ESTIMATING CRASH MODIFICATION FACTORS USING CROSS-SECTIONAL AND CASE-CONTROL METHODS FOR RUMBLE STRIPS AND PAVED SHOULDERS

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1 0 ESTIMATING CRASH MODIFICATION FACTORS USING CROSS-SECTIONAL AND CASE-CONTROL METHODS FOR RUMBLE STRIPS AND PAVED SHOULDERS Uditha Galgamuwa Graduate Research Assistant Department of Civil Engineering Fielder Hall Kansas State University Manhattan, KS Tel: --00; Sunanda Dissanayake, Ph.D., P.E. (Corresponding Author) Professor Department of Civil Engineering Fielder Hall Kansas State University Manhattan, KS Tel: --0: 0 Word count:,0 words text + tables/figures x 0 words (each) =, 0 words Submission Date: //0 0 A paper submitted for presentation at the th Annual Meeting of the Transportation Research Board and for publication in the Journal of the Transportation Research Record.

2 0 0 ABSTRACT This paper describes the application of case-control and cross-sectional methods to develop crash modification factors (CMFs) for lane departure countermeasures in two-lane rural undivided road segments in Kansas. Four commonly used countermeasures, namely -ft paved shoulders, centerline rumble strips, shoulder rumble strips, and shoulder & centerline rumble strips have been considered. CMFs were calculated for all severity and fatal & injury lane departure crashes. Generalized linear regression assuming a negative binomial error structure and logistic regression were used in developing models for cross-sectional and case-control methods respectively. Mean residuals and mean squared error (MSE) were used to validate the models developed for cross-sectional method. Classification tables were used to validate the models developed for case-control method. Cross-sectional method shows that all the countermeasures considered in this study were effective in reducing all severity and fatal & injury lane departure crashes. However, the range of CMF includes, for the shoulder rumble strips on curved road segments for all crash severities, which indicates that it has some crash increasing effect. The case-control study also shows that all the countermeasures have a crash reduction effect except shoulder rumble strips on curved road segments for all crash severities. Even though similar results were obtained from both methods, CMFs developed using the cross-sectional method demonstrated a narrower range than the case-control method indicating that the results from the cross-sectional method can be considered as more accurate and reliable than those from casecontrol method. Keywords: Cross-sectional method, Case-control method, Lane departure crashes, Countermeasure evaluation, Crash modification factors 0

3 0 0 0 INTRODUCTION Motor vehicle injuries are one of the ten leading causes of death worldwide (). According to the National Highway Traffic Safety Administration (NHTSA), nearly,000 people died due to motor vehicle crashes in the United States in 0 (). Since 00 to 0, more than 0 fatalities and approximately,00 disabling injuries have occurred in Kansas each year. According to the Kansas Crash Analysis and Reporting System (KCARS) database and Kansas Strategic Highway Safety Plan 0 (SHSP) (), a majority of fatal and disabling crashes are lane departure crashes which can be defined as a vehicle wheel path crossing over the either side of lane line and encroaching on either the shoulder or the adjacent lane (). For the time period of 00 to 0, lane departure crashes accounted for approximately 0% of total fatalities and disabling crashes in Kansas(). The Kansas Department of Transportation (KDOT) has implemented countermeasures such as rumble strips, paved shoulders, high-tension median cable barriers, safety edges, high-friction surface treatments, oversize chevrons, optical speed bars, and pavement legends in many road segments to reduce lane departure crashes. Crash Modification Factors (CMFs) have become popular in evaluating safety effectiveness of countermeasures with the recent introduction of the Highway Safety Manual (HSM) (). Although several studies have been conducted in Kansas to calculate CMFs for composite shoulders, unpaved shoulders, wide shoulders, and bypass lanes in work zones, more accurate CMFs for Kansas have not yet been fully accomplished. CMFs that are available in other regions or national-based studies may not be accurate for Kansas due to variations in spatial and temporal characteristics. Accordingly, having more localized CMFs is going to be an advantage in addressing lane departure crashes. Since majority of fatal and disabling lane departure crashes that in rural areas, this study focused on lane departure countermeasures on rural two-lane undivided road segments. This study identified commonly used countermeasures, paved shoulders and rumble strips, to estimate reliable and accurate CMFs for lane departure crashes. CMFs were developed for the presence of -ft wide paved shoulders in rural two-lane undivided road segments. For rumble strips, CMFs were developed for the presence of centerline rumble strips, shoulder rumble strips and both centerline & shoulder rumble strips. Both cross-sectional and case-control methods were used to develop CMFs because the date of implementation could not be easy to be found for those countermeasures. Developed CMFs could be used to guide the decision-making process when implementing lane departure countermeasures in Kansas. 0 LITERATURE REVIEW Road safety studies commonly require the evaluation of effectiveness of roadway safety measures for crashes. Nearly 0 % of transportation agencies in the United States use CMFs for safety evaluations of design alternatives, design expectations, and design consistency evaluations (). CMF is defined as the expected number of crashes with an action, divided by the expected number of crashes had the action not been taken (). Before-after with comparison group studies (, ), empirical Bayes before-after studies (, -), full Bayes studies (,,, ), crosssectional studies(,,, ), case-control studies( -,, ) and cohort studies (, ) are frequently used to calculate CMFs. Using different method available for developing CMFs, many research have been conducted to identify the safety effectiveness of various countermeasures.

