Evaluations of Low Cost Safety Improvements Pooled Fund Study
PPT version for Printing
Dr. Bhagwant Persaud
- Analytical basics of observational before–after studies:
- Why empirical Bayes (EB)?
- Empirical Bayes Approach – Fundamentals
- Study design
- Interpretation of results
Why Empirical Bayes?
- Problem with conventional (simple) before–after studies basics of observational before–after studies:
- Difficulty of "controlling" for changes in safety due to factors other than the treatment
- Regression to mean
- Traffic volume changes
Why Empirical Bayes?: Accounting for other changes
- Regression to the mean:
Actual data for untreated intersections
|Number of intersections
||Accidents/year/ intersection in 1974–76
||Accidents/intersection in 1977
- Traffic volume:
- Research shows that crashes are not proportional to AADT
- 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
- Need a method that accounts for regression to the mean and non–linear effects of traffic volume changes
- Empirical Bayes method does this
Empirical Bayes Approach –– Fundamentals
- Compares the crash counts in the "after" period to an estimate of what would have occurred in the absence of the treatment (B).
- B is a weighted average of the counts in the "before period" and the number of crashes expected to occur at similar sites (P).
- P is estimated from a safety performance function (SPF) that links crashes to traffic volumes and site characteristics.
- The SPF is calibrated from crash, volume and geometric data from reference sites "similar" to the treatment sites.
- Sample sizes for treatment sites based on:
- Expected percent change in crashes in each category
- Desired level of significant (confidence)
- Minimum sample size
- Desired Sample size
Interpretation of Results –– Example
- Percent reduction = 20 percent with standard error = 11 percent
- Result is not significant at the 5 percent level (95 percent confidence level) since 20/11 (=1.82) is not larger than 1.96
- Or 95 percent confidence interval of +/– 1.96 standard errors is between –1.6 and 41.6 and includes zero
- Result is significant at the 10 percent level since 20/11 (=1.82) is larger than 1.64 or since +/– 1.64 standard deviations DOES NOT include zero
- 20/11 = 1.82 standard deviations – – >> significant result at the 7 percent level (93 percent confidence level)
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