Evaluation of Pavement Safety Performance

CHAPTER 5. ANALYSIS

ANALYSIS OBJECTIVES

As discussed, the objective of this analysis was to estimate the effect of various low-cost pavement treatments on crashes using treatments from several States. These treatments were installed primarily for pavement preservation and not necessarily for safety improvement. As presented in chapter 3, the following treatments were evaluated:

• Chip seal (single, double, and triple layer).
• Diamond grinding (concrete pavement only).
• Grooved concrete pavement.
• Microsurfacing (asphalt and concrete pavement).
• OGFC (asphalt and concrete pavement).
• Slurry seal (asphalt pavement).
• Thin HMA (asphalt and concrete pavement).
• UTBWC (asphalt and concrete pavement).

The basic objective of the crash data analysis was to estimate the change in target crashes. Only nonintersection, nonanimal related crashes and crashes not involving snow or ice were considered. Crash types examined included the following:

• Total.
• Injury.
• ROR.
• Wet-Road.
• Dry-Road.
• Wet-Road ROR.

Further questions of interest examined included the following:

• Do effects vary by level of traffic volumes?
• Do effects vary by underlying pavement type?
• Do effects vary by posted speed limit or by urban-rural environments?
• Do effects vary by the site-specific expected crash frequency prior to treatment?
• Do effects vary by State and road class?
• What is the overall effect, measured by the economic costs of crashes, by crash type and severity?

Meeting these objectives placed some special requirements on the data collection and analysis tasks, including the need to do the following:

• Select a large enough sample size to detect, with statistical significance, what may be small changes in safety for some crash types.
• Carefully select reference sites to properly account for changes in safety not due to the treatments, including regression-to-the-mean, traffic volume changes, and time trends.
• Properly account for traffic volume changes.
• Pool data from multiple jurisdictions to improve the reliability of the results and facilitate broader applicability of the research products.

As discussed in chapter 4, roadway, pavement data, traffic volume, and crash data were acquired for sites in Pennsylvania, Minnesota, North Carolina, and California to facilitate the analysis. The States also provided information related to the installation of the pavement improvement (i.e., location and date).

ANALYSIS METHODOLOGY

The general analysis methodology applied is the EB before-after approach. The methodology is well documented by Hauer.⁽⁴³⁾ The advantages of the EB method include the following:

• Properly accounting for regression-to-the-mean.
• Overcoming the difficulties of using crash rates in normalizing for volume differences between the before and after periods.
• Reducing the level of uncertainty in the estimates of safety effect.
• Providing a foundation for developing guidelines for estimating the likely safety consequences of contemplated installations.
• Properly accounting for differences in crash experience and reporting practice in amalgamating data and results from diverse jurisdictions.

The approach comprises three basic steps:

• Step 1: Predict what safety would have been in the "after" period had the status-quo been maintained.
• Step 2: Estimate what the actual safety was in the "after" period.
• Step 3: Compare the two.

The EB procedure requires the calibration of SPFs, as outlined in the next section, relating crashes of different types and severities to traffic flow and other relevant factors for each jurisdiction for locations without the treatment, with appropriate adjustments for temporal effects. This will enable the simultaneous accounting for temporal and possible regression-to-the-mean effects, as well as those related to changes in traffic volume.

DEVELOPMENT OF SAFETY PERFORMANCE FUNCTIONS

Fundamental to the EB approach is the use of the SPFs to represent the conditions before installation. Where sufficient data are available for a reference population of sites similar to those treated, it is desirable to calibrate these functions directly for the jurisdiction and analysis period of interest.

Data required for SPF development are: crash, traffic, and geometric data for a sample of reference sites that are similar to those for which the SPF would be applied. The data are required for each year of the analysis period (i.e., the period of before and after at the treatment sites).

The direct calibration of SPFs was accomplished with generalized linear modeling (GLM) using the R software package. This procedure allows the specification of a negative binomial error structure, which is now recognized as more appropriate for crash counts than the normal distribution that is assumed in conventional regression modeling. The GLM procedure also estimates the overdispersion parameter k of the negative binomial distribution that is used in the EB estimation. Crash counts at locations in the reference group are used as estimates of the dependent variable, which is the expected number of crashes per year by type and severity, while corresponding road characteristics and traffic data are used as estimates of the independent variables.

SPECIFICS OF THE EMPIRICAL BAYES BEFORE-AFTER EVALUATION

Overall Safety Effects

In the EB evaluation of the effect of a treatment, the change in safety for a given crash type at a treated site is given by the equation in figure 17:

Figure 17. Equation. Change in safety for a given crash type at a treated site.

Where:

B = expected number of crashes that would have occurred in the after period without the treatment
A = number of reported crashes in the after period.

Because of changes in safety that may result from changes in traffic volume, from regression-to-the-mean, and from trends in crash reporting and other factors, the count of crashes before a treatment by itself is not a good estimate of B-a reality that has now gained common acceptance.⁽⁴³⁾ Instead, B is estimated from an EB procedure in which a safety performance function is 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 a treatment site being analyzed.⁽⁴³⁾ The sum of these annual SPF estimates (P) is then combined with the count of crashes (x) in the before period at the treatment site to obtain an estimate of the expected number of crashes (m) before the treatment. This estimate of m is shown in figure 18:

Figure 18. Equation. Estimate of the expected number of crashes before treatment.

