Safety Evaluation of Centerline Plus Shoulder Rumble Strips

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 a sample required to statistically detect an expected change in safety and also determined what changes in safety can be detected with likely available sample sizes.

Sample Size Estimation Overview

Sample size estimations require assumptions of the expected treatment effect and the average crash rate at treatment sites prior to treatment. Minimum and desired sample sizes were calculated assuming a conventional before-after with comparison group (C-G) study design, as described in Hauer and a literature review of likely safety effects.⁽⁶⁾ 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 are conservative because the more robust EB methodology is 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, run-off-road, head-on plus sideswipe-opposite-direction, and all target crashes (run-off-road plus head-on plus sideswipe-opposite-direction)), as shown in table 3. Intersection-related and animal crashes are not included in these crash rates. These crash rates, which were obtained from preliminary data for the untreated reference group data collected for the EB analysis, represent a range of mean crash rates. Only crash rates from Pennsylvania and Kentucky were used at the time of the sample size analysis. The study design assumed that the number of comparison sites would be equal to the number of treatment sites for a C-G study.

Table 3. Before period crash rate assumptions.

¹Non-injury crash type proportions assumed to be same as Pennsylvania for run-off-road, head-on, and sideswipe-opposite-direction.

Table 4 provides estimates of the required number of before and after period mile-years for statistical significance at both a 90- and 95-percent confidence level for both crash rate assumptions. The minimum sample indicates the level for which a study seems worthwhile; that is, it is feasible to detect with the level of confidence the largest effect that may reasonably be expected based on what is 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 are 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 are available so far for 3 years since implementation, then there are a total of 27 mi-year of after period data available for the study.

Table 4. Minimum required before period mile-years for treated sites.^1,2

¹Assumes equal number of mile-years for treatment and comparison sites and equal length of before and after periods.
²Bold indicates sample size values recommended in this study.

The sample size values recommended in this study are highlighted in bold in table 4. These values are recommended 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 comparison group that had to be assumed for the calculations. Estimates may be predicted with greater confidence or a smaller reduction in crashes will be detectable if there are 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 was assumed.

Following the data collection for both the before and after periods, the total mile-years of data available was 6,392 for the before period and 2,623 for the after period. For the available data, the minimum percentage change in crash frequency that could be statistically detectable at 95- and 90-percent confidence levels was estimated using the same crash rates found in table 3. The calculations are based on methodology in Hauer.⁽⁶⁾ The results, which are shown in table 5, indicate that the data should be able to detect the recommended crash reduction values from table 4, if such an effect were present. Using these results, a decision was made to proceed with the evaluation using the data available at the time.

Table 5. Analysis for crash effects detectable with available sample size.

¹Minimum percent reduction detectable for crash rate assumption. Minimum percent reduction is rounded to nearest 2.5 percent.