Empirical-Bayes Screening of a Four-Lane Undivided Arterial
A 1.10-mi segment of a four-lane undivided suburban arterial (35 mph, 12,500 vpd, 12-ft lanes, no median, curb and gutter, signalized intersections at both ends, 14 unsignalized driveways) recorded 47 reported crashes in five years (2018-2022): 2 fatal, 9 incapacitating, 14 minor injury, 22 property-damage-only. Crash typing shows 16 angle, 9 left-turn-opposing, 8 rear-end, 6 fixed-object, 8 other. A regional safety performance function predicts 5.6 crashes per year for comparable segments with a dispersion parameter k = 0.24. The agency's HSIP screening uses an empirical-Bayes expected frequency and prioritizes sites where the severe-crash proportion exceeds 15 percent.
1. Compute the empirical-Bayes expected crash frequency and the excess over the predicted value, and determine whether the site qualifies for the screening list.
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Observed. 47 crashes in 5 years = 9.4/yr. Severe (fatal + incapacitating) = 11 of 47 = 23.4 percent, against a 15 percent threshold -> the site passes the severity screen.
Predicted over the same period. 5.6/yr x 5 = 28.0 crashes.
Empirical Bayes weighting
- w = 1/(1 + k x sum of predicted) = 1/(1 + 0.24 x 28.0) = 1/7.72 = 0.130
- EB expected (5 yr) = 0.130 x 28.0 + 0.870 x 47 = 3.63 + 40.9 = 44.5
- EB expected = 44.5/5 = 8.9 crashes per year
Excess = 8.9 - 5.6 = 3.3 crashes per year above what comparable segments produce.
Interpretation of w. The weight of 0.13 means the regional model is given very little credence here because the dispersion is high and the observed count is well above the prediction. That is the correct behavior: the EB estimate sits close to the observed count but is pulled measurably toward the model, which is the regression-to-the-mean correction. A site selected because it ranked high in a single period will usually fall back on its own; the EB estimate prices that in and prevents the agency from claiming credit for a drop that would have happened anyway.
Judgment. The site qualifies twice over - high absolute excess frequency and a severe share well above the threshold. Note that 25 of 47 crashes (53 percent) are angle or left-turn-opposing, which is the signature of unmanaged access on an undivided four-lane, and that should steer countermeasure selection.
2. Rank the following countermeasures by cost-effectiveness (crashes prevented per dollar) and state which you would fund first. (a) Raised median with turn bays, CMF 0.70 for all crashes, $1.6M. (b) Consolidate/convert driveways to right-in/right-out, CMF 0.85 for all crashes, $180,000. (c) Convert the two signals to flashing yellow arrow, CMF 0.85 for angle and left-turn crashes only, $60,000.
Read the worked answer
Crashes prevented per year = EB expected x (1 - CMF), applied to the crashes each CMF actually covers.
(c) Flashing yellow arrow - covers angle + left-turn-opposing only, 25/47 = 53 percent of the crash experience, so the affected EB frequency is 8.9 x 0.53 = 4.71/yr. Prevented = 4.71 x 0.15 = 0.71/yr. Cost per crash prevented = 60,000/0.71 = $85,000.
(b) Driveway consolidation / RIRO - all crashes: prevented = 8.9 x 0.15 = 1.34/yr. Cost per crash prevented = 180,000/1.34 = $134,000.
(a) Raised median - all crashes: prevented = 8.9 x 0.30 = 2.67/yr. Cost per crash prevented = 1,600,000/2.67 = $599,000.
Ranking by pure cost-effectiveness: c, then b, then a.
But do not stop there. (c) is cheapest per crash but does not touch the fixed-object and rear-end crashes, and the flashing yellow arrow's benefit depends on the existing phasing being protected-only - verify that before claiming the CMF. (a) prevents the most crashes in absolute terms and is the only measure that removes the left-turn-exposure conflict for the entire 1.10-mi segment, including the 14 driveways the signals do not control.
Judgment. Fund (c) and (b) first from HSIP as a low-cost package, and program (a) as the capital project - but sequence them so the median design incorporates the consolidated driveways. Building a median without consolidating access wastes the design opportunity. Also check the CMF applicability conditions: the 0.70 median CMF generally assumes a reasonable number of openings per mile, which 14 driveways in 1.10 mi does not satisfy.
3. What cautions would you attach to this analysis before the agency commits the funds?
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Statistical and methodological cautions
- Small sample: 47 crashes is enough to rank the site but not enough to detect the effect of a single countermeasure after installation. Do not design an evaluation that expects to demonstrate a 15 percent reduction on 8.9 crashes/yr within two years.
- Reporting effects: 2020-2021 counts include pandemic traffic changes; confirm the five-year window is not dominated by a reporting or volume anomaly, and check whether the state switched crash-reporting thresholds or systems mid-period.
- CMF transferability: every CMF in the ranking carries applicability conditions (traffic volume range, number of lanes, access density, whether the treatment is new or a retrofit). Document the conditions checked, not just the value used.
- Severity weighting: the ranking above is unweighted. Weighting by comprehensive crash cost (a fatal crash is worth roughly 20 to 200 times a PDO crash) may flip the ordering toward whichever measure touches the angle/left-turn crashes - which reinforces (c) and (a) together.
Practical cautions
- Multiple comparisons / site selection bias: the EB method already corrects for regression to the mean, but do not apply the same correction twice or omit it entirely in the final benefit estimate.
- Scope: the corridor is only 1.10 mi with signals at both ends; a median on this segment may simply move the left-turn conflict to the intersections or to the next segment.
- Maintenance of traffic and access impacts: a raised median restricts business access. Expect objections, and budget for a public process before the design is fixed.
Judgment. The countermeasure ranking is robust, but the benefit estimate is not precise enough to support a specific 'crashes reduced per year' commitment in a grant application. Report a range, state the assumptions, and pre-commit to a before/after evaluation with a comparison group rather than a naive comparison.