4 Among many different countermeasures, centerline rumble strips, shoulder rumble strips () and paved shoulders have been identified as few of the most effective countermeasures in two-lane roadways. Following studies have summarized the effect of paved shoulders and rumble strips on lane departure related crashes. A study conducted for rural two-lane highways in Kansas found that upgrading narrow unpaved shoulders to ft composite shoulders reduced shoulder related crashes up to % and reduced fatal & injury crashes up to % (). A study conducted using data from seven states in the United States concluded that adding paved shoulders of -ft for shoulder widths between 0-ft and -ft reduced related crashes by % (0). Shoulder rumble strips contributed to a. % crash reduction in single-vehicle run-offthe-road crashes on rural freeways in California and Illinois (). However, a study conducted in Washington State for rural undivided two-lane highways found that shoulder rumble strips tend to increase lane departure collisions for all injury severities by.% (). Centerline rumble strips were shown to reduce cross-centerline crashes by. % on two-lane highways in Michigan (), and a combination of centerline and shoulder rumble strips reduced crashes by. % on two-lane rural highways in Michigan (). A study conducted on rural two-lane roads in Kentucky, Missouri, and Pennsylvania showed that lane departure crashes decreased by. % as a result of centerlines and shoulder rumble strips (). Another study showed that lane departure crashes in Washington State, decreased by.% on rural two-lane undivided highways due to centerline and shoulder rumble strips (). Although many methods are available for evaluating safety effectiveness and estimating CMFs, every method cannot be used in every situation due to limited data availability and expected accuracy. Before-and-after studies require crash data for before time period and after time period for treatment and non-treatment sites (), but cross-sectional and case-control methods require only after data for treatment and non-treatment sites (,,, ). Crosssectional and case-control methods were used in this research because the date of implementation was not known or rather difficult to be found accurately. Studies Using Cross-Sectional Method The cross-sectional method is commonly used to estimate the expected number of crashes in transportation safety research (). A study conducted in Texas used the cross-sectional method to calculate CMFs for median characteristics on urban and rural freeways or rural multilane highways (). Another study used the cross-sectional method to calculate CMFs for the presence of wider lanes, shoulder widths, and edge markings in rural frontage roads in Texas (). Studies conducted in Minnesota and Pennsylvania also used the cross-sectional method to calculate CMFs for the presence of roadway lighting at grade intersections and lane & shoulder widths on rural two-lane highways (). The cross-sectional method has also been used to calculate CMFs in order to evaluate safety effectiveness of composite shoulders, wide unpaved shoulders, and wide paved shoulders on rural two-lane undivided roadways in Kansas (). However, this frequently used method has inherent strengths and weaknesses, where strengths include its ability to be used when multiple treatments are applied on corresponding road segments () and for sensitivity analysis to identify alternative highway improvements (). The cross-sectional method also does not require the date of implementation of the countermeasure (). However, one weakness of the cross-sectional method is that it does not capture the effects of factors not included in the model (). This method also requires a relatively large sample size, and the accuracy of estimates often varies according to data quality

