Low Cost Safety Improvements
Pooled Fund Study

Analytical Basics

Dr. Bhagwant Persaud

Overview

• 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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