Safety Evaluation of Edge-Line Rumble Stripes on Rural Two-Lane Horizontal Curves

Chapter 4. Methodology

The EB methodology for observational before–after studies was used for the evaluation conducted in this study. 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, safety performance functions (SPFs) were used, which did the following:

• Overcame the difficulties of using crash rates in normalizing for volume differences between the before and after periods.
• Accounted for time trends.
• Reduced the level of uncertainty in the estimates of safety effect.
• Properly accounted for differences in crash experience and reporting practice in amalgamating data and results from diverse jurisdictions.
• Provided 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 in 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 effects of regression-to-the-mean 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). 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 is used to first estimate the number of crashes that would be expected in each year of the before period at locations with characteristics similar to the one being analyzed (i.e., traffic volume and reference sites). 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 installation, as shown in figure 4.

Where w is estimated from the mean and variance of the SPF estimate, which is shown in figure 5.

Where k is constant for a given model.

k 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 λ. 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 λ is also summed over all sites in the strategy group.

Figure 6 illustrates the estimate of the index of effectiveness (θ).

Figure 7 illustrates the standard deviation of θ.

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 30-percent reduction in crashes with a standard deviation of 12 percent.