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SAFETY EFFECTS OF SHOULDER AND CENTERLINE RUMBLE STRIPS: A BAYESIAN PROPENSITY SCORE MATCHING FRAMEWORK
ABSTRACT
To develop a reliable and accurate safety effect estimate is one of the fundamental objectives in the traffic safety study. Transportation engineering practitioners use the safety effect estimates to identify and deploy a variety of safety countermeasures to reduce the frequency and severity of traffic accidents. Researchers have developed several methodologies to estimate the safety treatment effect in the observational study. The current state-of-the-practice is the empirical Bayes before-after study, which utilized the before and after treatment data to evaluate the treatment effect. The advantage of this methodology is that it corrects the regression-to-themean. Another prevalent method is the cross-sectional regression models. It can be used to manage cross-sectional data and estimate the effect of multi-level treatments. In recent years, the propensity score matching-potential outcomes framework has been introduced into the traffic safety study. This method is capable to balance the covariates between treatment and control (or reference) groups, and thus, reveal the causal relationship between the treatment and outcome. Recent traffic safety studies showed the strength of this method in estimating countermeasure safety effectiveness. However, the issue in the traffic safety data such as the unobserved heterogeneity may still affect the effectiveness and robustness of this propensity score matching method. This study explores an alternative way to conduct propensity score matching by incorporating Bayesian methods into the propensity score estimation. In order to explore the potential benefits of the Bayesian propensity score matching, a no-treatment analysis and a simulation-based analysis were conducted in the research. The data used in the analysis is the Pennsylvania two-lane rural highway crash database with the treatment of the duel application of shoulder and centerline rumble strips.
The no-treatment analysis focused on investigating the effectiveness of the Bayesian propensity score matching framework. The regional-level samples such as statewide, district-level and county-level data were used respectively in the no-treatment analysis. The simulation-based analysis focused on investigating the robustness of this framework when there is unobserved heterogeneity. In each analysis, the Bayesian propensity score matching was conducted with different Bayesian prior settings, matching ratios and caliper widths. In addition, the ability to balance covariates and yield unbiased safety effect estimates was compared between the proposed methodology and the traditional propensity score matching method. The findings indicated that:
- The Bayesian propensity score matching method is superior to the traditional propensity score matching method in reducing bias of safety effect estimates when there are sufficient samples in the analysis. When the sample size is limited, incorporating Bayesian method would still improve the matching performance in balancing the covariates.
- The Bayesian propensity score matching method has the potential to yield unbiased estimates under the influence of unobserved heterogeneity.
- The estimates from Bayesian propensity score matching method is sensitive to the choice of Bayesian prior and matching configuration such as ratio and caliper width. Decisions need to be made when applying this framework to the real data according to the sample size and number of measured covariates.
The research also provides the guideline for the application of Bayesian propensity score matching method. A step-by-step flowchart is developed to help the researchers and practitioners to implement this framework.
TABLE OF CONTENTS
LIST OF FIGURES ………………………………………………………………………………………………….. vii
LIST OF TABLES ……………………………………………………………………………………………………. ix
ACKNOWLEDGEMENTS ……………………………………………………………………………………….. xi
Chapter 1 Introduction ……………………………………………………………………………………………… 1
1.1 Background …………………………………………………………………………………………………. 1
1.2 Development of Safety Effect Estimates …………………………………………………………. 2
1.3 Shoulder and Centerline Rumble Strips …………………………………………………………… 4
1.4 Research objectives ………………………………………………………………………………………. 6
Chapter 2 Literature Review ……………………………………………………………………………………… 9
2.1 Safety Effects of Shoulder and Centerline Rumble Strips ………………………………….. 9
2.2 Summary of Existing Safety Effect Estimate Methodologies ……………………………… 12
