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Publication Number:  FHWA-HRT-16-035    Date:  June 2016
Publication Number: FHWA-HRT-16-035
Date: June 2016

 

Safety Evaluation of Intersection Conflict Warning Systems

Chapter 4. Methodology

The EB methodology for observational before–after studies was used for the evaluation. This methodology was considered rigorous in that it accounted for RTM using a reference group of similar sites without ICWS installation. In the process, SPFs were used for the following reasons:

In the EB approach, the change in safety (Δ) for a given crash type at a site is given by figure 2.

Figure 2. Equation. Estimated change in safety. The change in safety equals lambda minus pi.

Figure 2. Equation. Estimated change in safety.

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 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 reference sites. Annual SPF multipliers were calibrated to account for temporal effects on safety (e.g., variation in weather, demography, and crash reporting).

In the EB procedure, the SPF was used to first estimate the number of crashes that would be expected 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 an installation site to obtain an estimate of the expected number of crashes (m) before installation, as shown in figure 3.

Figure 3. Equation. Empirical Bayes estimate of expected crashes. m equals the sum of w times P plus the quantity one minus w end quantity times x.

Figure 3. Equation. Empirical Bayes estimate of expected crashes.

Where w is estimated from the mean and variance of the SPF estimate, as shown in figure 4.

Figure 4. Equation. Empirical Bayes weight. w equals one divided by the sum of one plus the quantity k times P.

Figure 4. Equation. Empirical Bayes weight.

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

The index of effectiveness (θ) is estimated in figure 5.

Figure 5. Equation. Index of effectiveness. Theta equals pi subscript sum divided by lambda subscript sum, end of quotient, divided by one plus the quantity quotient of the variance of lambda subscript sum, divided by lambda subscript sum squared end quotient, end quantity.

Figure 5. Equation. Index of effectiveness.

The standard deviation of θ is given in figure 6.

Figure 6. Equation. Standard deviation of index of effectiveness. The standard deviation of theta equals the square root of theta squared times the quantity the sum of the variance of pi subscript sum, divided by pi subscript sum squared plus the variance of lambda subscript sum divided by lambda subscript sum squared end quantity divided by the square of the quantity one plus the variance of lambda subscript sum divided by lambda subscript sum squared end quantity.

Figure 6. Equation. Standard deviation of index of effectiveness.

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.

 

 

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