Crash modification factors; crash modification functions; multiple treatments; safety effects; highway safety manual; before after analysis; cross sectional analysis; statistical modeling


Traffic safety is a major concern for the public, and it is an important component of the roadway management strategy. In order to improve highway safety, extensive efforts have been made by researchers, transportation engineers, Federal, State, and local government officials. With these consistent efforts, both fatality and injury rates from road traffic crashes in the United States have been steadily declining over the last six years (2006~2011). However, according to the National Highway Traffic Safety Administration (NHTSA, 2013), 33,561 people died in motor vehicle traffic crashes in the United States in 2012, compared to 32,479 in 2011, and it is the first increase in fatalities since 2005. Moreover, in 2012, an estimated 2.36 million people were injured in motor vehicle traffic crashes, compared to 2.22 million in 2011. Due to the demand of highway safety improvements through systematic analysis of specific roadway cross-section elements and treatments, the Highway Safety Manual (HSM) (AASHTO, 2010) was developed by the Transportation Research Board (TRB) to introduce a science-based technical approach for safety analysis. One of the main parts in the HSM, Part D, contains crash modification factors (CMFs) for various treatments on roadway segments and at intersections. A CMF is a factor that can estimate potential changes in crash frequency as a result of implementing a specific treatment (or countermeasure). CMFs in Part D have been developed using high-quality observational before-after studies that account for the regression to the mean threat. Observational before-after studies are the most common methods for evaluating safety effectiveness and calculating CMFs of specific roadway treatments. Moreover, cross-sectional method has commonly been used to derive CMFs since it is easier to collect the data compared to before-after methods. Although various CMFs have been calculated and introduced in the HSM, still there are critical limitations that are required to be investigated. First, the HSM provides various CMFs for single treatments, but not CMFs for multiple treatments to roadway segments. The HSM suggests that CMFs are multiplied to estimate the combined safety effects of single treatments. However, the HSM cautions that the multiplication of the CMFs may over- or under-estimate combined effects of multiple treatments. In this dissertation, several methodologies are proposed to estimate more reliable combined safety effects in both observational before-after studies and the cross-sectional method. Averaging two best combining methods is suggested to use to account for the effects of over- or under- estimation. Moreover, it is recommended to develop adjustment factor and function (i.e. weighting factor and function) to apply to estimate more accurate safety performance in assessing safety effects of multiple treatments. The multivariate adaptive regression splines (MARS) modeling is proposed to avoid the over-estimation problem through consideration of interaction impacts between variables in this dissertation. Second, the variation of CMFs with different roadway characteristics among treated sites over time is ignored because the CMF is a fixed value that represents the overall safety effect of the treatment for all treated sites for specific time periods. Recently, few studies developed crash modification functions (CMFunctions) to overcome this limitation. However, although previous studies assessed the effect of a specific single variable such as AADT on the CMFs, there is a lack of prior studies on the variation in the safety effects of treated sites with different multiple roadway characteristics over time. In this study, adopting various multivariate linear and nonlinear modeling techniques is suggested to develop CMFunctions. Multiple linear regression modeling can be utilized to consider different multiple roadway characteristics. To reflect nonlinearity of predictors, a regression model with nonlinearizing link function needs to be developed. The Bayesian approach can also be adopted due to its strength to avoid the problem of over fitting that occurs when the number of observations is limited and the number of variables is large. Moreover, two data mining techniques (i.e. gradient boosting and MARS) are suggested to use 1) to achieve better performance of CMFunctions with consideration of variable importance, and 2) to reflect both nonlinear trend of predictors and interaction impacts between variables at the same time. Third, the nonlinearity of variables in the cross-sectional method is not discussed in the HSM. Generally, the cross-sectional method is also known as safety performance functions (SPFs) and generalized linear model (GLM) is applied to estimate SPFs. However, the estimated CMFs from GLM cannot account for the nonlinear effect of the treatment since the coefficients in the GLM are assumed to be fixed. In this dissertation, applications of using generalized nonlinear model (GNM) and MARS in the cross-sectional method are proposed. In GNMs, the nonlinear effects of independent variables to crash analysis can be captured by the development of nonlinearizing link function. Moreover, the MARS accommodate nonlinearity of independent variables and interaction effects for complex data structures. In this dissertation, the CMFs and CMFunctions are estimated for various single and combination of treatments for different roadway types (e.g. rural two-lane, rural multi-lane roadways, urban arterials, freeways, etc.) as below: 1) Treatments for mainline of roadway: - adding a thru lane, conversion of 4-lane undivided roadways to 3-lane with two-way left turn lane (TWLTL) 2) Treatments for roadway shoulder: - installing shoulder rumble strips, widening shoulder width, adding bike lanes, changing bike lane width, installing roadside barriers 3) Treatments related to roadside features: - decrease density of driveways, decrease density of roadside poles, increase distance to roadside poles, increase distance to trees Expected contributions of this study are to 1) suggest approaches to estimate more reliable safety effects of multiple treatments, 2) propose methodologies to develop CMFunctions to assess the variation of CMFs with different characteristics among treated sites, and 3) recommend applications of using GNM and MARS to simultaneously consider the interaction impact of more than one variables and nonlinearity of predictors. Finally, potential relevant applications beyond the scope of this research but worth investigation in the future are discussed in this dissertation.


If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at

Graduation Date





Abdel-Aty, Mohamed


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Civil, Environmental, and Construction Engineering

Degree Program

Engineering and Computer Science








Release Date

August 2015

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)


Dissertations, Academic -- Engineering and Computer Science; Engineering and Computer Science -- Dissertations, Academic