Safety Evaluation of Cable Median Barriers in Combination With Rumble Strips on Divided Roads

CHAPTER 3. STUDY DESIGN

When planning a before–after safety evaluation study, it is vital to ensure that enough data are included to detect the expected change in safety with statistical confidence. Even though those designing the study do not know the expected change in safety in the planning stage, it is still possible to make a rough determination of how many sites are required based on the best available information about the expected change in safety. Alternatively, one could estimate the statistically detectable change in safety for the number of available sites. For a detailed explanation of sample size considerations, as well as estimation methods, see chapter 9 of Hauer.⁽¹⁰⁾ The sample size analysis cases presented in this report address (1) how large a sample would be required to statistically detect an expected change in safety and (2) the change in safety that could be detected with available sample sizes.

Case 1: Sample Size Required to Detect an Expected Change in Safety

For this analysis, the research team assumed that a conventional before–after study with comparison group design would be used because available sample size estimation methods were based on this assumption. The sample size estimates from this method would be conservative in that the EB methodology proposed would likely require fewer sites. To facilitate the analysis, the research team also assumed that the number of comparison sites was equal to the number of treatment sites, which again, was a conservative assumption.

As discussed earlier in the literature review, the crash types that cable median barriers and rumble strips on the inside shoulder would most affect would be cross-median crashes. For the study design, the research team assumed that crashes that were coded as head-on and opposite-direction sideswipe were cross-median. The research team used crash rates from the reference groups for total crashes and injury and fatal crashes; they used crash rates from the treatment group after reducing by 25 percent for cross-median crashes. (The team chose this reduction percentage based on the work by Bahar, which indicated that possible bias due to regression-to-the-mean was not likely to be higher than 25 percent.)⁽¹¹⁾Table 2 provides the crash rate assumptions.

Table 3 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 at which a study would seem to be worthwhile; that is, it would be feasible to detect with the desired level of confidence the largest effect that might reasonably be expected based on what was currently known about the strategy. The research team based these sample size calculations on the methodology in Hauer and on specific assumptions regarding the number of crashes per mile and years of available data.⁽¹⁰⁾ Mile-years are the number of miles of highway on which 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 10-mi segment and data were available so far for 4 years since implementation, then there would be a total of 40 mi-year of after-period data available for the study.

The sample size values recommended in this study are indicated with an asterisk in table 3. 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 were 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 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 was assumed.

Case 2: Change in Safety That Can be Detected With Available Sample Sizes

The standard deviations of the estimated percent change in safety describe the statistical accuracy attainable for a given sample size. From this, one can estimate p-values for various sample sizes and expected change in safety for a given crash history based on the method in Hauer.⁽¹⁰⁾

For the available data in the three States in this evaluation, the research team estimated the minimum percentage changes in crash frequency that could be statistically detectable at 5- and 10-percent significance levels, as shown in table 4. For these calculations, the research team assumed that data would be available until the end of 2012. The results indicated that the data should be able to detect the recommended crash reduction values from table 3 if such an effect were present. Using these results, the authors made a decision to proceed with the evaluation using the data available at that time.