5 (). In addition, calculation of CMFs using the cross-sectional method requires a model to predict crashes () and regression methods can be used to estimate the systematic relationship between crashes and highway design attributes (0). Studies Using Case-Control Method The case-control method has been used for many safety studies in the transportation sector (,,,, ). Defining case and control is essential in this method. Cases are defined as road segments that have experienced at least one crash during a particular year; controls are segments that have not experienced a single crash during that same year (, ). Although few studies have focused on the effects of geometric elements () in the past, recent studies have used the casecontrol method to calculate CMFs for geometric improvements of a road network. Two studies in Pennsylvania used the case-control method to calculate CMFs for change in shoulder width () and safety effectiveness of lane and shoulder widths () of rural two-lane undivided highway segments. CMF for bypass lanes at rural intersections in Kansas () and presence of lighting at intersections in Minnesota () were also calculated using case-control method. The case-control method, however, also demonstrates unique strengths and weaknesses. Strengths of the method include its ability to study rare events, calculate multiple risk factors from one sample, and control confounding variables using the matched design (, ). Weaknesses of this method are its inability to measure the probability of an event and its need to collect retrospective data for risk factors and outcome status (). In addition, the traditional case-control method cannot distinguish whether the segment has a single crash or multiple crashes (). Even though the matched case-control method can control confounding variables, it increases the complexity of data collection and sample selection, especially if there are many matching variables to be considered (). DATA AND METHODOLOGY Data Geometric and traffic-related information for the Kansas roadway network and lane departure crashes between 00 and 0 were extracted from the Control Section Analysis System (CANSYS) and KCARS database respectively. Crashes in each road segment were extracted using ArcGIS 0. (). Geometric data in the CANSYS database were then imported into ArcGIS, and road segments with uniform characteristics were identified using the linear referencing technique. Lane departure crashes were mapped using KCARS data, then combined with road segments, and the number of lane departure crashes in each road segment was obtained. A total of 0, and, all severity lane departure crashes and fatal & injury lane departure crashes between 00 to 0, respectively, occurred on 0, miles long rural twolane undivided road segments. Since the selected countermeasures demonstrate unique safety effectiveness at tangent and curved road segments, separate models were developed for each category. Table summarizes the data for tangent and curved road segments for all lanedeparture crashes and fatal & injury severity lane departure crashes.

6 0 TABLE Summary of Data for Road Severity Level All Fatal & Injury Geometry Number of segments Segment length (miles) Number of crashes Number of segments with crashes Number of segments with no crashes Tangent,0,0,,00, Horizontal curves,,,,,0 Tangent,0,0,0,0, Horizontal curves,,, The data showed ten potential variables for modeling crashes on tangent road segments; five variables were used as categorical variables, which are passing restrictions, lane width, speed limit, presence of rumble strips, and presence of -ft wide paved shoulders. Average Annual Daily Traffic (AADT), percentage of heavy commercial vehicles, AADT of medium trucks, AADT of heavy trucks, and segment length were considered as continuous variables when developing the model for tangent road segments. The same variables were used to model lane departure crashes in curved road segments, with the addition of horizontal curvature, which was also treated as a continuous variable. 0 0 Methodology Since categorical variables with several levels were used in the model, one level in each categorical explanatory variable was treated as the reference level. No no-passing zones, norumble strips and no-paved shoulders were selected as reference levels for passing restrictions, rumble strips and -ft paved shoulders. A lane width of less than -ft and 0 mph or higher posted speeds were selected as reference levels for lane width and speed limit, respectively. Cross-Sectional Method Two correlation matrixes were developed for the variables of tangent and curved segments in order to identify multicollinearity, hence to select statistically significant independent variables. The correlation coefficient of 0. or higher illustrates high multicollinearity (), so the cutoff threshold for the correlation coefficient was treated as 0., as used in previous traffic-related research (, ). Results showed that AADT is correlated with AADT of medium trucks (0.0) and AADT of heavy trucks (0.) for tangent and curved road segments, respectively. AADT of heavy trucks is also correlated with rumble strips (-0.) and paved shoulders (0.). Therefore, AADT of medium trucks and AADT of heavy trucks were removed from consideration when developing the models. Before developing models, the dataset was randomly divided in to two parts, containing two-third and one-third of total dataset to be treated as training dataset and validation dataset. Training dataset was used to develop the model and validation dataset was used to validate the

