Traffic Safety Analysis: Rates, SPFs, and Empirical Bayes
Measuring safety
Crash frequency alone rewards high-volume sites, so analysts also compute crash rates. For a segment, rate per 100 million vehicle-miles = (A × 100,000,000)/VMT; for an intersection, crashes per million entering vehicles (MEV) use total entering volume as exposure. Severity is reported as KABCO (fatal, incapacitating, non-incapacitating, possible injury, property damage only).
The HSM framework
The predictive method multiplies a safety performance function (SPF) by crash modification factors (CMFs) and a local calibration factor. The empirical Bayes method then blends prediction with observation: expected crashes = w × predicted + (1 − w) × observed, with weight w = 1/(1 + k × predicted), where k is the overdispersion parameter.
Traps
- Ranking sites by raw crash count and ignoring exposure and regression to the mean.
- Using a national SPF without calibrating it to local data.
- Multiplying CMFs for treatments that overlap or interact.
- Skipping the EB adjustment in a before-after study, so a natural dip in crashes is credited to the countermeasure.
- Forgetting that minor property-damage-only crashes are underreported, biasing severity comparisons.
Worked example
An SPF predicts 10 crashes/yr; k = 0.4; the site actually recorded 16. Then w = 1/(1 + 0.4 × 10) = 1/5 = 0.20, and the EB estimate is 0.20(10) + 0.80(16) = 2.0 + 12.8 = 14.8 crashes/yr - the site is safer than its raw count suggests.