Quantitative Safety Analysis for
Intersections on Washington State
Two-lane Rural Highways
Master’s Thesis Defense
Ngan Ha Nguyen
8/15/2007
Department of Civil Engineering
University of Washington
Overview
Introduction
 Study Routes and Data
 Methodology
 Data Analysis
 Accident Risk Modeling
 Conclusions and Recommendations

2
Introduction: Traffic Accidents
Traffic accidents are
leading causes of
death
 Huge economic loss
to the society


Improving traffic
safety is an
important task
Average Comprehensive Cost by Injury Severity
Death
$3,840,000
Incapacitating injury
$193,800
Nonincapacitating evident injury
$49,500
Possible injury
$23,600
No injury
$2,200
Leading Causes of U-I Deaths, U.S., 1969-2005
3
Introduction: National Statistics

Rural fatal accident rate is more than twice as high
as urban fatal accident rate
Fatal Crashes in 2003, US.
Total Crashes in 2003, US.
25%
39%
61%
75%
Two-lane rural road
Others
4
Introduction: National Statistics

More than 1 death per hour in accidents at
intersections
Reported Crashes.
Fatal Crashes.
28%
45%
55%
72%
Intersection accidents
Others
5
Introduction: Washington State Stats

4.5% increase in total accidents from 2004 to 2005
Total annual VMT.
Fatal and Disabling Accidents
25%
44%
56%
75%
Two-lane rural highways
Others
6
Introduction: Objective
Analyze causal factors of intersection
accidents
 Identify cost-effective solutions for
intersection safety improvements

7
Overview
Introduction
 Study Routes and Data
 Methodology
 Data Analysis
 Accident Risk Modeling
 Conclusions and Recommendations

8
Study Routes and Data : Collecting

Three sources:




Six years data ( 1999 -2004)





Highway Safety Information System (HSIS)
WSDOT Office of Information Technology
WSDOT online tool, State Route Web (SRWeb)
Roadway data
Accident data
Traffic data
Intersection data
141 state routes
9
Study Routes and Data : preliminary steps
Focus on 3-legged and 4-legged intersections
 Classify manually based on SRWeb.
 Link intersection file to roadway files:





Roadway characteristic file,
Curvature file
Gradient file
Complicated process  not applicable for all
141 state routes  select six representative
study routes
10
Study Routes and Data : six study routes

Two criteria


Route length
Geographic location and spatial alignment
Route
SR-02
SR-12
SR-20
SR-21
SR-97
SR-101
Length (mile)
237.83
268.79
366.03
188.01
234.58
317.86
11
Overview
Introduction
 Study Routes and Data
 Methodology
 Data Analysis
 Accident Risk Modeling
 Conclusions and Recommendations

12
Methodology: Data Organization

Intersection approach section:
Decreasing approach
Increasing approach
Xs
Xs
Increasing milepost direction
13
Methodology: Data Organization

Determining “intersection section” by using
“Stopping Sight Distance” (SSD):
V2
XS  V t 
2d
•V = Approach speed, fps ( feet per
second)
•t = Perception/reaction time ( typically
1 sec)
•d = Constant deceleration rate, fps2
(feet per second square)
•t = 1 sec
•d =10 ft/sec2
14
Methodology: Data Organization
Entity-Relationship
(E/R) Diagram
 Microsoft SQL
Server are used to
manage and query
data

15
Methodology: Hypothesis testing

Test whether a variable has a significant
impact on accident rate


T-test  testing variable has 2 groups
F-test (ANOVA)  testing variable has more than
2 groups
16
Methodology: Modeling

Nature of accident data:




Discrete
Non-negative
Randomly distribute
Poisson model
i  EXP(X i )
•λi is the expected accident frequency
•Xi is a vector of explanatory variables
• β is a vector of estimable coefficient
17
Methodology: Modeling
Over-dispersion problem: mean not equal
variance
 Negative binomial model:

i  EXP(X i   i )
EXP(εi) is a gamma-distributed error term with mean 1 and variance α2

