1. Session 2 History How did SPF come into being and why is it here to stay? Geni Bahar, P.E. NAVIGATS Inc.

2. Outline Overview of two issues – Variability of crash occurrence and regression to the mean (RTM) – Misleading meaning of crash rate Estimation method & safety performance functions (SPFs) Applications References Next steps July 29 and 30, 2009 2

3. Once upon a time... Before-after safety evaluation studies – Based on crash counts before and after the implementation of a treatment – The difference between these counts was considered the safety effect of the given treatment – Example: 3years of data Before: 12 crashes; After: 8 crashes Thus: [(12-8)/12] x 100= 34% decrease in crashes July 29 and 30, 20093

4. And then... We noticed that at similar locations, not treated and with the same before-crash records, also showed a decrease in crashes Question?? Is it true that 34% decrease in crashes is due to the treatment or were there other factors? July 29 and 30, 20094

5. We also noted that... The sites selected and treated had very high crash occurrence The crash occurrence varied greatly; crashes were rare and random Let’s see a few examples July 29 and 30, 20095

6. 25-Period Crash Counts on a Non-Treated Site July 29 and 30, 20096 Poisson-distributed counts- Average of 4.23 crashes/period

7. California Rural Stop-controlled Untreated Intersections 7 Source: HSIS Data by Dr. Persaud July 29 and 30, 2009

8. Issue 1:Regression to the Mean (RTM) Counts above or below will move toward an average value; thus above normal crash counts at a site will be followed by a reduced count even if the site is unchanged Thus, selecting sites for improvement with high number of crashes / a short time periods will indeed – Lead to an over-estimation of the treatment effect – Lead to selecting sites not necessarily the ones that the treatment is most effective 8July 29 and 30, 2009

9. Introducing Traffic Volumes Traditionally, we use crash rates to take into account the difference in exposure Crash rate = average crash frequency exposure July 29 and 30, 20099

10. Crash Rate= Crash/exposure July 29 and 30, 200910 Crashes per 10 8 VkmT Crash rate depends on the hourly volume (Jean-Louis 2002) Vehicles per hour Crash rate decreases with increasing traffic volume non-uniformly (Zegeer 1981) Crashes per MVM Vehicles per day

11. Crash Frequency July 29 and 30, 200911 Vehicles per hour Crashes per km-year (Jean-Louis 2002) The relationship between crashes and traffic volumes is NON- LINEAR and it is named Safety Performance Function (SPF) (Zegeer 1981) Crashes per mile Vehicles per day Exact same data – a different graphical presentation

12. Issue 2: Crash Rate Crash rate is not linear; the SPF is a curve with diminishing slope, not a straight line through the origin Crash rate does not separate the safety effect from change in traffic flow Differences in traffic volumes cannot be accounted for by crash rates July 29 and 30, 200912

13. In Conclusion, We Need an Estimation Method That would account for regression to the mean when: – Selecting sites for treatment – Evaluating the safety effect of treatment That would estimate the safety of a site – With greater precision than direct counts for a short period of time That would incorporate exposure 13July 29 and 30, 2009

14. Methodology Empirical Bayes (EB) method meets these conditions EB in highway safety was studied in- depth for more than 30 years EB uses two “clues” – the historical crash counts of a single site – the average crash estimate of similar sites (same category and same traffic volume) represented by the SPF July 29 and 30, 200914

15. EB Methodology * N predicted Crashes/year AADT * N observed * N expected SPF (Observed frequency) (Predicted frequency) (EB Expected frequency) July 29 and 30, 200915 (Similar Facilities)

16. Safety Performance Function Development “Fits a curve” to observed crash data – Provides equation so y (=crash) value may be predicted from x (=AADT) value – Distinct curves for injury and non-injury The statistical “base” modeling process generates regression parameters and provide a “weight” to correct a RTM bias and increase precision July 29 and 30, 200916

17. Typical SPFs SPFs are available for several facilities and crash severity types – Signalized and stop-controlled intersections – Roundabouts – Two-lane and multi-lane roadways – Freeways – Urban and rural environments SPFs are representative of the jurisdiction data used for their development July 29 and 30, 200917

18. Some Applications What is the expected number and severity of crashes for a site with one year or more years of observed crash data? What is the predicted number and severity of crashes with an increase of traffic volume and/or design or operational change? What is the difference in future crashes after the implementation of either of two optional treatments? July 29 and 30, 200918

19. Comparison between sites and highway facility types July 29 and 30, 200919 Crashes/year Vehicles/hour A A’

20. Some References “Estimating Safety by the Empirical Bayes Method: A Tutorial” by Hauer et al (2002) (in your folder) -”Observational Before-After Studies in Road Safety” by Hauer (1997) “Highway Safety Manual” (2010) July 29 and 30, 200920

21. Where are we now? Preparing data Developing own jurisdictional SPFs Calibrating base SPFs for each jurisdiction using calibration process (HSM Part C) Using own applications and/or national tools such as:IHSDM; SafetyAnalyst, and HSM Developing and deploying training July 29 and 30, 200921

22. Where are we going? EB method will become the standard of professional practice in the estimation of road safety – Estimating the safety of a location – Prioritizing potential sites for improvement – Evaluating safety effects of treatments – Assessing potential safety savings due to site improvements July 29 and 30, 200922

23. Thank you genibahar@navigats.com July 29 and 30, 200923