Safety Evaluation of Profiled Thermoplastic Pavement Markings

Chapter 3. Methodology

The empirical Bayes (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 also used to do the following:

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

The methodology derived and documented in detail by Hauer is only summarized here. It also provides a foundation for developing guidelines for estimating the likely safety consequences of a contemplated strategy.⁽³⁾ The SPFs for roadways without profiled thermoplastic pavement markings can be used with observed crash histories to estimate the number of crashes without treatment, and the crash modification factors (CMFs) developed can be applied to this number to estimate the number of crashes with treatment.

In the EB approach, the estimated change in safety for a given crash type at a site is given by the equation 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, which relate crashes of different types to traffic flow and other relevant factors for each jurisdiction based on untreated sites (i.e., 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 first used to estimate the number of crashes that would be predicted to occur in each year of the before period at reference sites having 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 predicted number of crashes (m) before strategy. This estimate of m is calculated using the equation in figure 4.

Where w is estimated from the mean and variance of the SPF estimate using the equation in figure 5.

Where k is an overdispersion parameter estimated from the SPF calibration.

In specifying the SPF, a negative binomial distributed error structure is assumed, with k being the overdispersion parameter of this distribution and that is estimated along with the other parameters of the SPF.

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.

The index of effectiveness (θ) is estimated using the equation in figure 6.

The standard deviation of θ is given by the equation in figure 7.

The percent change in crashes is calculated as 100(1 - θ); thus, a value of θ = 0.70 with a standard error (SE) of 0.12 indicates a 30-percent reduction in crashes with an SE of 12 percent.