7 0 0 accuracy of the developed model. The negative binomial log linear model is commonly used in the cross-sectional method to develop crash frequency model (, -). Equation shows the general form of the negative binomial regression model (, 0) that is modified to the crash frequency modeling. ln y = xβ +ε i () where: y = n observations of crashes β = p vector of estimated regression parameters corresponding to geometric design and traffic volume related explanatory variables x = n p known explanatory model matrix of geometric design and traffic volume related variables ε i = n random vector variables (error) The mean variance relationship of negative binomial distribution can be expressed as in Equation (, ). Var (y)= E(y) + k E(y) () where: Var (y) = variance of observed crashes E(y)= μ = expected crash frequency k = overdispersion parameter The maximum likelihood method estimates the coefficient in the linear regression model, as described in Equation (0). L(y, x, β,σ ) = (πσ ) n/ exp [ σ n i= (y μ )] () 0 Cook s distance was calculated for response variable, which is the number of crashes per year in road segments, for outlier analysis and if Cook s distance of any data point is greater than one, it was considered as an outlier (0). The stepwise method of selecting significant variables from the candidate variables was used to develop the models. The number of crashes per year per segments was taken as the response variable, and previously selected variables were considered as explanatory variables to develop a regression model according to Equation. Model validation was carried out using two commonly used criteria, which are to check mean residual and mean squared error (MSE) after fitting the estimated model using validation data set. If the mean residual is approximately close to the zero and MSE calculated using validation dataset is approximately equal to the model MSE, the model is considered as a good model(0) for predicting lane departure crashes in two-lane rural undivided highways.

8 Case-Control Method One of the commonly used method in the case-control method is to developed logistic regression model with matched data (, ) or without matching the data. The matched case-control design directly controls confounding variables (), and therefore, the matched case-control design was used in this study. A typical matched case-control method uses a logistic regression model, as shown in Equation (0) E(y i ) =π i = exp (X, i β), +exp (X i β) () where: E(y i ) = expected crashes at location I β i = estimated coefficients for explanatory variables x i = unmatched explanatory variables associated with road geometry The response variable of the extracted dataset must be modified so that if the number of crashes is equal or greater than, then must be assigned to the crash column of the corresponding road segment, else zero. The same dataset used in cross- sectional method was used for this model development by modifying it this manner. The same variables used in the cross-sectional method were used in case-control method and maximum likelihood estimation was used to estimate regression parameters, as shown in Equation. n y L(y, y,. y, β) = π i y i ( π i i ) y i i= () The stepwise method was used select the variables in developing models and Receiver Operational Characteristic (ROC) was used to evaluate the predictive power of models for a binary outcome. Classification tables were used to implement this method (). Predictions were made using predictor variables in validation dataset and the estimated parameters. If the predicted probability of crash occurrence is equal or greater than 0. it is considered as (crash) otherwise considered as 0 (no-crash). The accuracy, sensitivity and specificity were then calculated for each model. Accuracy is the proportion of correct predictions to the total number of observations. Sensitivity and specificity are the proportion of events (crash segments) that are correctly predicted to the total number of crash segments and proportion of non-events (no-crash segments) that are correctly predicted to the total number of no-crash segments, respectively. RESULTS AND MODEL VALIDATION Descriptive statistics of categorical and continuous variables were calculated for the general understanding and shown in Table.

9 TABLE Descriptive Statistics of Categorical and Continuous Variables Tangent Road Curved Road Categorical Variable Number of Total Length of segments (miles) Percentage of Length (%) Number of Total Length of segments (miles) Percentag e of Length (%) Passing Restrictions, 0.,. (both directions) Passing Restrictions,0,0., 0. (one direction) No No-Passing Zones,0,.. Lane Width (<-ft), 0.. Lane Width ( -ft),,.,,0.0 Speed Limit (<0 mph),,., Speed Limit ( 0 mph),,.,. Centerline Rumble Strips,0,0.. Centerline and Shoulder,0. 0. Rumble Strips Shoulder Rumble Strips,0,00..0 No Rumble Strips,,0.,0. ft Paved Shoulder (both sides),0,.0,. No Paved Shoulders,,., 0.0 Continuous Variables Min Max Avg SD Min Max Avg SD AADT (vehicles per day) 0,00,, 0,0,, Percentage of Commercial Heavy Vehicles (%) AADT of Medium Trucks (Medium trucks per day) AADT of Heavy Trucks (Heavy Trucks per day) 0, Segment Lengths Horizontal Curvature (Degree of curvature ) na* na* na* na* na*-not applicable for the developed model, Min/Max-Minimum/Maximum, Avg-Average, SD-Standard Deviation

