CE 552 Week 9

Crash statistical approachesIdentification of problem areas - High

crash locations

NCHRP 295

• purpose of its synthesis was to summarize the current practice and research on statistical methods in highway safety analysis, useful for:– establishing relationships between crashes and

associated factors – identifying locations for treatment– evaluating the safety effect of engineering

improvements

– Also useful for driver and vehicle safety analyses

The Empirical Bayes Method for Before and

After Analysis

Key Reference

Hauer, E., D.W. Harwood, F.M. Council, M.S. Griffith, “The Empirical Bayes method for estimating safety: A tutorial.” Transportation Research Record 1784, pp. 126-131. National Academies Press, Washington, D.C.. 2002

http://www.ctre.iastate.edu/educweb/CE552/docs/Bayes_tutor_hauer.pdf

Open This Document and read through as you go along on PPT

Safety

Definition: expected number of crashes, by type and severity

What is expected cannot be knownMust be estimatedPrecision of estimates measured in standard deviation

Need a high frequency at a site to have a precise estimate

The “imprecision” problem …

Assume 100 crashes per year, and 3 years of data, we can reliably estimate the number of crashes per year with (Poisson) standard deviation of about…

However, if there are relatively few crashes per time period (say, 1 crash per 10 years) the estimate varies greatly …

or 5.7% of the mean

or 180% of the mean!

Regression to the mean problem …

High crash locations are chosen for one reason (high number of crashes!)

Even with no treatment, we would expect, on average, for this high crash rate to decrease

This needs to be accounted for, but is often not, e.g., reporting crash rate reductions after treatment by comparing before and after rates over short periods

The Empirical Bayes Approach

Empirical Bayes: an approach to before and after crash studies that attempts to estimate more accurately the real impact of high crash location countermeasuresSimply comparing what occurred before with what happened after is naïve and potentially very inaccurate

The Empirical Bayes Approach

Simple definition:Compares what safety was versus what safety would have been with no change.

Uses that comparison as the basis for making an estimate of the real impact of a change.

Empirical Bayes

Increases precisionReduced RTM biasUses information form the site, plus …Information from other, similar sites

Concept

Mr. Smith had no crashes last year The average of similar drivers is 0.8 crashes

per year What do we expect is the number of crashes

Mr. Smith will have next year … 0?, 0.8? … neither! (pretend you would like to insure Mr. Smith)

Answer … use both pieces of information and weight the expectation

EB applications

IHSDMCHSIM (now Safety Analyst)

EB Procedures

AbridgedLast 2-3 years dataTraffic volume

FullCan use more data Includes other factors

Empirical Bayes Procedure

Actual change or improvement in safety=B-A

Where:B is the estimate of the expected number of crashes that would have occurred in a location in the before time period without a change or safety project

A is the actual number of crashes reported in the after period

Empirical Bayes

Weight should be based on sound logic and real data

Maryland Modern Roundabout Conversion Data (Five Locations 1994)

Empirical Bayes Estimate Of Expected Crashes Without Improvement (B)

Actual After Period Crash Count (A) with treatment

Crash Reduction Estimate

36.71 14 22.71 (62%)

24.63 14 10.63 (43%)

14.38 2 12.38 (86%)

14.33 10 4.33 (30%)

15.16 4 11.16 (74%)

Treatment effects often vary considerably!

The SPF – Safety Performance Function

An example SPF:

So, if ADT = 4000

So what is the expected number of crashes for facilities of this type? Develop a (negative binomial) regression model to fit all the data – must have data to do this!

Note: this SPF depends only on ADT … it needn’t

μ=average crashes/km-yr (or /yr for intersections)

The overdispersion parameter

The negative binomial is a generalized Poisson where the variance is larger than the mean (overdispersed)

The “standard deviation-type” parameter of the negative binomial is the overdispersion parameter φ

variance = η[1+η/(φL)] Where …

μ=average crashes/km-yr (or /yr for intersections) η=μYL (or μY for intersections) = number of crashes/time φ=estimated by the regression (units must be complementary with L, for intersections, L is taken as one)

Example 1:

How many crashes should we have expected last year???

Example 1: road segment, 1 yr. of data

Is this distribution “over” dispersed???

Example 1: computing the weight

What happens when Y is large (compared to μ/φ)? When μ is small compared to φ?

Example 1 (cont):

Example 2:

3 years of data: 12, 7, 8 4000 vpd Step 1: Step 2: Step 3:

Note effect of more data

As before

Example 3: AMFs

1.2 meter shoulders (instead of 1.5) AMF = 1.04 (4% increase in crashes) Step 1: Step 2: Step 3:

Why is weight lower?

Example 4: subsections

Total length = 1.5km, 11 crashes in 2 years

Example 5: Severity

2.41 x 0.019 = 0.046 … 1.8 x 3 x 0.046 = 0.247

Note: φ stays same (mult dist. by constant);

Large for fatals (helps you not to “chase” them

Note: 20.357 ≠ 23.9 (from prob 2) … why? What is an ad hoc solution?

Example 6: intersection

ADT=230

ADT=4520

AMF = 1.277 crashes in 3 years

Step 1:

Step 2:Step 3:

Example 7: group of intersections

11 crashes in 3 years

Step 1: Step 2: (simplistic)

However, not clear what to use

Example 7: (cont)

Example 7: (cont)

Step 3: using w=0.088,

Why so much confidence in the actual number?Is it because we have 3 yrs of data?Is it because 11 is smaller than 20.7?What would happen if 11 had been, say, 32?

The full procedure

Example 8

1.8 km, 9 yrs. Unchanged road ADT varies, AMF = 0.95, 74 total crashes

μ =

Example 8, cont.

(If all μ are equal)

Why so small???

Example 9: Secular Trends

Yearly multipliers can be used like AMFs to account for weather, technology changes (must be able to get them)

Example 10: Projections

Projections can be made by using a simple ratio of ADTs (raised to the appropriate power) multiplied by the corresponding ratio of AMFs or yearly multipliers

Some thought questions

Does EB eliminate RTM as stated? What happened if the SPF is not appropriate for your

site What does appropriate mean?

Software for Homework

You will need some software to develop the NB regression model for your SPF – that is the “R project” program. Investigate that now (see HW).

http://www.r-project.org/ (info on “R”) http://cran.mtu.edu/bin/windows/base/R-2.8.1-

win32.exe (download “R”) R for Windows FAQ

Dr. Souleyrette, May I be excused? My brain is full.

Gary Larson, The Far Side, ©1986