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Session 2HistoryHow did SPF come into being and why is it here to stay? Geni Bahar, P.E. NAVIGATS Inc.
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
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
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?
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
25-Period Crash Counts on a Non-Treated Site Poisson-distributed counts- Average of 4.23 crashes/period
California Rural Stop-controlled Untreated Intersections Source: HSIS Data by Dr. Persaud
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 treatmentis most effective Issue 1:Regression to the Mean (RTM)
Introducing Traffic Volumes Traditionally, we use crash rates to take into account the difference in exposure Crash rate = average crash frequency exposure
Crash Rate= Crash/exposure Crash rate depends on the hourly volume (Jean-Louis 2002) Crashes per 108 VkmT Crash rate decreases with increasing traffic volume non-uniformly (Zegeer 1981) Vehicles per hour Crashes per MVM Vehicles per day
Crash Frequency Exact same data – a different graphical presentation (Jean-Louis 2002) Crashes per km-year Vehicles per hour (Zegeer 1981) The relationship between crashes and traffic volumes is NON-LINEAR and it is named Safety Performance Function (SPF) Crashes per mile Vehicles per day
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
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 In Conclusion, We Need an Estimation Method
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
(Observed frequency) * Nobserved (EB Expected frequency) * Nexpected SPF (Predicted frequency) Crashes/year * Npredicted AADT EB Methodology (Similar Facilities)
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
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
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?
Comparison between sites and highway facility types A A’ Crashes/year Vehicles/hour
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)
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
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