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ALTERNATIVE METHODS FOR ESTIMATING SAFETY EFFECTIVENESS ON RURAL, TWO-LANE HIGHWAYS:CASE-CONTROL AND COHORT METHODS
ABSTRACT
There is a need to better understand the safety implications of geometric improvements on rural, two-lane highways. Funding for transportation safety improvement projects is often limited so it is important to estimate the relative safety effectiveness of each proposed improvement and select those that are likely to produce the greatest benefit. Safety, efficiency, and economic costs are all competing factors in the cost-effectiveness of highway improvements. While engineers are able to evaluate efficiency and monetary costs quantitatively, safety is often evaluated qualitatively based on expert judgment or past experiences. Estimating the change in expected crashes due to a particular improvement (i.e. the crash modification factor or CMF) is one method for evaluating safety quantitatively. Alternatively, safety effectiveness may be estimated as the relative probability of a crash. Case-control and cohort methods are proposed and evaluated to estimate the relative probability of a crash for specific lane and shoulder widths. The estimated safety effectiveness is then compared to CMFs developed in the Highway Safety Manual to test the validity of the methods.
As highway safety has evolved, a number of different methods have been applied to estimate the safety performance of roadway segments. This research summarizes current methods in highway safety analysis and evaluates two alternative methods for estimating the safety implications of roadway features. Methods derived from epidemiological studies are proposed. Epidemiology often seeks to relate risk factors within a population to a particular outcome or disease. In the highway safety context, the “outcome” is a crash and the “risk factor” is a particular geometric feature or countermeasure within a specific population of roadway segments.
There is a direct application of epidemiological methods in highway safety. Case-control and cohort designs estimate the effect of risk factors using the odds ratio and relative risk, respectively. The odds ratio and relative risk represent the expected percent change in the probability of a crash due to a particular risk factor. In highway safety, crash modification factors represent the expected percent change in the number of crashes due to a given geometric improvement. There is a need for better methods to estimate crash modification factors or alternative measures of safety effectiveness and epidemiological designs appear well suited for this task.
This research reviews the strengths and weaknesses of the case-control and cohort approaches and evaluates their effectiveness for estimating safety effectiveness of geometric
design elements. Empirical examples are provided using data from Pennsylvania and Washington. Geometric, traffic and crash data were obtained for more than 25,000 rural, two-lane highway segments in Pennsylvania for years 1997 – 2001 inclusive. Similar data were obtained for more than 55,000 rural, two-lane highway segments in Washington for years 1993 – 1996 and 2002 – 2003 inclusive. Case-control and cohort designs are applied to evaluate the incremental safety effects of lane and shoulder width from the odds ratio and relative risk, respectively. Matching is applied in the case-control design to isolate the effects of lane and shoulder width by accounting for confounding variables, such as ADT, speed limit, and segment length. Conditional logistic regression is used to account for the matching procedure and estimate the odds ratio. Confounding is addressed in the cohort study by including potential confounders as covariates in the model. Survival and count models are applied with the cohort design to estimate the relative risk for lane and shoulder width.
Base models were estimated without adjustment for confounding variables, and the estimated safety effectiveness for lane and shoulder width were inconsistent with the CMFs presented in the Highway Safety Manual. A thorough analysis of several potential confounding variables identified ADT, speed and segment length as the most critical confounders when estimating safety effectiveness for lane and shoulder width. Enhanced models were developed with adjustment for ADT, speed, and segment length; results were consistent with the Highway Safety Manual indicating a general decrease in crash risk as lane and shoulder width increase. These findings were consistent for both the case-control and cohort designs. Based on the consistency of results from this investigation, the case-control and cohort methods appear to be well suited for estimating safety effectiveness for lane and shoulder width.
