Topic 4

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Topic 4 Before-After Studies CEE 763
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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

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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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AN EXAMPLE

• R.I.D.E. (Reduce Impaired Driving Everywhere)
  Program

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FREQUENCY OR RATE?
Expected of Accidents/ year
C
Without Rumble Strip
B
A
With Rumble Strip
AADT

• What conclusions would you make by using rate or
  frequency?

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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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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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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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RIGHT-TURN-ON-RED CASE

• Case 3 Right-turn-on-red policy

Target Comparison
Before 167 3566
After 313 6121
Comparison accidents are those that do not
involve any right-turn vehicles
Right-turn Other Total
Before 2192 28656 30848
After 2808 26344 29152
Other accidents are those that do not involve
any right-turn vehicles
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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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PREDICTION

• One-year before (173)
• Three-year before average (184)
• Regression (165)
• Comparison group (160)

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FOUR-STEP PROCESS FOR A B-A STUDY

• Step 1 Estimate ? and predict p
• ? is the expected number of target accidents in
  the after period
• p is what the expected number of target accidents
  in an after period would have been had it not
  been treated
• Step 2 Estimate VAR? and VARp
• Step 3 Estimate d and ?
• d is reduction in the expected number of
  accidents
• ? is safety index of effectiveness
• Step 4 Estimate VARd and VAR?

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EQUATIONS
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EXAMPLENAÏVE 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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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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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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C-G METHOD
Treatment Group Comparison Group
Before K M
After L N
Odds ratio
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EQUATIONS
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EXAMPLE

• The table shows the accident counts for the
  R.I.D.E. program at both treatment sites and
  comparison sites.

Treatment Group Comparison Group
Before K173 M897
After L144 N870
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THE EB METHOD
EB estimate of the expected number of after
accidents had the treatment not been implemented.
Y is the ratio between before period and
after period
If not giving, use the actual counts K (before
period) to estimate population mean, Ek
s2 is sample variance for the before period
Variance if before has multiple years
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EXAMPLE

• Accidents recorded at 5 intersections over a
  two-year period are shown in the table. What is
  the weighting factor, a for the EB method?

Site Accident
1 0
2 3
3 2
4 0
5 1
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EQUATIONS
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EXAMPLE

• Using the EB method to conduct the B-A study
  based on the information in the table.

1 Site 2 Before 3 After 4 K 5 L 6 K(acc/er yr) 7 L (acc/ yr) 8 Ek - reference sites Acc/yr 9 S2 acc/yr2 10 VARk acc/yr2 11 a 12 Ek/K
1 71-73 75-77 14 6 4.67 2.00 0.092 0.151 0.06 0.34 3.10
2 73-75 77-79 16 3 0.091 0.146
3 71-73 75-77 18 6
4 71-73 75-77 28 7
5 71-73 75-77 15 3
6 72-74 76-78 28 1 0.091 0.153
7 75-76 78-79 4 0 2.00 0.00 0.093 0.145 0.05 0.47 1.10
8 71-73 75-77 11 3
9 75-76 78-79 6 2
10 72-74 76-78 6 2