The weight w is estimated using the equation in figure 19 :

Figure 19. Equation. Estimate of weight.

Where:

k = overdispersion parameter of the negative binomial distribution that is assumed for the crash counts used in estimating the SPF. The value of k is estimated from the SPF calibration process with the use of a maximum likelihood procedure.

A factor is then applied to m from the equation in figure 18 to account for the length of the after period, differences in traffic volumes between the before and after periods, and other unknown differences between these two periods accounted for by using the yearly factors of the SPF. 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 B. The procedure also produces an estimate of the variance of B, the expected number of crashes that would have occurred in the after period without the treatment.

The estimate of B is then summed over all sites in a treatment group of interest (to obtain Bsum) and compared with the count of crashes during the after period in that group (Asum). The variance of B is also summed over all sites in the group of interest.

The index of safety effectiveness (θ) is estimated using the equation in figure 20:

Figure 20. Equation. Estimate of the index of safety effectiveness.

The standard deviation of θ is given by the equation in figure 21 :

Figure 21. Equation. Standard deviation of the estimated index of safety effectiveness.

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

Effects on Different Severity and Impact Types

The methodology is essentially the same as outlined earlier. The difference is that crashes of interest are used along with SPFs specific to these crash types.

Effects of Design, Traffic, Operational, and Safety Characteristics

Where samples were large enough, the study sought to isolate sites with certain levels of a given variable and to estimate the separate effects for each level by road class. In the case of continuous variables, such as traffic volume, aggregation was attempted over specified ranges of that variable, and regression models were estimated to relate the safety effect to the value of that variable. These include the effects of the following:

• Annual precipitation levels.
• Level of safety before installation measured as the expected crash frequency.
• Traffic volume levels.

Differential Effects Over Time

The EB procedure facilitated the estimation of differential effects over time for certain treatment types. This was important given the belief that the effects of some treatments deteriorate over time. A minor adjustment to the procedure allowed the investigation of effects for each year starting immediately after installationas opposed to calendar years. This refinement was necessary to examine the effects over time, for example at 1, 2, and 3 years after installation, to the extent that the small sample sizes facilitated this investigation.

SAFETY PERFORMANCE FUNCTIONS

This section presents the SPFs developed. The SPFs are used in the EB methodology to estimate the expected number of crashes in the after period without treatment.

GLM was used to estimate model coefficients andassumed a negative binomial error distribution, which is consistent with the state of research in developing these models. Alternative models were evaluated by comparing the magnitude and statistical significance of the variables included as well as the value of the overdispersion parameter, which in itself, is a reliable goodness-of-fit measure, with a smaller overdispersion parameter indicating a model that better captures the overdispersion in the data.

Separate SPFs were developed for each State and for different site and crash types. SPFs were not estimated for dry-road crashes because logically the EB estimates for these crashes could be derived as the difference between the estimates for total and wet-road crashes.

Pennsylvania

The model form for the Pennsylvania SPFs is shown in figure 22:

Figure 22. Equation. Model form for Pennsylvania SPFs.

Where:

AADT = Average Annual Daily Traffic
Urbrur = 1 if rural environment; 0 if urban
Shldwid = average shoulder width in ft

α, the βs, and the overdispersion parameter, k, are parameters estimated in the modeling process.

Table 19 provides the parameter estimates and standard errors.

Table 19 . SPF parameter estimates and standard errors for Pennsylvania treatment sites.

s.e. = Standard error
ROR = Run-off road

North Carolina

The model form for the North Carolina SPFs is shown in figure 23:

Figure 23. Equation. Model form for North Carolina SPFs.

Where:
AADT = Average Annual Daily Traffic
Urbrur = 0 if rural environment; 1 if urban

α, the βs, and the overdispersion parameter, k, are parameters estimated in the modeling process.

Table 20 provides the parameter estimates and standard errors.

Table 20. SPF parameter estimates and standard errors for North Carolina treatment sites.

s.e. = Standard error
ROR = Run-off road

California

The model form for the California SPFs is shown in figure 24:

Figure 24. Equation. Model form for California SPFs.

Where:

AADT = Average Annual Daily Traffic
Urbrur = 0 if rural environment; 1 if urban
Surftype = 1 if asphalt; 0 if concrete
Medwid = median width in ft
Avgshldwid = average of left and right shoulder width in ft
Lanewid = lane width in ft
Terrain = flat, rolling, or mountainous
Divided = 0 if undivided; 1 if divided

α, the βs, and the overdispersion parameter, k, are parameters estimated in the modeling process.

Table 21 provides the parameter estimates and standard errors.

Table 21 . SPF parameter estimates and standard errors for California treatment sites.

s.e. = Standard error
ROR = Run-off road

Minnesota

The model form for the Minnesota SPFs is:

Figure 25. Equation. Model form for Minnesota SPFs.