TABLE OF CONTENTS
LIST OF FIGURES…………………………………………………………………………………………………………. viii
LIST OF TABLES…………………………………………………………………………………………………………… xii
ACKNOWLEDGEMENTS………………………………………………………………………………………………. xv
CHAPTER I INTRODUCTION………………………………………………………………………………………….. 1
1.1 Background…………………………………………………………………………………………………………… 1
1.2 Proposed Research and Objectives…………………………………………………………………………… 4
1.3 Outline of Thesis……………………………………………………………………………………………………. 4
CHAPTER II PREVIOUS STUDIES FOR HIGHWAY SAFETY RESEARCH……………………….. 5
2.1 Previous Methods to Estimate Safety Effectiveness of Highway Design Variables………… 5
2.1.1 Historical Crash Data…………………………………………………………………………………………… 5
2.1.2 Predictions from Statistical Models……………………………………………………………………….. 6
2.1.3 Before-After Studies……………………………………………………………………………………………. 7
2.1.4 Expert Judgments………………………………………………………………………………………………… 9
2.2 Current Methods for Estimating Safety Effectiveness…………………………………………………. 9
2.2.1 Interactive Highway Safety Design Model……………………………………………………………… 9
2.2.2 Highway Safety Manual………………………………………………………………………………………. 9
2.3 Relationship between Roadway Geometry and Expected Crashes………………………………. 12
2.4 Alternative Methods for Estimating Safety Effectiveness………………………………………….. 16
2.4.1 Case-Control Applications………………………………………………………………………………….. 17
2.4.2 Cohort Applications…………………………………………………………………………………………… 21
2.5 Relationship of Case-Control and Cohort Designs to Previous Methodologies…………….. 22
CHAPTER III CONCEPTUAL FRAMEWORK FOR CMF DEVELOPMENT……………………… 23
3.1 Overview of Crash Modification Factors………………………………………………………………… 23
3.2 The Prototype Crash Modification Factor……………………………………………………………….. 23
3.3 Development of CMF Using Cross-Sectional Data…………………………………………………… 25
CHAPTER IV METHODOLOGY AND APPROACH………………………………………………………… 27
4.1 Overview…………………………………………………………………………………………………………….. 27
4.2 Case-Control Design…………………………………………………………………………………………….. 27
4.3 Matched Case-Control Design……………………………………………………………………………….. 33
4.4 Analysis of Matched Case-Control Designs…………………………………………………………….. 36
4.5 Cohort Study Design…………………………………………………………………………………………….. 39
4.6 Analysis of Cohort Studies……………………………………………………………………………………. 43
4.6.1 Survival Models………………………………………………………………………………………………… 44
4.6.2 Count Models……………………………………………………………………………………………………. 47
4.7 Application of Case-Control and Cohort Methods in Highway Safety………………………… 49
CHAPTER V DATA SETS AND SAMPLING METHOD…………………………………………………… 50
5.1 Overview of Datasets……………………………………………………………………………………………. 50
5.1.1 Pennsylvania Overview……………………………………………………………………………………… 50
5.1.2 Washington Overview……………………………………………………………………………………….. 53
5.2 Descriptive Statistics…………………………………………………………………………………………….. 56
5.2.1 Pennsylvania…………………………………………………………………………………………………….. 56
5.2.2 Washington………………………………………………………………………………………………………. 59
5.3 Creation of Categorical Variables…………………………………………………………………………… 62
5.4 Selection of Case and Control Segments…………………………………………………………………. 63
5.4.1 Case-Control Design………………………………………………………………………………………….. 63
5.4.2 Cohort Design…………………………………………………………………………………………………… 65
5.5 Sample Size and Power…………………………………………………………………………………………. 65
5.5.1 Case-Control Design………………………………………………………………………………………….. 65
5.5.2 Cohort Design…………………………………………………………………………………………………… 67
CHAPTER VI ANALYSIS AND INTERPRETATION OF RESULTS…………………………………. 69
6.1 Introduction…………………………………………………………………………………………………………. 69
6.2 Bivariate Plots……………………………………………………………………………………………………… 69
6.3 Structure of Empirical Design……………………………………………………………………………….. 79
6.4 Estimating Safety Effectiveness: The Case-Control Method……………………………………… 81
6.4.1 Base Models……………………………………………………………………………………………………… 84