Over-dispersion parameter : select between
Poisson model and negative binomial model
18
Methodology: Modeling

Parameters estimation using log-likelihood
functions:

Poisson model
m
ln L(  )    EXP( X i )  ni xi  ln( ni !)
i 1

Negative binomial model
ni
 ((1 /  )  n )  1 /  1/  



i
i

 
 
L(i )   LN 

(
1
/

)
n
!
(
1
/

)


(
1
/

)



i 1
i
i 
i  



m
•ni: number of accident happened during 6 consecutive study years
•λi:expected accident frequency in 6 years
•: over-dispersion parameter
19
Methodology: Modeling

Goodness of Fit:

The likelihood ratio test statistic is
X 2  2[ LL(  R  LL(  U )]

Sum of model deviances
G 2  2 mi LN (

mi
)
ˆ

i
The ρ-statistic
 2  1
LL(  U )
LL(  R )
20
Overview
Introduction
 Study Routes and Data
 Methodology
 Data Analysis
 Accident Risk Modeling
 Conclusions and Recommendations

21
Data Analysis: Preliminary Analysis
Accident by Type on 6 routes
3%
1%
1%
3%
REAR END
4%
27%
5%
STRIKE AT ANGLE
STRIKE OTHER OBJECT
OVERTURN
ANIMAL/BIRD
7%
STRIKE APPURTENCE
FRONT END
ROADWAY DICH
8%
SIDESWIPES
RANOVER EMBANKMENT
8%
23%
HEAD ON
OTHER
10%
22
Data Analysis: Statistical Analysis t-test
Variable
Control
CurvConsist
Groups
N
Mean
No
Yes
3648
114
2.14
6.191
Not consistent
1200
2.46
2521
1513
2208
3119
2.16
2.423
2.143
2.166
643
2.732
390
1.807
Consistent
Curvy
CurvStraight
Straight
Zero
DiffSW
Greater than
zero
Less than or
equal to 5%
SlopedB
Greater than
5%
Less than or
SlopedE
equal to 5%
3372
2.315
390
1.82
t-value
p-value
Significant
at α=0.05
-4.32
0
YES
1.865
0.062
FAIRLY
1.862
0.063
FAIRLY
-2.458
0.014
FAIRLY
-2.067
0.039
YES
-1.995
0.047
YES
23
Data Analysis: Statistical Analysis t-test
Variable
Groups
No
Yes
No
SlopeVaried
Yes
Less than or
equal to 6
feet
SWA
Greater than
6 feet
SlopeFlat
SWB
N
Mean
3560
202
2848
914
2.321
1.224
2.085
2.817
2302
2.377
1460
2.082
Less than or
equal to 6
feet
2303
2.373
Greater than
6 feet
1459
t-value
p-value
Significant at
α=0.05
3.9
0
YES
-3.322
0.001
YES
2.134
0.033
YES
2.061
0.039
YES
2.088
24
Data Analysis: Statistical Analysis F-test
Variable
Group 1
(A)
Group 2
(B)
Group 3
(C)
Group 4
(D)
Greater
10001500than 3000
1500 feet 3000 feet
feet
Greater
10001500than 3000
1500 feet 3000 feet
feet
Greater
10001500than 3000
1500 feet 3000 feet
feet
N
DOF
3720
3
3720
3
3720
3
Less than
From 2%- Greater
SlopeChange or equal
4%
than 4%
to 2%
3762
2
Less than
Greater
From 30or equal
than 30
50 mph
to 30 mph
mph
3762
2
RadCurvA
0-1000
feet
RadCurvB
0-1000
feet
RadCurvE
0-1000
feet
Splim
25
Data Analysis: Statistical Analysis F-test
5
5
4
4
3
2
1
F-crit
2.606
2.606
2.999
2.999
p-value
0
0
0
0
0
3
2
1
A
B
C
RADCURVA
D
0
A
B
C
RADCURVE
D
Least Squares Means
Least Squares Means
3
4
3
ACCRATE
Fvalue
8.737
4.818
10.067
17.195
ACCRATE
Variable
RadCurvA
RadCurvE
SlopeChange
Splim
Significant
when
α<=0.05
YES
YES
YES
YES
Least Squares Means
ACCRATE
ACCRATE
Least Squares Means
2
2
1
1
0
0
A
B
C
SLOPECHANGE
A
B
SPLIM
C
26
Overview
Introduction
 Study Routes and Data
 Methodology
 Data Analysis
 Accident Risk Modeling
 Conclusions and Recommendations

