1. 1 CEE 763 Fall 2011 Topic 4 – Before-After Studies CEE 763

2. 2 CEE 763 Fall 2011 2 BEFORE-AFTER STUDIES  Experiment  Controlled environment  e.g.: Physics, animal science  Observational Study  Cross-Section (e.g., stop vs. yield)  Before-After* Ezra Hauer, “Observational Before-After Studies in Road Safety”, ISBN 0-08-043053-8

3. 3 CEE 763 Fall 2011 3 WHAT IS THE QUESTION  Treatment – a measure implemented at a site for the purpose of achieving safety improvement.  The effectiveness of a treatment is the change in safety performance measures purely due to the treatment.  It is measured by the difference between “what would have been the safety of the site in the ‘after’ period had treatment not been applied” and “what the safety of the site in the ‘after’ period was”.

4. 4 CEE 763 Fall 2011 4 AN EXAMPLE  R.I.D.E. (Reduce Impaired Driving Everywhere) Program

5. 5 CEE 763 Fall 2011 5 FREQUENCY OR RATE? AADT Expected # of Accidents/ year Without Rumble Strip With Rumble Strip A B C  What conclusions would you make by using rate or frequency?

6. 6 CEE 763 Fall 2011 6 TARGET ACCIDENTS  Target accidents – Those accidents the occurrence of which can be materially affected by the treatment.  Case 1 – R.I.D.E:  An enforcement program in Toronto to reduce alcohol- related injury accidents  Target accidents: alcohol-impaired accidents or total accidents?

7. 7 CEE 763 Fall 2011 7 TARGET ACCIDENTS (continued)  Case 2 – Sound-wall effect  The study was to look at whether the construction of sound-walls increased crashes or not.  Target accidents: run-off-the-road accidents or total accidents?

8. 8 CEE 763 Fall 2011 8 TARGET ACCIDENTS (continued)  Case 3 – Right-turn-on-red policy  The study was to look at whether allowing vehicles to make right turns on red increased crashes or not.  Target accidents: accidents that involve at least one right-turn vehicle or total accidents?

9. 9 CEE 763 Fall 2011 9 RIGHT-TURN-ON-RED CASE  Case 3 – Right-turn-on-red policy TargetComparison* Before1673566 After3136121 *Comparison accidents are those that do not involve any right-turn vehicles Right-turnOther*Total Before21922865630848 After28082634429152 *Other accidents are those that do not involve any right-turn vehicles

10. 10 CEE 763 Fall 2011 10 PREDICTION AND ESTIMATION  Prediction – to estimate what would have been the safety of the entity in the ‘after’ period had treatment not been applied.  Many ways to predict.  Estimation – to estimate what the safety of the treated entry in the ‘after’ period was.

11. 11 CEE 763 Fall 2011 11 PREDICTION  One-year before (173)  Three-year before average (184)  Regression (165)  Comparison group (160)

12. 12 CEE 763 Fall 2011 12 FOUR-STEP PROCESS FOR A B-A STUDY  Step 1 – Estimate λ and predict π  λ is the expected number of target accidents in the ‘after’ period  π is what the expected number of target accidents in an ‘after’ period would have been had it not been treated  Step 2 – Estimate VAR{λ} and VAR{π}  Step 3 – Estimate δ and θ  δ is reduction in the expected number of accidents;  θ is safety index of effectiveness  Step 4 – Estimate VAR{δ} and VAR{θ}

13. 13 CEE 763 Fall 2011 13 EQUATIONS

14. 14 CEE 763 Fall 2011 14 EXAMPLE NAÏVE BEFORE-AFTER STUDY  Consider a Naïve B-A study with 173 accidents in the ‘before’ year and 144 accidents in the ‘after’ year. Determine the effectiveness of the treatment.

15. 15 CEE 763 Fall 2011 15 COMPARISON GROUP (C-G) B-A STUDY  Comparison group – a group of sites that did not receive the treatment  Assumptions  Factors affecting safety have changed from “before” to “after” in the same manner for the treatment group and the comparison group  These factors influence both groups in the same way Whatever happened to the subject group (except for the treatment itself) happened exactly the same way to the comparison group

16. 16 CEE 763 Fall 2011 16 EXAMPLE  Where R.I.D.E. was implemented, alcohol-related crash was changed from 173 (before) to 144 (after). Where R.I.D.E. was NOT implemented, alcohol- related crash was changed from 225 (before) to 195 (after). What would be the crash in the after period had R.I.D.E. not been implemented?

17. 17 CEE 763 Fall 2011 17 C-G METHOD Treatment Group Comparison Group BeforeKM AfterLN Odds ratio

18. 18 CEE 763 Fall 2011 18 EQUATIONS

19. 19 CEE 763 Fall 2011 19 EXAMPLE Treatment Group Comparison Group BeforeK=173M=897 AfterL=144N=870  The table shows the accident counts for the R.I.D.E. program at both treatment sites and comparison sites.

20. 20 CEE 763 Fall 2011 20 THE EB METHOD If not giving, use the actual counts K (‘before’ period) to estimate population mean, E{k} Variance if ‘before’ has multiple years Y is the ratio between ‘before’ period and ‘after’ period s 2 is sample variance for the ‘before’ period EB estimate of the expected number of ‘after’ accidents had the treatment not been implemented.

21. 21 CEE 763 Fall 2011 21 EXAMPLE  Accidents recorded at 5 intersections over a two- year period are shown in the table. What is the weighting factor, α for the EB method? SiteAccident 10 23 32 40 51

22. 22 CEE 763 Fall 2011 22 EQUATIONS

23. 23 CEE 763 Fall 2011 23 EXAMPLE Using the EB method to conduct the B-A study based on the information in the table. 1 Site 2 Before 3 After 4K4K 5L5L 6 K(acc/er yr) 7 L (acc/ yr) 8 E{k} - reference sites Acc/yr 9 S 2 [acc/yr] 2 10 VAR{k} [acc/yr] 2 11 α 12 E{k/K} 171-7375-771464.672.000.0920.1510.060.343.10 273-7577-791630.0910.146 371-7375-77186 471-7375-77287 571-7375-77153 672-7476-782810.0910.153 775-7678-79402.000.000.0930.1450.050.471.10 871-7375-77113 975-7678-7962 1072-7476-7862