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

Chapter 3. Study Design

The study design involved a sample size analysis and prescription of needed data elements. The sample size analysis assessed the size of sample required to statistically detect an expected change in safety and also determined what changes in safety could be detected with likely available sample sizes.

Sample size estimations required assumptions of the expected treatment effect and the average crash rate at treatment sites prior to treatment. The project team calculated minimum and desired sample sizes assuming a conventional before–after with comparison group (C-G) study design, as described in Hauer, and a literature review of likely safety effects.⁽³⁶⁾ The sample size analysis undertaken for this study addressed the size of sample required to statistically detect an expected change in safety. The sample size estimates were conservative because the more robust EB methodology was actually used in the before–after analysis rather than the C-G methodology.

Sample sizes were estimated for various assumptions of the likely annual crash rate in the before period and likely safety effects of the strategy. Annual crash rates were assumed for five crash types (i.e., total, injury, ROR, nighttime, and nighttime ROR) as shown in table 3. Intersection-related and animal crashes were not included in these crash rates.

The horizontal curve site crash rates for the all and injury crash types were obtained directly from Torbic et al. (rates A and B) and before-period data from Kentucky (rate C) and Ohio (rate D).⁽¹⁰⁾ The crash rates for Washington (rate A) and Minnesota (rate B) were selected in particular because they represented the general upper and lower range of national crash rates. For instance, estimated crash rates for sites in Pennsylvania and Missouri from the same NCHRP report were 1.75 total crashes per mi/yr and 2.11 total crashes per mi/yr, respectively, which were both within that range. The before-period crash rates for Washington and Minnesota were used for planning purposes during the development of the study design, and the rates for Kentucky and Ohio were provided to show the actual rates. The before-period rates for Kentucky and Ohio were greater than those assumed during the planning stages, indicating that sufficient sample sizes were more achievable.

The Washington and Minnesota crash rates for the ROR crash type were estimated by multiplying the total crash rate by the ratio of ROR crashes to total crashes based on data from Washington between 2001 and 2005. The nighttime crash rates were estimated by multiplying the total crash rate by the ratio of nighttime collisions to total collisions based on 2008 Kentucky crash data. The nighttime ROR crash rates were estimated by multiplying the nighttime crash rate by the same ROR crashes ratio.

Table 4 through table 8 provide estimates of the required number of before- and after-period mile-years for both the 90- and 95-percent confidence levels on horizontal curve sites by crash type. The minimum sample indicated the level for which a study seemed worthwhile (i.e., it was feasible to detect with the level of confidence the largest effect that might reasonably be expected based on what was currently known about the strategy). These sample size calculations were based on specific assumptions regarding the number of crashes per mile and years of available data. Mile-years is the number of miles where the strategy was implemented multiplied by the number of years of data before or after implementation. For example, if a strategy was implemented at a 9-mi segment and data were available for the 3 years since implementation, then a total of 27 mi-years of after-period data would be available for the study.

The sample size values recommended in this study are highlighted with an asterisk in table 4 through table 8. These were selected based on the likeliness of obtaining the estimated sample size as well as the anticipated effects of the treatment. As noted, the sample size estimates provided are conservative in that the state-of-the-art EB methodology proposed for the evaluations would require fewer sites than the less robust conventional before–after study with a C-G that was assumed for the calculations. Estimates can be predicted with greater confidence or a smaller reduction in crashes would be detectable if there were more site-years of data available in the after period. The same holds true if the actual data used for the analysis had a higher crash rate for the before period than had been assumed.

¹Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.
²95-percent confidence level.
³90-percent confidence level.
*Sample size values recommended in this study.

¹Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.
²95-percent confidence level.
³90-percent confidence level.
*Sample size values recommended in this study.

¹Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.
²95-percent confidence level.
³90-percent confidence level.
*Sample size values recommended in this study.

¹Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.
²95-percent confidence level.
³90-percent confidence level.
*Sample size values recommended in this study.

¹Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.
²95-percent confidence level.
³90-percent confidence level.
*Sample size values recommended in this study.

Following the data collection for both the before and after periods, the total mile-years of data available was 90.38 for the before period and 34.36 for the after period in Kentucky. Ohio had 217.01 mi-yr for the before period and 120.99 mi-yr for the after period. The States are reported separately because Ohio had additional statewide safety treatments (e.g., in-curve and advance horizontal curve warning signage) applied at the same time as the ELRS installation. The statistical accuracy attainable for a given sample size is described by the standard deviations of the estimated percent change in safety. From this, one can estimate P-values for various sample sizes and the expected change in safety for a given crash history. A set of such calculations is shown in table 9 for Kentucky and table 10 for Ohio. The calculations were based on methodology in Hauer.⁽³⁶⁾

For the available data, the minimum percentage changes in crash frequency that could be statistically detectable at 5- and 10-percent significance levels were estimated using the same crash rates in table 3. The results indicate that the data should allow detection of the anticipated crash reduction effects highlighted in table 4 through table 8 (i.e., 20-percent reductions for all crash types except for nighttime ROR) in Ohio, if such an effect were present. It might be more difficult to use the Kentucky data to detect the crash reduction effects highlighted in table 4 through table 8. However, as noted previously, the values were conservative because the EB methodology requires fewer sites than a conventional before–after with C-G methodology. Using these results, a decision was made to proceed with the evaluation using the data available at the time.

¹Minimum percent reduction detectable for crash rate assumption. Minimum percent reduction is rounded to nearest 5 percent.
Note: Mile-years in before period = 90.38; mile-years in after period = 34.36.

¹Minimum percent reduction detectable for crash rate assumption. Minimum percent reduction is rounded to nearest 5 percent.
Note: Mile-years in before period = 217.01; mile-years in after period = 120.99.