6.4.2 Enhanced Models with Confounder-Adjustment Schemes……………………………………… 92
6.4.2.1 Enhanced Model A: Match on ADT and Speed………………………………………………….. 92
6.4.2.2 Enhanced Model B: Match on ADT and Speed with Segment Length as a Covariate 97
6.4.2.3 Enhanced Model C: Match on ADT, Speed and Horizontal Curvature………………… 102
6.4.2.4 Enhanced Model D: Match on ADT, Speed and Vertical Curvature……………………. 105
6.4.3 Matching Scheme versus Covariates………………………………………………………………….. 108
6.4.3.1 ADT and Speed: Matching versus Covariates…………………………………………………… 108
6.4.3.2 Segment Length: Matching versus Covariate……………………………………………………. 110
6.4.3.3 Horizontal Curvature: Matching versus Covariate…………………………………………….. 112
6.4.3.4 Vertical Curvature: Matching versus Covariate………………………………………………… 115
6.4.4 Alternative Response Models:…………………………………………………………………………… 117
6.4.4.1 Related Crashes versus Total Crashes……………………………………………………………… 117
6.4.4.2 Ordinal Response versus Binary Response……………………………………………………….. 121
6.4.5 Case-Control Summary…………………………………………………………………………………….. 125
6.5 CMF Estimation: The Cohort Method…………………………………………………………………… 126
6.5.1 Base Models without Adjustment for Confounders………………………………………………. 128
6.5.2 Enhanced Models with Adjustment for ADT, Speed and Segment Length……………… 133
6.5.2.1 Cox Proportional Hazard Method……………………………………………………………………. 133
6.5.2.2 Negative Binomial Method…………………………………………………………………………….. 137
6.5.3 Enhanced Models using Segment-Length-Days as Exposure………………………………… 139
6.5.4 Cohort Summary……………………………………………………………………………………………… 142
6.6 Model Transferability and Validation……………………………………………………………………. 143
6.7 Discussion…………………………………………………………………………………………………………. 146
CHAPTER VII CONCLUSIONS…………………………………………………………………………………….. 148
CHAPTER VIII DIRECTIONS FOR FURTURE RESEARCH…………………………………………… 150
REFERENCES………………………………………………………………………………………………………………. 153
APPENDIX A Model Estimates for Case-Control Analyses……………………………………………….. 156
A.1 Enhanced Models Adjusted for ADT and Speed (Matching)……………………………………… 156
A.2 Enhanced Models Adjusted for ADT and Speed (Matching) and Segment Length (Covariate) 158
A.3 Enhanced Models Adjusted for ADT, Speed, and Horizontal Curvature (Matching)…….. 160
A.4 Enhanced Models Adjusted for ADT, Speed, and Vertical Curvature (Matching)………… 161
A.5 Case-Control Matching versus Covariate Schemes for ADT and Speed………………………. 162
A.6 Case-Control Matching versus Covariate Schemes for Segment Length……………………… 163
A.7 Case-Control Matching versus Covariate Schemes for Horizontal Curvature………………. 164
A.8 Case-Control Matching versus Covariate Schemes for Vertical Curvature…………………… 165
A.10 Multinomial Logit Models Adjusted for ADT, Speed and Segment Length……………….. 167
A.11 Base Models Adjusted for ADT, Speed and Segment Length (Covariates)………………… 170
APPENDIX B Model Estimates for Cohort Analyses…………………………………………………………. 172
B.1 Survival Models Adjusted for ADT, Speed, and Segment Length………………………………. 172
B.2 Negative Binomial Models Adjusted for ADT, Speed, and Segment Length………………… 174
CHAPTER I INTRODUCTION
1.1 Background
The highway transportation system is very forgiving in the sense that it can handle a great deal of variability in driver performance, vehicle characteristics and environmental conditions before the breakdown of the system and occurrence of a crash. Crashes are truly rare events, not from a national perspective, but from a localized point of view. At any given location the occurrence of a crash event is relatively rare when compared to the level of traffic. However, with more than four million miles of roadway in the United States, these rare local events add-up to a real problem; more than six million crashes and over 40,000 fatalities annually (USDOT, 2005).