2.2.1 Counterfactual Framework Assumptions ……………………………………………….. 13
2.2.2 Cross-sectional regression model ………………………………………………………….. 14
2.2.3 Empirical Bayes Before-after Study ………………………………………………………. 15
2.2.4 Propensity Score Matching ………………………………………………………………….. 16
2.2.5 Limitations in Safety Effect Estimations ………………………………………………… 17
2.3 Prospect of Bayesian Propensity Score Matching Framework ……………………………. 19
Chapter 3 Methodology ……………………………………………………………………………………………. 24
3.1 Counterfactual framework …………………………………………………………………………….. 24
3.1.1 Introduction ……………………………………………………………………………………….. 24
3.1.2 Treatment Effect Estimates ………………………………………………………………….. 26
3.2 Bayesian Propensity Score Matching Method ………………………………………………….. 28
3.2.1 Overview of Propensity Score Matching ……………………………………………….. 28
3.2.2 Bayesian Propensity Score Model …………………………………………………………. 303.2.3 Matching Algorithms ………………………………………………………………………….. 363.2.4 Matching Considerations ……………………………………………………………………… 40
3.2.5 Outcome Model ………………………………………………………………………………….. 43
3.3 Summary …………………………………………………………………………………………………….. 44
Chapter 4 Research Data …………………………………………………………………………………………… 47
4.1 Data Sources and Structures …………………………………………………………………………… 474.2 Summary Statistics ……………………………………………………………………………………….. 48
4.3 Discussion of the Study Assumptions ……………………………………………………………… 52
Chapter 5 No-treatment Analysis on Regional Data ……………………………………………………… 53
5.1 Background …………………………………………………………………………………………………. 53
5.2 Data Description ………………………………………………………………………………………….. 55
5.3 Propensity Score Matching Analysis ……………………………………………………………….57
5.3.1 Estimation of the Negative Binomial Regression Model before Matching ….. 57
5.3.2 Estimation of Propensity Scores……………………………………………………………. 60
5.3.3 Covariate Balance Assessment ……………………………………………………………… 66
5.3.4 Treatment Effect Estimates after Matching …………………………………………….. 73
5.4 Sensitivity Analysis ………………………………………………………………………………………. 78
5.4.1 Background ……………………………………………………………………………………….. 78
5.4.2 Analysis of Covariate Balance ……………………………………………………………… 79
5.4.3 Analysis of CMF Estimates ………………………………………………………………….. 83
5.5 Summary …………………………………………………………………………………………………….. 87
Chapter 6 Simulation-Based Treatment Effect Analysis ……………………………………………….. 90
6.1 Background …………………………………………………………………………………………………. 90
6.2 Data Simulation and Description ……………………………………………………………………. 92
6.3 Results and Sensitivity Analysis …………………………………………………………………….. 100
6.3.1 Summary of BPSM and PSM results …………………………………………………….. 100
6.3.2 Analysis of Covariate Balance ……………………………………………………………… 108
6.3.3 Analysis of CMF Estimates ………………………………………………………………….. 111
6.4 Further Iterative Analysis of the Simulation-based Study ………………………………….. 117
6.4.1 Configurations of the Iterative Analysis ………………………………………………… 117
6.4.2 Results of the Iterative Analysis ……………………………………………………………. 118
6.5 Summary …………………………………………………………………………………………………….. 120
Chapter 7 Safety Effect of Shoulder plus Centerline Rumble Strips ……………………………….. 123
7.1 Background …………………………………………………………………………………………………. 123
7.2 Data Description ………………………………………………………………………………………….. 123
7.3 Results ………………………………………………………………………………………………………… 126
7.3.1 Propensity Score Estimation ………………………………………………………………… 126
7.3.2 Covariate Balance Assessment ……………………………………………………………… 128
7.3.3 Treatment Effect Estimation ………………………………………………………………… 131
7.4 Summary …………………………………………………………………………………………………….. 135
Chapter 8 Conclusions and Recommendations …………………………………………………………….. 137
8.1 Conclusions …………………………………………………………………………………………………. 1378.3 Application of the Methodology …………………………………………………………………….. 140
8.4 Recommendations for Future Work ………………………………………………………………… 142
Reference ………………………………………………………………………………………………………………… 145
Appendix Computation Code ……………………………………………………………………………………. 154
Chapter 1
Introduction
1.1 Background
Transportation safety has been a worldwide issue since the automotive industry exploded globally in the early 20th century. The impact of traffic accidents not only affects human life, but also limits the development of society. The United States (U.S.) retains the world’s largest roadway network and highest car ownership. At the beginning of the 21st century, there were more than 40,000 fatalities resulting from traffic accidents every year in the U.S. This number dropped below 33,000 in 2013 and 2014, but increased to 35,485 in 2015, and 37,461 in 2016 (1). Additionally, there were more than 2.3 million annual injuries caused by traffic accidents in 2016
(2).
