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REPORT 
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Publication Number: FHWAHRT17077 Date: November 2017 
Publication Number: FHWAHRT17077 Date: November 2017 
This study employed the EB methodology for observational before–after studies.^{(5)} This methodology is considered rigorous in that it accounts for RTM using a reference group of similar but untreated sites. In the process, safety performance functions (SPFs) were used, which did the following:
Figure 2 shows the change in safety for a given crash type at a site in the EB approach.
Where:
λ = Predicted 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 effects of RTM and changes in traffic volume were explicitly accounted for using SPFs, relating crashes of different types to traffic flow and other relevant factors for each jurisdiction based on untreated sites(reference sites). The research team 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 SPF is used to first estimate the number of crashes that would be expected in each year of the before period at locations (i.e., reference sites) with traffic volumes and other characteristics similar to the one being analyzed. The sum of these annual SPF estimates (P) is then combined with the count of crashes (x) in the before period at a strategy site to obtain an estimate of the expected number of crashes (m) before strategy. Figure 3 shows this estimate of m:
Where w, the EB weight, is estimated from the mean and variance of the SPF estimate as seen in figure 4 .
Where:
k = Constant for a given model, which is estimated from the SPF calibration process with the use of a maximum likelihood procedure. In that process, a negative binomial distributed error structure is assumed with k being the overdispersion parameter of this distribution.
A factor is 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 is 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, is an estimate of . The procedure also produces an estimate of the variance of λ.
The estimate of λ is 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 is also summed over all sites in the strategy group.
Figure 5 shows how to estimate the index of effectiveness (θ).
The standard deviation of θ is shown in figure 6 .
The percent change in crashes is calculated as 100(1  θ ); thus, a value of θ = 0.7 with a standard deviation of 0.12 indicates a 30percent reduction in crashes with a standard deviation of 12 percent.