10 0 Results Cross-Sectional Method SAS. () was used to develop two models each, for tangent and curved road segments using all severity and fatal & injury severity lane departure crashes. Table shows the parameter estimates for the final models that were developed using the cross-sectional method with standard deviation and p-value of the estimates. TABLE Parameter Estimates of the Model Developed using the Cross-Sectional Method Variable Tangent Road (all crash Parameter Estimate Standard Error (p-value) Intercept Passing Restrictions (both directions) Passing Restrictions (one direction) Speed Limit 0 mph na*-not applicable for the developed model Curved Road (all crash Parameter Estimate Standard Error (p-value) Tangent Road (fatal and injury crash Parameter Estimate (0.0) na* na* (0.0) (0.0) Standard Error (p-value) na* na* (0.) (0.0) Lane Width _ft na* na* na* na* na* na* Percentage of Commercial Heavy Vehicles Centerline Rumble Strips Shoulder Rumble Strips Centerline and Shoulder Rumble Strips ft Paved Shoulder Horizontal Curvature (0.0) na* na* na* na* (0.) (0.0) (0.) (0.) (0.00) (0.00) na* na* (0.) ln(segment length) ln(aadt) (0.) (0.00) (0.) Curved Road (fatal and injury crash Parameter Estimate Standard Error (p-value) (0.0) (0.) na* na* (0.00) (0.) (0.) (0.) (0.0) (0.00) (0.0) na* na* (0.0) (.000)

11 Estimated regression parameters for the presence of -ft paved shoulders on both sides, centerline rumble strips, shoulder rumble strips, and both shoulder & centerline rumble strips were transformed into CMFs using the expression, CMF = exp(β)(). A CMF less than implied that the respective treatment reduced the number of crashes on those road segments. Maximum and minimum values for CMFs were calculated using standard error; results are shown in Table. TABLE CMFs for Paved Shoulders and Rumble Strips using the Cross-Sectional Method Countermeasure Tangent Road (all crash CMF (CMF min, CMF max ) Centerline Rumble Strips 0. (0.,0.) Shoulder Rumble Strips 0. (0.,0.) Centerline and 0. Shoulder Rumble Strips (0.,0.) ft Paved Shoulder (Both sides) 0. (0.,0.0) Curved Road (all crash CMF (CMF min, CMF max ) 0. (0.0,0.) 0. (0.,.0) 0. (0.,0.) 0. (0.,0.) Tangent Road (fatal and injury crash CMF (CMF min, CMF max ) 0. (0.,0.) 0. (0.,0.) 0. (0.,0.) 0. (0.,0.) Curved Road (fatal and injury crash CMF (CMF min, CMF max ) 0. (0.,0.) 0. (0.,0.) 0. (0.,0.) 0. (0.,0.) 0 According to the results of cross-sectional method, both centerline & shoulder rumble strips together can be identified as the most effective countermeasure among the considered four countermeasures to reduce number of all severity and fatal & injury lane departure crashes in tangent and curved road segments. Even though CMF for shoulder rumble strips for all severity lane departure crashes in curved road segments is 0., it might not always reduce number of lane departure crashes since the range of CMF includes. 0 Case-Control Method Two models each for tangent and curved road segment were developed using SAS. () for all severity and fatal & injury lane departure crashes. Model parameter estimates with standard deviation and p-value of each estimate are presented in Table.Odds ratios were calculated using estimated parameters. Since no-rumble strips and no-paved shoulders were set as reference levels for rumble strips and paved shoulders, odds ratios can be directly considered as the CMF. Calculated CMFs for the four countermeasures are shown in Table with maximum and minimum values for CMF.

