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

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2 CEE 763 Fall 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

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3 CEE 763 Fall 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”.

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

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5 CEE 763 Fall 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?

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6 CEE 763 Fall 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?

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7 CEE 763 Fall 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?

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8 CEE 763 Fall 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?

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9 CEE 763 Fall RIGHT-TURN-ON-RED CASE Case 3 – Right-turn-on-red policy TargetComparison* Before After *Comparison accidents are those that do not involve any right-turn vehicles Right-turnOther*Total Before After *Other accidents are those that do not involve any right-turn vehicles

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10 CEE 763 Fall 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.

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

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12 CEE 763 Fall 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}

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13 CEE 763 Fall EQUATIONS

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14 CEE 763 Fall 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.

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15 CEE 763 Fall 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

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16 CEE 763 Fall 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?

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

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18 CEE 763 Fall EQUATIONS

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19 CEE 763 Fall 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.

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20 CEE 763 Fall 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.

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21 CEE 763 Fall 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

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22 CEE 763 Fall EQUATIONS

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23 CEE 763 Fall 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}

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