Where:

AADT = Average Annual Daily Traffic
Pavetype = 1 if asphalt; 0 if PCC
Lanes = 0 if 4 or fewer lanes; 1 if greater than 4
Urbrur = 0 if rural; 1 if urban
Lanewid = lane width in ft

α, the βs, and the overdispersion parameter, k, are parameters estimated in the modeling process.

Table 22 provides the parameter estimates and standard errors.

Table 22 . SPF parameter estimates and standard errors for Minnesota treatment sites.

s.e. = Standard error
ROR = Run-off road
n/a = Not applicable

USE OF CLIMATE DATA

Objective

In the study work plan, climatic data were identified as of interest for the study. The hypothesis was that climate conditions are likely related to the risk of crashes that may be treatable through improved pavement friction conditions.

The study design for developing CMFs is applying the EB before-after methodology. In this approach, factors that may affect expected crash frequencies but that are not related to the treatment of interest are accounted for through the use of SPFs. This is done is by calibrating the SPFs using a reference group and determining yearly factors that represent time trends in crashes owing to demographics, reporting trends, weather, etc. These SPFs also include as many geometric-related variables and traffic exposure variables as possible so that changes in traffic are accounted for and predictions are as site-specific as possible.

To directly include weather-related measurements in the EB analysis, these variables would need to be used in the SPFs. This would in fact be attractive because site-specific differences between the before and after periods in temperature and/or precipitation could be accounted for when predicting expected crashes without treatment.

The climate data of interest included average monthly temperatures and average monthly precipitation. When using any data that change over time, there is a need to aggregate up to a reasonable level of analysis while leaving the data as disaggregated as possible so that variation is still observed. It was felt that using monthly data provided a reasonable balance between these two needs.

The feasibility of including average temperatures and precipitation was explored using the reference group from North Carolina.

Source of Data

As mentioned above, the two variables that were identified for treatment site climate data were temperature and precipitation. Temperature data consisted of average monthly temperatures for each month during the before and after analysis period for each site. Precipitation data consisted of actual monthly precipitation during the analysis period for each site.

The project team initially examined the feasibility of collecting climate data for each individual treatment site by selecting an appropriate weather station for each site. Considering the thousands of treatment sites and reference sites, this would have required a tremendous amount of effort to first identify viable weather stations, and then link each treatment site to a station. A second option was to collect climate data by county, because the county in which each treatment site is located is known. This did not prove to be a feasible option either because there are no known sources for climate data by county.

The most viable option identified by the team was to collect weather data by National Climatic Data Center (NCDC) divisions. Each State is broken down into several divisions (up to 10 per State) encompassing several counties each, with the borders of the divisions generally (but not always) following county boundaries. The NCDC uses an algorithm to compile and summarize climate data by division using the various weather stations within the division. This helps to eliminate uncertainty associated with the reliability of individual weather stations in the NCDC network.

Therefore, in compiling climate data for this effort, the project team established the NCDC division for each treatment or reference site based on the county in which each site is located. The monthly temperature and precipitation data for each division during the before and after analysis time period are then obtained from NCDC using the Land-Based Station Data.

Methodology and Results

The pilot test of climate data involved reestimating the SPFs using the reference group from North Carolina and comparing with the previously estimated SPFs. The difference now is that the unit of analysis is the monthly crash count rather than the sum of the observed crashes over the study period. The modeling applied the General Estimating Equations regression approach, which is required to account for temporal correlations that arise because each site is in the data as a separate observation for each month.

The evaluation of the new SPFs included a comparison with the earlier SPFs, the magnitude and significance of the estimated parameters, and a comparison of the estimated overdispersion parameters with and without the climate data.

The development of SPFs was attempted for total, injury, and ROR crashes. These were attempted for freeway, two-lane, multilane divided, and multilane undivided roads. Table 23 shows which SPFs were successful and which were not for the monthly data. Of the 12 SPFs attempted, no SPF was successfully calibrated for 7 categories. For the five categories for which an SPF was possible using the monthly data there was no improvement in the goodness of fit of the model for three. For the remaining two the improvement in goodness of fit was only slight.

Table 23. Summary of pilot test results of including climatic data.

ROR = Run-off road
SPF = Safety performance function

Conclusions on the Use of Climate Data

The use of monthly data makes the estimation of SPFs difficult because of the preponderance of zero counts. It was found that when using monthly data, SPFs could not be estimated for 7 of 12 site type/crash groups.

For the SPFs estimated with monthly data, the difference in model fit as measured by the overdispersion parameter between those SPFs with and without the climate data variables is negligible.

Considering the difficulty in estimating SPFs using monthly data and the negligible improvement in model fit using climate data where those SPFs were possible, it is was not recommended to further consider climate data in the reference group SPFs.

An additional concern with the monthly data is that the effects of climate are likely correlated to traffic volumes. The volume variable available is the average for the entire year. Fluctuations in volume throughout the year would be expected (e.g. the summer driving season), and these are likely correlated to average temperatures and precipitation. Unfortunately, average daily traffic volumes by month are not available.