Although the number of fatal crashes increased slightly (0.7 percent) from 2000 to 2001, the fatality rate reached a historic low of 1.51 fatalities per 100 million vehicle miles of travel in 2001 (USDOT, 2002). Traffic-related fatality rates are showing a slow decline due to increases in vehicle-miles of travel each year, but the total number of fatalities has leveled-off around 42,000 annually. The occupant fatality rate per 100,000 persons in the population declined by 23 percent from 1975 to 1992, but decreased by only 1 percent from 1992 to 2001. Similarly, the occupant injury rate per 100,000 persons in the population declined by 14 percent during the five year period from 1988 to 1992, but decreased by only 11 percent during the ten year period from 1992 to 2001 (USDOT, 2002). In 2002, motor vehicle crashes were the number one cause of death among Americans 4 to 34 years of age and the eighth leading cause of death overall (USDOT, 2005). With such a vast network and limited budget for highway safety improvements, it is important to identify locations and improvements that will realize the greatest benefits. Therefore, it is critical to analyze these rare events, determine the factors contributing to each event, devise methods to reduce the likelihood of an event, and estimate the effectiveness of each particular improvement.
The road user, vehicle, and roadway environment are all factors that may contribute to the occurrence of a crash event and there are often multiple factors involved at once. Indiana University’s tri-level study of the causes of traffic accidents reported that human error was a definite causal factor in about 65-70 percent of roadway crashes and a probable cause in over 90 percent of crashes. The roadway was reported as a definite causal factor in 15-20 percent of crashes with the vehicle reported as the definite cause in just 4 percent (Treat et al., 1977). While the human factor plays a significant role in the event of a crash, it is often the most difficult factor to control due to the large variability of user characteristics in the driving population and sensitivity to regulations. The roadway and vehicle are, however, easier to control through the design process. Vehicle designs, for example, must meet several safety standards and frequently undergo rigorous performance and safety testing in a controlled environment before and after they appear on the market. Roadway designs must also adhere to guidelines, however, the engineer may choose from a range of design values to develop several alternative designs. The question remains, which alternative will result in the best design with regard to safety, mobility, cost, and the environment?
Cost and environmental impacts are easily quantified during the preliminary design process, but the level of safety is more difficult to realize. Randomized clinical trials would be the most powerful method for evaluating the safety of alternative roadway designs. Unfortunately, road safety testing in a controlled environment is not practical or ethical. The only true measure of the safety performance for a new highway is to observe the number of crashes experienced after construction. It may be possible, however, to estimate the number of expected crashes for a particular design based on existing highways with similar characteristics. It would be even more useful to estimate the relative safety effect of each geometric element (e.g. lane width, shoulder width, degree of curvature, and length of curve), thereby allowing the engineer to evaluate each design by parts. This results in the use of observational studies to evaluate roadway safety by associating particular roadway features with crashes.
Preventing a crash event or at least reducing the likelihood of a crash occurrence should be the primary concern of highway safety professionals. Geometric and traffic control improvements may play a significant role in reducing the likelihood of a crash, thereby reducing morbidity and mortality on our nation’s highways. The effectiveness of such improvements, however, is yet to be determined in many cases. Some have even argued that geometric improvements do not have a significant impact on the safety performance of highways (Noland, 2003). While these claims seem of dubious merit, there have been relatively few well-designed studies that show the safety effects of geometric and traffic control features. It is reasonable to assume that the geometric design and traffic control of a roadway can contribute to the overall safety of the facility; but, the question remains, how much?
