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CEE 763 Fall 2011
Topic 4 – Before-After Studies
CEE 763
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CEE 763 Fall 20112
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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CEE 763 Fall 20113
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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CEE 763 Fall 20114
AN EXAMPLE
R.I.D.E. (Reduce Impaired Driving Everywhere) Program
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CEE 763 Fall 20115
FREQUENCY OR RATE?
AADT
Without Rumble Strip
With Rumble StripAB
C
What conclusions would you make by using rate or frequency?
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CEE 763 Fall 20116
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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CEE 763 Fall 20117
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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CEE 763 Fall 20118
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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CEE 763 Fall 20119
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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CEE 763 Fall 201110
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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CEE 763 Fall 201111
PREDICTION
One-year before (173)
Three-year before average (184)
Regression (165)
Comparison group (160)
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CEE 763 Fall 201112
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}
]/}{1/[ 2 VAR
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CEE 763 Fall 201113
EQUATIONS
]/}{1/[ 2 VAR
}{}{}{ VARVARVAR
22222 ]/}{1/[]/}{/}{[}{ VARVARVARVAR
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CEE 763 Fall 201114
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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CEE 763 Fall 201115
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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CEE 763 Fall 201116
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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CEE 763 Fall 201117
C-G METHOD
Treatment Group
Comparison Group
Before K M
After L N
M
NrC
KrT
TC rr KrC
T
C
r
r Odds ratio
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CEE 763 Fall 201118
EQUATIONS
L
M
Nrr CT KrC
}]{VARNMK
[}{VAR 1112
L}{VAR
]/}{1/[ 2 VAR
}{}{}{ VARVARVAR
22222 ]/}{1/[]/}{/}{[}{ VARVARVARVAR
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CEE 763 Fall 201119
EXAMPLE
Treatment Group
Comparison Group
Before K=173 M=897
After L=144 N=870
00550.}{VAR
The table shows the accident counts for the R.I.D.E. program at both treatment sites and comparison sites.
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CEE 763 Fall 201120
THE EB METHOD
K)()k(E}K/k{E 1
}k{E}k{VAR
Y
1
1
}/{)1(.. KkEds
K}K{E}k{E If not giving, use the actual counts K (‘before’ period) to estimate population mean, E{k}
Ks}k{E}K{VAR}k{VAR 2
Variance if ‘before’ has multiple years
Y is the ratio between ‘before’ period and ‘after’ period
]Ks[Y}k{VAR 22
s2 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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CEE 763 Fall 201121
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?
Site Accident
1 0
2 3
3 2
4 0
5 1
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CEE 763 Fall 201122
EQUATIONS
L
]K/k{E
L}{VAR
]/}{1/[ 2 VAR
}{}{}{ VARVARVAR
22222 ]/}{1/[]/}{/}{[}{ VARVARVARVAR
}K/k{E)(}{VAR 1
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CEE 763 Fall 201123
EXAMPLE
Using the EB method to conduct the B-A study based on the information in the table.
1Site
2Before
3After
4K
5L
6K(acc/er yr)
7L (acc/ yr)
8E{k} - reference sites
Acc/yr
9S2
[acc/yr]2
10VAR{k}[acc/yr]2
11α
12E{k/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