27
All-type Accident Risk Modeling
Negative binomial model applied
 Over-dispersion parameter is significant
 Model:

i  10 8  (6  365  AADT ) EXP(  X i   i )
28
All-type Accident Risk Modeling

Result:
Estimated Standard
Variable Parameter
error
Constant
0.6
0.154
Control
1.018
0.116
SlopeChange 0.33
0.127
Splim
0.378
0.028
SR12
0.133
0.063
SR20
0.192
0.063
SWA
-0.397
0.092
DegCurvA
0.367
0.058
T4leg
-0.355
0.059
Featillum
0.159
0.062
Alpha
1.267
0.084
t-statistic
3.902
8.745
2.602
13.272
2.115
3.026
-4.307
6.365
-5.997
2.538
15.038
P-value
0.000
0.000
0.005
0.000
0.035
0.003
0.000
0.000
0.000
0.011
0.000
Elasticity
0.64
0.04
1.89
0.12
0.17
-0.2
0.05
-0.43
0.15
-
29
All-type Accident Risk Modeling

Goodness of fit:
Goodness Of Fit
LL(β)
LL(0)
Value
-4394.61
-4547.75
2
0.03
X2
306.29
2
19260.91
ρ
G
30
Strike-At-Angle Accident Risk Modeling
Negative binomial model applied
 Over-dispersion parameter is significant
 Model:

i  10 8  (6  365  AADT ) EXP(  X i   i )
31
Strike-At-Angle Accident Risk Modeling

Result:
Variable
Constant
Control
Splim
SR2
SWA
T4leg
DiffSW
Featillum
WallB
ALPHA
Estimated Standard
Parameter
error
t-statistic
-0.392
0.256
-1.531
1.135
0.168
6.769
0.331
0.049
6.763
-0.616
0.119
-5.187
-0.346
0.162
-2.137
-0.895
0.098
-9.16
0.176
0.114
1.542
0.722
0.109
6.606
1.119
0.506
2.213
0.71
0.09
7.929
P-value
0.000
0.005
0.000
0.035
0.003
0.000
0.000
0.000
0.000
0.000
Elasticity
0.68
1.65
-0.85
-0.18
-1.45
0.16
0.51
0.67
-
32
Strike-At-Angle Accident Risk Modeling

Goodness of fit
Goodness Of Fit
LL(β)
LL(0)
Value
-1769.94
-1893.73
2
0.07
X2
247.59
2
4014.95
ρ
G
33
Overview
Introduction
 Data Processing
 Methodology
 Data Analysis
 Accident Risk Modeling
 Conclusions and Recommendations

34
Conclusions:
1.
2.
3.
4.
5.
6.
Reduce speed limit at the intersection
Put more signage ahead of the intersections
Increase shoulder width (greater than 6 feet)
around the intersection area
Keep the shoulder width consistent along the
intersection sections
Decrease the degree of curvature at the
intersection locations
Decrease the slopes (less than 5%) along the
intersection area
35
Recommendations
Negative binomial model is chosen over
Poisson model for modeling accident
frequency
 Before-and-after studies on safety at
intersections that have traffic control device
or feature illumination installed are needed
 More data:




Crossing roads
Human activity
Detailed intersection layout
36
Ngan Ha Nguyen
nganhanguyen@gmail.com
37