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Potential crash reduction benefits of shoulder rumble strips in two-lane rural highways
Accident Analysis and Prevention 75 (2015) 35–42
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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 xxx
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: [email protected] (M. Khan), [email protected] (A. Abdel-Rahim), [email protected] (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).
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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
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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
Crash counts
AADT
Before
Number of years 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
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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
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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
0.14 0.13
<.0001 <0.001
0.22 0.12
0.041 0.112
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
Roadway traffic characteristics Log (AADT)
0.684
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 Time effect Year (year 2009 is the base) Year = 2001 Year = 2002 Year = 2003 Year = 2004 Year = 2005 Year = 2006 Year = 2007 Year = 2008 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
p-value
<.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
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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 0 19 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
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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.
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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. References American Association of State Highway Transportation Officials (AASHTO), 2010. Highway Safety Manual, 1st ed. AASHTO, Washington, D.C. Appiah, Naik, B., Wojtal, R., Rilett, L.R., 2011. Safety effect of dilemma-zone protection using actuated advance warning systems. Transport. Res. Rec. 2250, 19–24. Bamzai, R., Lee, Y., Li, Z., 2011. Safety impacts of highway shoulder attributes in Illinois. Illinois Center for Transportation Research Report ICT-11-078. El-Basyouny, K., Sayed, T., 2012. Linear and nonlinear safety intervention models: novel methods applied to evaluation of shoulder rumble strips. Transport. Res. Rec. 2280, 28–37. Federal Highway Administration (FHWA), Roadway departure safety. 2013. Retrieved June 23, 2013 from http://safety.fhwa.dot.gov/roadway_dept/. Federal Highway Administration (FHWA) Resource Center, Rumble strips. 2004. Retrieved June 23, 2013 from http://www.fhwa.dot.gov/resourcecenter/teams/ safety/safe_8rum.cfm. Feldman, M., Manzi, J.G., Mitman, M.F., 2010. An empirical bayesian evaluation of the safety effects of high-visibility school (yellow) crosswalks in San Francisco. Transport. Res. Rec. 2198, 8–14. Fitzpatrick, K., Park, E.S., 2010. Safety effectiveness of the hawk pedestrian crossing treatment. Technical Report. Federal Highway Administration FHWA-HRT-10042. Gårder, P.E., Davies, M., 2006. Safety effect of continuous shoulder rumble strips on rural interstates in Maine. Transport. Res. Rec. 156–162. Griffith, M.S., 1999. Safety evaluation of rolled-in continuous shoulder rumble strips installed on freeways. Transport. Res. Rec. 1665, 28–34.
Hauer, E., 1997. Observational Before–After Studies in Road Safety. Pergamon Publications, London. Hauer, E., Harwood, D.W., Council, F.M., Griffith, M.S., 2002. Estimating safety by the empirical Bayes method: a tutorial. Transport. Res. Rec. 1784, 126–131. Liu, C., Ye, T.J., 2011. Run-off-road crashes: an on-scene perspective. Technical Report. U.S. Department of Transportation, American National Highway Traffic Safety Administration, Washington, D.C DOT HS 811 500. Liu, C., Subramanian, R., 2009. Factors related to fatal single-vehicle run-off-road crashes. Technical Report. U.S. Department of Transportation, American National Highway Traffic Safety Administration, Washington, D.C DOT HS 811 232. Park, J., Abdel-Aty, M., Lee, M., 2014. Exploration and comparison of crash modification factors for multipletreatments on rural multilane roadways. Accid. Anal. Prev. 70, 167–177. Patel, R.B., Council, F.M., Griffith, M.S., 2007. Estimating safety benefits of shoulder rumble strips on two-lane rural highways in Minnesota: empirical Bayes observational before-and-after study. Transport. Res. Rec. 2019, 205–211. Persaud, B.N., Retting, R.A., Lyon, C.A., 2004. Crash reduction following installation of centerline rumble strips on rural two-lane roads. Accid. Anal. Prev. 36 (6), 1073–1079. Persaud, B., Lan, B., Lyon, C., Bhim, R., 2010. Comparison of empirical Bayes and full Bayes approaches for before?after road safety evaluations. Accid. Anal. Prev. 42 (1), 38–43. Sayed, T., deLeur, P., Pump, J., 2010. Impact of rumble strips on collision reduction on BC highways: a comprehensive before and after safety study. Transport. Res. Rec. 1865, 57–63. Shen, J., Gan, A., 2003. Development of crash reduction factors: methods, problems, and research needs. Transport. Res. Rec. 1840, 50–56. Srinivasan, R., Persaud, B., Eccles, K.A., Carter, D.L., Baek, J., 2010. Safety evaluation of improved curve delineation with signing enhancements. Transportation Research Board 89th Annual Meeting (No. 10-3568). Torbic, D.J., Hutton, J.M., Bokenkroger, C.D., Bauer, K.M., Harwood, D.W., Gilmore, D. K., Dunn, J.M., Ronchetto, J.J., Donnell, E.T., Sommer III, H.J., Garvey, P., Persaud, B., Lyon, C., 2009. NCHRP Report 641: Guidance and Design of Shoulder and Centerline Rumble Strips. Transportation Research Board of the National Academies, Washington, D.C., USA.
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 xxx
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: [email protected] (M. Khan), [email protected] (A. Abdel-Rahim), [email protected] (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).
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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
Crash counts
AADT
Before
Number of years 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
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
0.14 0.13
<.0001 <0.001
0.22 0.12
0.041 0.112
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
Roadway traffic characteristics Log (AADT)
0.684
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 Time effect Year (year 2009 is the base) Year = 2001 Year = 2002 Year = 2003 Year = 2004 Year = 2005 Year = 2006 Year = 2007 Year = 2008 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
p-value
<.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
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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 0 19 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
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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.
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