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Evaluations of Low Cost Safety Improvements Pooled Fund Study


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Analytical Basics

header image – Picture shows series of three scenarios: a vehicle on a meandering road, safety personnel at work, and a car that is very badly damaged after it appears to have collided into a telephone pole.

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 Percent Change
    256 0 0.25 Large increase
    218 0.33 0.55 67
    54 2.00 1.56 –22
    29 2.67 1.62 –39
  • 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.

Study Design

  • Sample sizes for treatment sites based on:
    • Crashes/site/year
    • 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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