Andrew Olsen and Dr. C. Shane Reese, Statistics
Thousands of people die in automobile crashes each year. Departments of Transportation are working continuously to reduce the number of fatalities through highway safety projects. One of their critical tasks is to evaluate the efficacy of these projects. We have developed a Bayesian hierarchical Poisson regression model that the Utah Department of Transportation may use to evaluate its traffic-accident intervention. The use of this method is illustrated with severe crashes on a raised median on University Parkway from mile 1.20 to mile 1.96.
The Bayesian hierarchical Poisson regression model is utilized to compare crash frequencies in before and after studies. The basic modeling strategy is to create unique intercepts for before and after time periods. Other covariates, such as annual average daily traffic (AADT), which is a measure of traffic volume, may also be used. Utilizing AADT is important in the analysis because traffic flow can change between before and after periods, and we expect that increased traffic will naturally result in more crashes. This model is written
When the posterior distributions are obtained, there are several summaries that are meaningful in determining whether or not a reduction in crashes has occurred in the after time period. One such summary is the ratio of the mean number of crashes in the after time period to the mean number of crashes in the before time period. The distribution of AoverBfor severe crashes on the University Parkway median is shown on the left of Figure 1. Each value may be interpreted as the factor change in crashes from the before to after time periods. Accordingly, values less than one indicate a reduction in crashes. This distribution shows there is a 100% chance that the mean number of severe crashes was reduced from the before period to the after period.
An additional posterior summary that is of interest is the posterior predictive distribution of differences. This distribution shows the probability that there were x fewer crashes per year per mile in the after period. The posterior predictive distribution of differences is shown on the right of Figure 1. From this distribution, we can calculate more specific probabilities, such as the probability that severe crashes were reduced by five or more crashes, which is equal to 0.43 for University Parkway. This distribution is extremely useful when quantifying the true benefit of a safety project.
With these two posterior summaries, we determine that raised medians were effective on University Parkway in reducing severe crashes. Similar analyses were performed on several other medians in addition to several cable barrier sites.
Two specific works have arisen from this research thus far. The first is entitled “Analyzing Raised Median Safety Impacts Using Bayesian Methods,” which was accepted for presentation in the Transportation Research Board (TRB) Annual Meeting in January 2011. Dr. Grant Schultz from Civil Engineering (first author), Daniel Thurgood (a student from Civil Engineering), my mentor Dr. Reese, and I are authors of this paper. The manuscript is also under revision for resubmission to the Transportation Research Record: Journal of the Transportation Research Board. The second work is entitled “Hierarchical Bayesian Modeling for Before and After Studies,” for which I was the first author with contributing authors Dr. Schultz, Daniel Thurgood, and Dr. Reese. This manuscript will also be presented at the TRB Annual Meeting in January. The research has also become my master’s project as I began graduate school this fall semester in the Department of Statistics. We expect at least two additional papers to arise as a result of this work.
I wish to thank the individuals that make student mentoring grants available at Brigham Young University. In this case, they have presented a wonderful opportunity for learning and contribution to the traffic research community in a positive and meaningful way that may in fact reduce loss of life on Utah and national roadways in years to come.