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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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Expected # of Accidents/ year
FREQUENCY OR RATE?
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 alcoholrelated 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 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



  
/[1  VAR { } /  2 ]
 Step 4 – Estimate VAR{δ} and VAR{θ}
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EQUATIONS
  

2
  /[1  VAR{ } /  ]

VAR{ }  VAR{ }  VAR{}
VAR{ }   2[VAR{} / 2  VAR{ } /  2 ] /[1  VAR{ } /  2 ]2
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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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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, alcoholrelated 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
N
rC 
M
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
rT 
K
rC  rT
rC

rT
Odds ratio
  rC K
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EQUATIONS
L
rT  rC 
VAR{  }  L
N
M
  rC K
VAR {  }   2 [
1 1 1

  VAR {  }]
K M N
  


/[1  VAR { } /  2 ]

VAR{ }  VAR{ }  VAR{}
VAR{ }   2[VAR{} / 2  VAR{ } /  2 ] /[1  VAR{ } /  2 ]2
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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
K=173
M=897
After
L=144
N=870
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VAR{  }  0.0055
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THE EB METHOD
E{ k / K }  E( k )  ( 1   )K
EB estimate of the expected number of ‘after’ accidents
had the treatment not been implemented.
s.d.  (1   )  E{k / K}

1
VAR{ k }
1 Y
E{ k }
Y is the ratio between ‘before’ period and ‘after’ period
E{ k }  E{ K }  K
If not giving, use the actual counts K (‘before’ period)
to estimate population mean, E{k}
VAR{ k }  VAR{ K }  E{ k }  s 2  K
VAR{ k }  Y 2 [ s 2  K ]
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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 twoyear period are shown in the table. What is the
weighting factor, α for the EB method?
CEE 763
Site
Accident
1
0
2
3
3
2
4
0
5
1
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EQUATIONS
L
VAR{  }  L
  E{ k / K ]
VAR{  }  ( 1   )  E{ k / K }
  


/[1  VAR { } /  2 ]

VAR{ }  VAR{ }  VAR{}
VAR{ }   2[VAR{} / 2  VAR{ } /  2 ] /[1  VAR{ } /  2 ]2
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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
1
71-73
75-77
14
6
2
73-75
77-79
16
3
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
7
75-76
78-79
4
0
8
71-73
75-77
11
3
9
75-76
78-79
6
2
10
72-74
76-78
6
2
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E{k} - reference sites
S2
Acc/yr
K(acc/er yr) L (acc/ yr)
[acc/yr]2
4.67
2.00
2.00
0.00
0.092
0.151
0.091
0.146
0.091
0.153
0.093
0.145
10
VAR{k}
[acc/yr]2
11
α
12
E{k/K}
0.06
0.34
3.10
0.05
0.47
1.10
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