In 2014, the Federal Highway Administration (FHWA) launched the Toward Zero Deaths (TZD) program (3) to address growing concerns related to traffic safety. The program serves as a platform for state transportation agencies, private industries, and other organizations to develop safety plans. The goal of this program is to unite and mobilize the efforts from all highway safety stakeholders to reduce fatalities and serious injuries related to traffic crashes. It is expected that, with the implementation of TZD, the vision of a highway system with zero fatalities may be achieved.
In the transportation industry, a variety of safety countermeasures have been developed and deployed in order to reduce the frequency and severity of traffic accidents. Among the proven safety countermeasures are the following: median barrier, safety edges, roundabouts, dedicated left- and right-turn lanes, and longitudinal rumble strips. Many other safety countermeasures, such as dynamic warning signs and dilemma zone protection systems, have been tried in the U.S., but rigorous safety evaluations have not been completed to confirm their effectiveness. Therefore, it is important for transportation agencies to use rigorous scientific methods to assess the safety performance of countermeasures.
1.2 Development of Safety Effect Estimates
Development of an objective, reliable, and accurate safety effect estimate motivates traffic safety researchers to estimate crash modification factors (CMFs), which are multiplicative factors used to compute the expected number of crashes after implementing a given countermeasure at a specific site. A CMF larger than one indicates expected safety disbenefits (i.e., increased crash frequency), and a CMF smaller than one indicates safety benefits (i.e., decreased crash frequency). A number of CMFs have been promoted in the American Association of State Highway and Transportation Officials’ (AASHTO) Highway Safety Manual (4) as modifiers to safety performance functions (SPFs). In addition, the FHWA CMF Clearinghouse includes more than 5,000 CMFs for a variety of safety countermeasures developed in the U.S. (5).
The CMF Clearinghouse rates CMFs on a scale of 1 to 5 stars (1 being “poor” and 5 being “excellent”). A 5-star rating is the most reliable, indicating that: 1) the study design is statistically rigorous and uses an empirical Bayes/full Bayes before-after study design, or before-after study design without bias in site selection; 2) the sample size is large, including 200 or more crashes in the before and after periods, or 200 to 400 total crashes in a cross-sectional study; 3) the CMF is significantly different from 1.0 at the 5 percent significance level; and 4) there is control for all potential bias.
There are two critical features in the estimation of the safety effectiveness of a countermeasure: study design and application of statistical methods. A randomized experiment is usually considered the optimal study design. However, it is generally not possible to implement a randomized experiment in traffic safety research due to financial and ethical reasons.
Observational data, however, are widely available to traffic safety researchers. As a result, crosssectional regression methods are often used to develop CMFs in traffic safety research. The negative binomial regression model is the most common method to model crash frequencies (6). In this method, an independent variable (i.e., indicator variable) in the model is used to develop the CMF. Observational before-after studies are also common methods used in traffic safety research to estimate the effectiveness of a countermeasure. The most common before-after study method employs the Empirical Bayes (EB) method, which corrects for regression-to-the-mean bias. In recent years, propensity score matching has also been used to estimate the effectiveness of safety improvements. Each of these methods (cross-sectional regression models, before-after studies, and propensity score matching) has strengths and limitations, which are described more fully in the literature review section.
The study design and statistical approach are key considerations when estimating CMFs. Current traffic safety research is focused on improving the reliability and precision of CMFs so that transportation agencies have confidence in the expected outcome of a chosen countermeasure(s). The objective of this thesis is to incorporate Bayesian methods into the propensity score matching framework and to evaluate the performance of this innovative technique. As propensity score matching is being used in more and more traffic safety research, the exploration of this alternative would provide some insights for the application of this methodological framework.
1.3 Shoulder and Centerline Rumble Strips
To evaluate the benefits of the proposed methodology, the safety effects of shoulder and centerline rumble strips were estimated and compared using the traditional and proposed frameworks. The traditional framework is the propensity score matching in a classical statistic modeling framework, while the proposed methodology is the Bayesian propensity score matching framework. Rumble strips are considered one of the most cost-effective safety countermeasures for lane-departure crashes on divided and undivided roads, and are one of the “proven” countermeasures in the U.S. Because there are many existing CMFs for this treatment, it is logical to use this countermeasure as the basis to evaluate the proposed methodological framework.
