Safety Evaluation of Cable Median Barriers in Combination With Rumble Strips on Divided Roads

CHAPTER 4. METHODOLOGY

This evaluation uses the EB methodology for observational before–after studies.⁽¹⁰⁾ This methodology is considered rigorous in that it accounts for regression-to-the-mean using a reference group of similar but untreated sites. In the process, the research team used safety performance functions (SPFs) for the following purposes:

• To overcome the difficulties of using crash rates in normalizing for volume differences between the before and after periods.
• To account for time trends.
• To reduce the level of uncertainty in the estimates of safety effects.
• To properly account for differences in crash experience and reporting practice in amalgamating data and results from diverse jurisdictions.

The methodology also provides a foundation for developing guidelines for estimating the likely safety consequences of a contemplated strategy.

In the EB approach, the change in safety for a given crash type at a site is given by figure 3.

Where:

λ = Expected number of crashes that would have occurred in the after period without the strategy.
π = Number of reported crashes in the after period.

In estimating λ, the authors used SPFs to explicitly account for the effects of regression-to-the-mean and changes in traffic volume, relating crashes of different types to traffic flow and other relevant factors for each jurisdiction based on untreated sites (reference sites). They calibrated annual SPF multipliers to account for temporal effects on safety (e.g., variation in weather, demography, and crash reporting).

In the EB procedure, the first step was to use the SPF to estimate the number of crashes that would be predicted in each year of the before period at locations with traffic volumes and other characteristics similar to the one being analyzed (i.e., reference sites). The sum of these annual SPF estimates (P) was then combined with the count of crashes (x) in the before period at a strategy site to obtain an estimate of the predicted number of crashes (m) before strategy. Figure 4 shows this estimate of m.

Where w, the EB weight, is estimated from the mean and variance of the SPF estimate as figure 5 illustrates.

Where k is the overdispersion parameter of a negative binomial regression model, which was estimated from the SPF calibration process with the use of a maximum likelihood procedure. k could be assumed as a constant or as a function of site characteristics, including segment length. Based on the recommendation from Hauer, k was estimated based on segment length and assumed to be , where k₁ is the overdispersion parameter for a 1-mi segment and l is the length of the segment.⁽¹²⁾

A factor was then applied to m to account for the length of the after period and differences in traffic volumes between the before and after periods. This factor was the sum of the annual SPF predictions for the after period divided by P, the sum of these predictions for the before period. The result, after applying this factor, was an estimate of λ. The procedure also produced an estimate of the variance of λ.

The estimate of λ was then summed over all sites in a strategy group of interest (to obtain λ_sum) and compared with the count of crashes observed during the after period in that group (π_sum). The variance of λ was also summed over all sites in the strategy group.

The index of effectiveness (θ) is estimated as shown in figure 6.

Figure 7 shows how the standard deviation of θ is calculated.

The percent change in crashes was calculated as 100(1 - θ); thus, a value of θ = 0.7 with a standard deviation of 0.12 indicates a 30-percent reduction in crashes with a standard deviation of 12 percent.

The analysis of the treatment sites in Missouri required a slightly different approach to the methodology. Missouri installed cable median barriers on a systemwide basis for certain road types. As a result, it was virtually impossible to identify comparable roadways without cable barriers for this road type presently or in the near future. For this reason, the research team did not identify a separate reference group of sites without rumble strips.

The research team applied an alternate approach to the standard method of estimating and applying SPFs for the EB before–after methodology. In short, this method used the before-period data at the treatment sites to develop SPFs to control for regression-to-the-mean and traffic volume changes. Because the State applied its policy of installation of cable barriers systemwide, regression-to-the-mean was not as big a concern as it otherwise might have been. The research team used SPFs calibrated from before-period data to account for time trends in the earlier part of the study period, before most of the sites had rumble strips installed. However, after a substantial number of sites had been treated, the number of sites was still too low to develop yearly factors to account for trends. Instead, the research team used time trends from the Missouri data that were used in the rural two-lane centerline plus shoulder rumble strips analysis to calculate the after-period trend when MoDOT had treated most or all of the sites.⁽¹³⁾ The research team adjusted the before-period yearly factors based on the ratio of the after-period factors to common years in the rural two-lane data.

To illustrate, consider the fictitious information in table 5. Using the SPFs calibrated for both the before and after periods, annual multipliers were estimated for each year. In 2006, there were no data for the after period, so a multiplier did not exist for that year for the after-period SPF. Similarly, there was no multiplier for 2009–2011 using the before-period data. The average of the multipliers for the common years (2007–2008) was computed. The after-period multipliers post-2007 were adjusted by dividing the values by the 2007–2008 average. Finally, the missing yearly multipliers for the before-period model were adjusted by multiplying the average from 2007–2008 (1.03) by the value of the adjusted after-period multiplier for each year. These were the annual multipliers used in the evaluation.