoulder rumble strips. This result is not surprising
because in low volume road sections drivers are more likely to
drive less attentively and rumble strips can alert drowsy drivers
when they are about to leave the road.
Two-lane highway sample road sections with moderate AADT
(daily traffic around 2500) and high AADT (daily traffic around
6500) AADT showed 4% and 17% reduction in ROR crashes after
shoulder rumble strip installation. Road sections with relatively
high volumes (AADT values around 6700) experienced 8%
reduction in ROR crashes after rumble strip installation. Surprisingly, the reduction in ROR crashes due to rumble strips was
marginal for AADT values around 2500. All the estimates are not
statistically significant at the 0.05-level, because of the limited
sample size in each AADT group and also because of the presence of
the variability within each group.
4.2.2. Treatment evaluation in context of road geometry type
The actual and expected number of ROR crashes for three
different road curvature types support our hypothesis about the
effect of road geometry on the effectiveness of shoulder rumble
strips in reducing the ROR crashes. Installing rumble strips in
two-lane rural highways resulted in 25% reduction in ROR crashes
for road sections with no horizontal curve (roadway curvature type
1), 22% reduction for road sections with moderate horizontal
curves (roadway curvature type 2), and 11% reduction for road
sections with sharp horizontal curves (roadway curvature type 3).
All the results are not statistically significant at the 0.05-level,
because of the limited sample size in each road geometry type
group and also because of the presence of the variability within
each group. The results indicate that shoulder rumble strips were
most effective in reducing ROR crashes for roads with relatively
moderate curvature (road curvature type 1 and type 2) and less
effective in sections with sharp horizontal curves. As expected,
drivers are more likely to be inattentive while driving in straight or
moderately curvy road sections. In such road sections, shoulder
rumble strips can help them the most when they are about to leave
the roadway.
4.2.3. Treatment evaluation in context of shoulder width
As expected, the effectiveness of shoulder rumble strips in
reducing ROR crashes are minimal for roadway sections having
narrower paved right shoulder (width 2 feet). Narrower right
shoulder provides less recovery area beyond the shoulder and can
reduce the effectiveness of the shoulder rumble strips. In such
roadway sections site specific road safety measures should be
evaluated. Right paved shoulder width of 3 feet and more shows a
higher reduction in ROR crashes after the treatment. Safe travel of
M. Khan et al. / Accident Analysis and Prevention 75 (2015) 35–42
41
Table 6
EB analysis results for different AADT levels, paved right shoulder widths and road curvature types.
AADT
Number of sites Length (mile) Count of crashes during after period Expected crashes
during after period
without treatment
AADT before
AADT after
734
2552
3504
7135
658
2425
3470
7228
Paved right
shoulder width
(feet)
15
13
6
4
70
58
30.6
20
Actual counts
EB estimates Std. dev.
12
36
33
11
18.62
37.1
39.23
11.3
2.4
3.84
4.22
2.6
Number of sites Length (mile) Count of crashes during after period Expected crashes during after
period without treatment
Actual counts
EB estimates
Std. dev.
% Change in Crash (% Std. dev, p-value)
37% (20%, p = 0.08)
4% (19%, p = 0.83)
17% (17%, p = 0.37)
8% (31%, p = 0.84)
% Change in crash (% Std. dev, p-value)
19
91.1
53
53.89
4.53
2% (16%, p = 0.88)
8
35.1
21
27.82
3.69
26% (19%, p = 0.21)
11
52.4
18
24.51
3.31
28% (19%, p = 0.18)
2
3 to 4
5
Road
curvature
type
Number of sites Length (mile) Count of crashes during after period Expected crashes during after period % Change in crash (% Std. dev, p-value)
without treatment
Actual counts
EB estimates
Std. dev.
4
21.6
5
6.16
1.78
25% (38%, p = 0.58)
13
56.4
22
27.74
3.5
22% (19%, p = 0.25)
21
100.7
65
72.98
5.51
11% (13%, p = 0.38)
1
2
3
all non-motorized travelers can also be positively affected by the
available wider right shoulder width (Torbic et al., 2009). All of
these results are not statistically significant at the 0.05-level,
because of the limited sample size in each road shoulder width
group and also because of the presence of the variability within
each group.
5. Conclusions
This paper examined the effectiveness of shoulder rumble
strips in reducing the number of ROR crashes on two-lane rural
highways in Idaho using an empirical Bayes (EB) before-and-after
analysis method. The results of this study demonstrate the safety
benefits of shoulder rumble strips in reducing the ROR crashes on
two-lane rural highways. The state of Idaho 2001–2009 crash data
was used as the primary data source for the study. The specification
adopted in the current paper for developing the safety performance function was comprehensive. The study finds a 14%
reduction in all ROR crashes after installation of shoulder rumble
strips on 178.63 miles of two-lane rural highways in Idaho. As
expected, the roadway geometry type and the paved right shoulder
width affect the effectiveness of shoulder rumble strips on
two-lane rural highways. The results indicate that shoulder
rumble strips were most effective in reducing ROR crashes for
roads with relatively moderate curvature (road curvature type
1 and type 2) and right paved shoulder width of 3 feet and more.
Since the installation cost of shoulder rumble strips are relatively
low, the results obtained in this study suggest application of the
shoulder rumble strip treatment in two-lane rural roadways roads
relatively moderate curvature (road curvature type 1 and type 2)
and right paved shoulder width of 3 feet and more should be
continued. Since wider shoulder width (3 feet and wider) provides
additional room for non-motorized travel, installation of shoulder
rumble strips is also recommended in shoulder widening projects
that can potentially help non-motorized traffic in the absence of
designated bike-path. For the roadway sections with shaper
horizontal curvature, shoulder rumble strips should be implemented with additional curve delineation treatments to reduce the
ROR and other crashes. The results obtained in this study are
consistent with earlier research studies. The reduction, specific to
different road geometry types due to shoulder rumble strips
installation, can also be used for two lane rural highways,
specifically in Pacific Northwest region, with similar roadway
operating and geometric configurations.
The paper, however, is not without its limitations. Because this
study focused on the effectiveness of shoulder rumble strips in
reducing all ROR crashes in two-lane rural highways in Idaho, the
effectiveness of this treatment for severe crashes (such as fatal
and/or incapacitating crashes) could not be investigated explicitly
because of the smaller sample size of severe crashes during the
analyzing periods in the control and test sections. Earlier research
studies, however, have shown the effectiveness of shoulder rumble
strips in reducing the severe ROR crashes.
A larger sample size of the severe ROR crashes can effectively
identify the treatment effect in reducing the severe ROR crashes.
Also, with several earlier studies, use of police reported crash data
may affect the reduction found in our study because minor crashes
are often found to be under-reported. Further, the time of day and
weather condition can also affect the frequency and severity of ROR
crashes. Specifically, shoulder rumble strips may have higher
benefit during nighttime compared to daytime crashes. Again
during the ice and snow storms, drivers are much more attentive
and therefore the effectiveness of shoulder rumble strips can be
different in different weather condition. The limited sample size of
the current study didn't permit the investigation specific to the
time of day. The individual result specific to different traffic
exposure (AADT), road geometry type and right shoulder width
was also not statistically significant because of the available
sample sites in each group. Any further research with a larger
sample roadway segments should be undertaken to further
examine this relationship.
42
M. Khan et al. / Accident Analysis and Prevention 75 (2015) 35–42
Acknowledgements
The authors are grateful to Lisa Smith for her help in formatting
this document. Three referees provided valuable comments on an
earlier version of this paper.
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