As shown in Figure 1–1, a rumble strip is a roadway surface treatment that can be implemented along the road edge line, shoulder, or centerline. As the motor vehicle drifts out of the travel lane and the tires pass over the rumble strip pattern, the driver receives a noise and vibration alert. This provides drivers with an opportunity to correct their steering path and prevent them from running off the road or encroaching into adjacent travel lanes (7).
A National Cooperative Highway Research Program (NCHRP) report offers guidance for the design and application of rumble strips (8). Shoulder rumble strips (SRS) are placed on highway shoulders, outside of the travel lane. Edge line rumble strips (ELRS) are regarded as another type of shoulder rumble strip, which is commonly used on roads with narrow shoulders. They are placed along the edge line of the road or on the pavement marking. SRS and ELRS are designed to mitigate single vehicle run-off-road (SVROR) crashes. Centerline rumble strips (CLRS) are placed on or near the centerline of an undivided roadway. These are designed to mitigate opposite-direction sideswipe and head-on crashes. Transverse rumble strips are used to alert drivers of some unexpected changes in the road, such as the need to slow down or stop. The dual application of SRS plus CLRS is the treatment in this study. The safety benefits of SRS plus CLRS have been demonstrated in many states and in many studies. However, there are also studies identifying the safety dis-benefits of SRS or CLRS. The CMF Clearinghouse includes various CMF estimates for CLRS or rumble strips that are less than or more than 1.0 (5). The major studies were identified in the literature review section.
Figure 1-1: Shoulder and Centerline Rumble Strips.
1.4 Research objectives
The main objective of this research is to explore the applicability of the Bayesian propensity score matching method in the context of a traffic safety countermeasure evaluation. In particular, the method will be examined with regards to effectiveness, robustness, and efficiency, each of which is described below:
- Effectiveness: Effectiveness here is defined as the ability to produce unbiased treatment effect estimates. It can be evaluated via the bias of the estimates.
- Robustness: Robustness is a standard to justify whether a statistical method is applicable to use under different conditions. It reflects the ability of a method to accommodate unexpected noise and secure a reliable result. This feature is important in traffic safety research since the crash database is usually incomplete. Issues such as unobserved heterogeneity, or insufficient sample sizes, often exist in traffic safety evaluations. The influence of sample size and unobserved heterogeneity were examined through the analysis of various regional levels of data, and controllable unobserved confounders.
- Efficiency: Statistical efficiency is a measure of whether an estimation method, or experimental design, is able to maximize the use of data. In another words, using the same dataset, a smaller variance of the estimator indicates better efficiency. Efficiency is measured by the mean square error (MSE), which incorporates the bias and variance of an estimator.
The characteristics of BPSM were investigated and compared to the results from standard propensity score matching. The reasons for conducting this comparison were to contrast the results from three different cross-sectional studies using the same types of model when estimating the treatment effect. The comparison is expected to reveal the benefits of incorporating Bayesian estimation in the PSM framework.
The research framework is shown in Figure 1-2. It is divided into two branches. The first branch focuses on investigating the robustness of BPSM in comparison to the conventional methods. A no-treatment before-period dataset is used to assess the estimation using different sample sizes. In this before-period dataset, the entities in the treatment group are actual treatment sites but have not received the treatment. Since the actual treatment is null, the potential outcomes are assumed to be the same under both the treated and untreated conditions. In this case, the CMF estimates are expected to be 1.0. Furthermore, the sensitivity of the unobserved heterogeneity is also a focus of the study. Manually adding some uncertainty in the data is a good way to examine the Bayesian propensity score estimates. This analysis will be conducted through a data simulation approach. An unobserved confounder was simulated as an indicator variable that is correlated to the treatment and the outcome. Various levels of influence caused by the unobserved confounder could be controlled by the simulation. In both of the no-treatment analysis and simulation-based analysis, the performance of BPSM framework is assessed and compared to the standard PSM framework based on the ability to balance the covariates as well as the ability to yield unbiased estimates. After all, the safety effect of SRS and CLRs were estimated using the proposed BPSM framework.
