1. Low Cost Safety Improvements Pooled Fund Study Analytical Basics Dr. Bhagwant Persaud

2. Overview u Analytical basics of observational before- after studies: l Why empirical Bayes (EB)? l Empirical Bayes Approach – Fundamentals l Study design l Interpretation of results

3. Why Empirical Bayes? u Problem with conventional (simple) before- after studies basics of observational before- after studies: l Difficulty of “controlling” for changes in safety due to factors other than the treatment Regression to mean Traffic volume changes

4. Why Empirical Bayes?: Accounting for other changes u Regression to the mean :

5. Why Empirical Bayes: Accounting for other changes u Traffic volume: l Research shows that crashes are not proportional to AADT l Therefore to account for traffic volume changes Cannot simply compare crashes per unit of traffic volume (see next slide) Must use a safety performance function (SPF) that specifies the (non-linear) relationship between crashes and traffic volume

6. Why Empirical Bayes: Accounting for other changes u Need a method that accounts for regression to the mean and non-linear effects of traffic volume changes u Empirical Bayes method does this

7. Empirical Bayes Approach -- Fundamentals u Compares the crash counts in the “after” period to an estimate of what would have occurred in the absence of the treatment (B). u B is a weighted average of the counts in the “before period” and the number of crashes expected to occur at similar sites (P). u P is estimated from a safety performance function (SPF) that links crashes to traffic volumes and site characteristics. u The SPF is calibrated from crash, volume and geometric data from reference sites “similar” to the treatment sites.

8. Study Design u Sample sizes for treatment sites based on: l Crashes/site/year l Expected percent change in crashes in each category l Desired level of significant (confidence) l Minimum sample size l Desired Sample size

9. Interpretation of Results -- Example u Percent reduction = 20 percent with standard error = 11percent u Result is not significant at the 5 percent level (95 percent confidence level) since 20/11 (=1.82) is not larger than 1.96 u Or 95 percent confidence interval of +/- 1.96 standard errors is between -1.6 and 41.6 and includes zero u Result is significant at the 10percent level since 20/11 (=1.82) is larger than 1.64 or since +/- 1.64 standard deviations DOES NOT include zero u 20/11 = 1.82 standard deviations -- >> significant result at the 7 percent level (93 percent confidence level)

10. Questions??