Safety effects of geometric designs and enhancements have not been fully explored and techniques for analyzing the effectiveness of roadway improvements have suffered from a number of limitations. Until recently, estimates of safety performance have been developed using averages from historical crash data, predictions from statistical models, results of before-after studies, and expert judgments (Harwood et al., 2000). These methods are discussed in detail in chapter two along with common limitations. Estimates from these studies have provided an idea of the relative safety effectiveness for many roadway improvements; however, due to the aforementioned limitations among others, the actual effectiveness is uncertain or unclear. For example, lane widening has been shown to produce reductions in crashes up to 40 percent (Zegeer et al., 1981). These reductions, however, may represent the effects of other unknown or unaccounted factors.
Appropriate tools and methods for analyzing the safety implications of alternative designs need to be provided for planners, designers and decision-makers to make well-informed decisions. Currently, there are still those who believe that safety is addressed through the design guides; however, many of the current design guidelines are not based on scientifically rigorous approaches with respect to safety. In addition, these guides typically allow a range of acceptable values and the resulting effects on safety are not well understood. In transportation, there is a need to move toward decisions that are based on a thorough analysis of safety implications in addition to the economic, environmental, and societal costs of improvements.
The proposed approach relies on the use of case-control and cohort methods to estimate safety effectiveness and approximate crash modification factors. CMFs are one tool that can be used by engineers and decision-makers to determine the relative effectiveness of geometric improvements. Safety performance functions provide an estimate of the expected number of crashes for a particular roadway segment or intersection under a set of base conditions, and crash modification factors are applied to adjust the estimate based on actual geometric conditions (Harwood et al., 2000). Currently, the development of crash modification factors has been based on a limited number of previous studies, which are discussed in chapter two.
In summary, safety has improved significantly over the last thirty years; however, there is still much room for improvement, particularly in addressing the issue at its source – the crash itself. Geometric improvements and related countermeasures are potential solutions to further enhance highway safety, but proper statistical analyses are necessary to unveil the actual effects on safety. It is critical for engineers and decision-makers to be equipped with the proper tools and analysis techniques to evaluate the safety implications of their decisions. If the actual effectiveness of roadway improvements is to be realized, then a sound methodology is required to separate the effects in question from the effects of other variables and potential confounders. The proposed methods seek to develop improved estimates of safety effectiveness, responding to limitations that exist in the current literature.
1.2 Proposed Research and Objectives
The previous discussion defines the problem and helps define two major research objectives. The first objective is to conceptualize an alternative process for developing a prototypical crash modification factor. Understanding the process for developing crash modification factors will help to identify strengths and weaknesses in current analysis techniques. In addition, this will help to layout a framework for building upon current techniques using alternative methods to develop crash modification factors. The second objective is to explore and evaluate alternative methods for developing crash modification factors. These alternative methods use the ratio of the odds and risk to directly estimate the incremental effects of roadway improvements on highway safety while controlling for other variables that affect crashes.
1.3 Outline of Thesis
The following chapter discusses traditional analysis techniques to estimate safety effectiveness of geometric elements as well as the strengths and weaknesses associated with each method. The use of case-control and cohort methods are identified in other areas of highway safety research and their application to highway safety research is discussed. The literature review also identifies studies estimating the expected safety benefits of lane and shoulder width improvements. These studies are evaluated based on the methods used and their ability to isolate the actual effects of the variable in question. Studies evaluating other geometric variables are identified to establish a basic understanding of their relationship to expected crashes, which is later used to determine potential confounding variables. Chapter three provides an overview of crash modification factors as well as a conceptual framework for the development of a prototypical crash modification factor. The proposed alternative designs are then discussed methodologically in chapter four followed by a discussion of the data used in the analyses. An empirical investigation of the methods is discussed in chapter six using data from Pennsylvania and Washington. The thesis concludes with a discussion of the major findings and opportunities for future research.
ALTERNATIVE METHODS FOR ESTIMATING SAFETY EFFECTIVENESS ON RURAL, TWO-LANE HIGHWAYS:CASE-CONTROL AND COHORT METHODS