12 TABLE Parameter Estimates of the Model Developed using the Case-Control Method Variable Intercept Passing Restrictions (both directions) Passing Restrictions (one direction) Speed Limit 0 mph Percentage of Commercial Heavy Vehicles Centerline Rumble Strips Shoulder Rumble Strips Centerline and Shoulder Rumble Strips -ft Paved Shoulder (both sides) Horizontal Curvature (Degree of Curvature) AADT (Vehicles per day) Segment Length (miles) Tangent Road (all crash Parameter Estimate -.0 Standard Error (p-value) (0.00) (0.) (0.) (0.0) (0.00) (0.00) na* na* na*-not applicable for the developed model Curved Road (all crash Parameter Estimate Standard Error (p-value) Tangent Road (fatal and injury crash Parameter Estimate Standard Error (p-value) (0.) (0.) (0.0) (0.) na* na* (0.) (0.) (0.) (0.0) (0.) (0.00) (0.) (0.) (0.0) (0.0) na* na* Curved Road (fatal and injury crash Parameter Estimate Standard Error (p-value) na* na* na* na* na* na* na* na* (0.) (0.) (0.00) (0.0)

13 TABLE CMFs for Paved Shoulders and Rumble Strips using the Case-Control Method Countermeasure Tangent Road (all crash CMF (CMF min, CMF max ) Centerline Rumble Strips 0. (0.,0.) Shoulder Rumble Strips 0. (0.,0.) Centerline and 0. Shoulder Rumble Strips ft Paved Shoulder (Both sides) (0.,0.) 0. (0.,0.) Curved Road (all crash CMF (CMF min, CMF max ) 0. (0.,.0). (.0,.) 0. (0.,0.) 0. (0.,0.) Tangent Road (fatal and injury crash CMF (CMF min, CMF max ) 0. (0.0,0.) 0.0 (0.,0.) 0. (0.,0.) 0. (0.,0.) Curved Road (fatal and injury crash CMF (CMF min, CMF max ) 0. (0.,.0) 0. (0.,0.) 0. (0.,0.) 0. (0.,0.) 0 0 Results showed that centerline & shoulder rumble strips and -ft paved shoulders have greater effect on reducing all severity and fatal & injury severity lane departure crashes on both tangent and curved road segments. It is difficult to identify the crash reduction effect of centerline rumble strips, because the ranges of CMFs include, except the CMF of fatal & injury lane departure crashes in tangent road segments. Shoulder rumble strips are not effective in reducing all severity lane departure crashes on of curved road segments. Validation of the Models Cross-Sectional Method Using the validation dataset, number of crashes in each segment was predicted using parameter estimates and the explanatory variables. Residuals were calculated for each data point by calculating the difference between predicted crashes and the observed crashes. MSE of the model for tangent road segments using all crash severities was 0.0. For the same model parameters, calculated mean residual and MSE for validation dataset were 0. and 0.0 respectively, and MSE of the model for curved road segments was 0.. Mean residual and MSE for the validation dataset were 0.and 0.0. MSE was 0. in the model developed for tangent road segments using fatal & injury crashes. For the same model parameters, mean residual and MSE in validation dataset were 0.00 and 0.0. Finally, the MSE in developed model for the curved road segments using fatal and injury crashes was 0.0 and mean residual and MSE for the validation dataset were 0. and 0.0. Based on these numbers it can be clearly seen that in all models, mean residuals are close to zero and MSE value of the validation dataset are approximately equal to model MSE. Therefore developed models using cross-sectional method are accurate enough and can be used to predict lane departure crashes in two-lane rural highways.

