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

Chapter 6. Development of Safety Performance Functions

This chapter presents the SPFs developed for each crash type. The SPFs were used in the EB methodology to estimate the safety effectiveness of this strategy.⁽³⁶⁾ Generalized linear modeling was used to estimate model coefficients assuming a negative binomial error distribution, which is consistent with the state of research in developing these models. In specifying a negative binomial error structure, the dispersion parameter, k, was estimated iteratively from the model and the data. For a given dataset, smaller values of k indicate relatively better models.

Crash Spillover and Migration

Before developing SPFs, the project team analyzed the separate reference groups to identify potential crash migration and spillover effects. An SPF was developed using data from both reference groups in order to develop yearly multipliers for each group. The form of the SPF is provided in figure 8, with parameter estimates presented in table 17.

Where:

AADT = annual average daily traffic volume.
L = segment length (mi).
invradius = inverse of the horizontal curve radius (ft).
right_shoulder = right shoulder width (ft).
a, b, c, d, e = parameters estimated in the SPF calibration process.
k = overdispersion parameter of the model.

Table 18 presents the observed crashes versus predicted crashes for each of the two reference groups in Kentucky. Group 1 was the reference group more than 5 mi downstream, and group 2 was the reference group immediately downstream of the treatment sites. Group 1 also included reference sites that were on different roadways than the treatment sites. The yearly factors were the ratio of observed crashes to predicted crashes for the given group within the given year. Spillover and crash migration effects would be apparent if the yearly factors became drastically different between group 1 and group 2 after treatment application (2010 for most sites). These effects would also become apparent if the yearly factor for group 2 increased or decreased markedly after treatment application. However, neither of these scenarios appeared to be the case. Figure 9 provides a graphical representation of the yearly factors from table 18.

The sample sizes for reference sites were too small to make a statistical observation of difference between the groups (i.e., fewer than 20 crashes per year were observed). However, both groups experienced an abnormally large number of total crashes in 2011 or 2012, and group 1 observed an abnormally low number of crashes in 2011. Therefore, data for 2011 and 2012 were removed for the reference sites for SPF development. Before-period data from treatment sites were combined with reference-site data to bolster sample size, and the project team estimated an interaction term for the pretreatment site indicator and AADT to determine whether there was a difference in the effect of traffic volume at treatment sites in the before period versus at the references sites. The results indicated that the reference data and pretreatment data could be combined for SPF estimation.

In addition, because of the lack of data at the reference curves in this dataset, the project team sought an alternative reference group for developing annual factors. The Kentucky reference data from Lyon et al. provided a robust dataset for estimating annual factors for the before and after periods from combined horizontal curves and tangents.⁽³⁰⁾ This reference set included sections that were eligible for resurfacing but had not yet received resurfacing and had texturing; this was consistent with the treatment group. The reference set also included those identified by Lyon et al. to be “resurfacing effort” sites but excluded sites that had SRSs in the prior condition.⁽³⁰⁾ In total, the reference group consisted of 401.21 roadway mi. The project team used the reference segments to develop predicted crashes, which were compared with observed crashes to develop annual factors. The after-period factor was 1.034 for 2009 installations, 0.993 for 2010 installations, and 0.982 for 2011 installations. Table 19 presents the observed crashes versus predicted crashes for each of the two reference groups in Ohio. As with Kentucky, group 1 represents the reference group more than 5 mi downstream, and group 2 represents the reference group immediately downstream of the treatment sites. Figure 10 provides a graphical representation of the yearly factors from table 19. The annual factors show that the reference sites, particularly those not adjacent to treatment sites, observed a substantial reduction, beginning in 2011, relative to the before period. This possibility was expected for group 2 but not for group 1.

The project team explored this finding further with statewide data for rural two-lane roadways and for horizontal curves on rural two-lane highways. Consistently, the trends showed an approximate 10- to 15-percent reduction in crashes beginning in 2011. The project team contacted ODOT to gain further insight into this finding to determine why this systematic reduction was observed statewide. ODOT noted that in 2010, the systemic program focused on upgrading signage for horizontal curves statewide. This included upgrading hundreds of curves. The upgraded signage included chevrons, curve ahead signs, and speed advisory signs, among others. Therefore, the project team considered using horizontal tangent sections as a potential reference group for developing annual factors to mitigate the impact of signage upgrades on the overall findings. Spillover effects were observed for short tangents; the annual multipliers for short tangents (i.e., tangents less than 0.5 mi in length) were found to match those of horizontal curves within 1.0 percent for each installation year. Tangents longer than 1.0 mi were used as a reference group for developing annual factors because no spillover effects were observed. The reference segments were used to develop predicted crashes, which were compared with observed crashes to develop annual factors. The after-period factor was 1.040 for 2010 installations, 1.043 for 2011 installations, and 1.038 for 2012 installations.

Safety Performance Functions

Figure 11 shows the form of the SPFs for combined reference groups, which are presented in table 20.

Where:

posted = posted speed.
f = parameter estimated in the SPF calibration process.

The Kentucky SPF was estimated using treatment site before period data and 2004 to 2010 reference site data. The Ohio SPFs were estimated using reference site data from 2005 to 2010.

N/A = not applicable.

In addition, the project team considered crash sample size for reference sites in the development of SPFs. In Kentucky, total crashes per year ranged from 65 to 77. Other crash types had smaller sample sizes. The Highway Safety Manual recommends a minimum of 100 crashes per year to produce reliable SPFs.⁽⁴⁰⁾ Therefore, an SPF was developed for total crashes, and proportion factors relating other crash types to total crashes were used in place of separate SPFs. In Ohio, total crashes ranged from 110 to 158. There were sufficient crashes to develop separate SPFs for total crashes and ROR crashes. To relate other crash types to total crashes, proportion factors were used in place of separate SPFs. The prediction from the SPF was multiplied by the proportion factor to determine the number of predicted crashes of each specific crash type. The following is a list of crash type proportions for Kentucky:

• Fatal and injury crashes = 0.370.
• ROR crashes = 0.603.
• Nighttime crashes = 0.289.
• Nighttime ROR crashes = 0.200.

The following is a list of crash type proportions for Ohio:

• Fatal and injury crashes = 0.403.
• Nighttime crashes = 0.373.
• Nighttime ROR crashes = 0.314.

In addition, observed crashes and predicted crashes were used to develop annual factors for time-based trends at reference sites. Factors were used as multipliers for predicted crashes at treatment sites in the after period. Factors greater than 1.00 indicate an increase in crashes at reference sites, and factors less than 1.00 indicate a decrease in crashes at reference sites. Table 21 provides the annual factors based on total crashes in Kentucky and Ohio for each installation year.

N/A = not applicable.