14 0 Case-Control Method The accuracy of the developed models for tangent road segments using all severity and fatal & injury severity lane departure crashes are 0. and 0., respectively. For curved road segments accuracy is 0. for all lane departure crashes and 0.0 for fatal & injury lane departure crashes. Since the accuracy is relatively high, the overall prediction power is high in these developed models. Sensitivity of models developed for tangent road segments using all severity and fatal & injury severity lane departure crashes are 0. and 0. respectively. For curved road segments, sensitivities are 0. and 0. respectively for all severity and fatal & injury severity lane departure crashes. Models developed both tangent and curved road segments predict crashes with more than 0% accuracy. Specificity of the models developed for tangent road segments are 0. and 0. respectively for all crash severity and fatal & injury crash severity. For curved road segments specificity are 0. and 0. respectively for all severity lane departure crashes and fatal & injury severity lane departure crashes. Therefore it can be concluded that all the models predict no-crash events accurately DISCUSSION According to the results of this study, the presence of -ft paved shoulders seems to have a % reduction in all lane departure crashes and a % reduction in fatal & injury lane departure crashes on two-lane rural undivided tangent road segments. Also, the -ft paved shoulders on two-lane rural undivided curved road segments shows the statistical association of an % reduction in all severity lane departure crashes and up to - % reduction in fatal & injury lane departure crashes. Similarly in the literature (, 0), to -ft paved shoulders caused a % reduction in all severity shoulder related/lane departure crashes and up to % reduction in fatal & injury shoulder related/lane departure crashes. Shoulder rumble strips shows a % reduction in all severity lane departure crashes and a 0 % reduction in fatal & injury crashes in two-lane rural undivided tangent road segments. However, the shoulder rumble strips provided mixed results using two methods for all severity lane departure crashes in curved two-lane rural undivided tangent road segments. Cross-sectional method shows that the number of all severity lane departure crashes reduce by % due to presence of shoulder rumble strips while case-control method shows otherwise, which is % increase of similar crashes. Similarly in the literature, both crash reduction and increase effect due to shoulder rumble strips can be identified such as in one study has shown a % reduction in the number of crashes due to shoulder rumble strips on rural freeways () and another study concluded that shoulder rumble strips increase lane departure collisions for all injury severities events by. % (). Centerline & shoulder rumble strips reduced all severity lane departure crashes by % and fatal & injury lane departure crashes by % on tangent road segments. Centerline & shoulder rumble strips reduced all severity lane departure crashes by % and caused a % reduction in fatal & injury lane departure crashes on curved road segments. Similar studies in the literature review (-) showed that a combination of centerline and shoulder rumble strips reduced the number of lane departure crashes % on rural undivided road segments. Centerline rumble strips reduced all severity lane departure crashes by % and reduced fatal & injury lane departure crashes by - % in tangent road segments. Also, the centerline rumble strips reduced all severity lane departure crashes by % and reduced fatal & injury lane

15 0 departure crashes by - % in curved road segments. Similar study conducted in Michigan shows that centerline rumble strips were shown to reduce cross centerline crashes by.% (). Even though this study focusses on lane departure crashes it is important to identify the safety effectiveness of the considered countermeasures on all crash types. Compared to the literature, results for -ft paved shoulders and centerline & shoulder rumble strips show similar range of crash reduction effect in fatal and injury lane departure crashes even though it shows greater crash reduction effect on all severity lane departure crashes. Centerline rumble strips show crash reduction effect even though the percent reduction is comparatively less than in the literature. However, shoulder rumble strips shows both crash reduction and growth effect. 0 0 CONCLUSIONS A majority of CMFs calculated using the cross-sectional method have higher values than the CMFs calculated using case-control method except CMF calculated for shoulder rumble strips using all severity lane departure crashes on curved road segments. Narrow ranges for CMFs were observed in the cross-sectional method compared to ranges obtained using case-control method. Although the values of CMFs differed, both methods accurately predicted positive countermeasure effectiveness. One of the possible reasons to get different CMF values using two methods is that the segments with high crash frequencies and low crash frequencies were assigned the same weight (= ) in the case-control method. In addition, % of segments had zero crashes, thereby affecting the representativeness of the developed model when predicting crashes. Also, the variables with higher p-values can be included in to the model if that variable must be included in to the model in order to calculate CMFs. In such cases it is advisable to select regression parameters using some selection criteria such as stepwise selection process with desired significance level. Then using those significant variables and the variable which must be included, final model can be developed. This study shows that results from the cross-sectional methods and case-control method are compatible. Since the range of CMFs obtained using casecontrol method is wider than cross-sectional method, it is possible to have a range which include for CMFs using case-control method, even though the cross-sectional method has a range without for the same countermeasure. Findings of this research and the literature from other studies show that for given CMFs, crash reduction effect in one state could be different from another state, even though the there are few similarities. Therefore it is beneficial to have localized/state based CMF for more accurate safety evaluation. 0 Acknowledgements Authors are thankful for Midwest Transportation Center (MTC) for providing funds for conducting this research. Thanks also go to Mr. Steven Buckley and Ms. Elsit Mandal for the tireless support provided for finding data and to Mr. Steephanson Anthonymuthu, Ms. Sanjeewani Weerasingha and Ms. Narmadha Mohankumar for the support given in developing statistical models.

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