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Introduction Results ConclusionsMethods
A Spatial Analysis of the Iowa Child Passenger Safety Survey
Based on Generalized Linear Mixed Models
Presented by Zunqiu Chen
Advisor: Dr. CavanaughDepartment of Biostatistics
University of Iowa
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Introduction Results Conclusions Background Restraints Study DesignMethods
Child Passenger Safety
• According to statistics from the National SAFE KIDS Coalition, motor vehicle crashes are the leading cause of death in the United States among children from 1 to 14 years of age. (CDC, 2006)
• During 2006, 32 children under age 11 were killed in Iowa traffic crashes. (Iowa Department of Public Safety, 2007)
• 40-60 young children are seriously injured in Iowa vehicle crashes each year. (Iowa Department of Public Safety, 2007)
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Introduction Results Conclusions Background Restraints Study DesignMethods
• Child safety seats reduce the risk of death by 71% for infants, and by 54% for toddlers age 1 to 4 years. (National Highway Traffic Safety Administration, 2005)
• For children age 4 to 7 years, booster seats reduce injury risk by 59% compared to seat belts alone. (Durbin et al., 2003)
• The proper use of child safety seats, booster seats, and seat belts is the best protection we have to keep children safe.
Importance of Safety Protection
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Introduction Results Conclusions Background Restraints Study DesignMethods
• In 2001, the National SAFE KIDS Coalition graded each state’s child restraint laws. Iowa received an "F", ranking 46 out of 51 (50 states and the District of Columbia).
• In July of 2004, the Iowa child passenger restraint law was strengthened.
Iowa History
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Introduction Results Conclusions Background Restraints Study DesignMethods
Proper Child Safety Seat Use Chart(Buckle everyone. Children age 10 and under in back!)
INFANTS TODDLERSYOUNG
CHILDREN
AGE birth to 1 year age 2-5 years Age 6-10 years
TYPE of SEAT
rear-facing safety seatsafety seat/booster seat
booster seat/ seat belt
SEAT POSITION
rear-facing only forward-facing forward-facing
Using a restraint is not the same as using a restraint properly.
Proper Restraint
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Introduction Results Conclusions Background Restraints Study DesignMethods
Rear-Facing Safety Seat
From 0-1 year old, child should be put in a rear-facing safety seat.
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Introduction Results Conclusions Background Restraints Study DesignMethods
Front-Facing Safety Seat
From 2- 5 years old, child should be put in a safety seat or a booster seat.
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Introduction Results Conclusions Background Restraints Study DesignMethods
Booster Seat / Seat Belt
From 6 – 10 years old, child should be put in a booster seat and/or restrained with a seat belt.
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Introduction Results Conclusions Background Restraints Study DesignMethods
Proper Restraint vs. Restraint
Proper Restraint Use by Age Level Restraint Use by Age Level
0-1 2-5 6-100%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
96.57%
70.73%79.47%
3.43%
29.27%20.53%
Not Properly Restrained Properly Restrained
0-1 2-5 6-100%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
98.89%90.01%
79.47%
1.11%
9.99%20.53%
Not Restrained Restrained
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Introduction Results Conclusions Background Restraints Study DesignMethods
Purpose of Investigation
• Investigate if spatial correlation exists among the pattern of proper restraint use.
• Discover the factors that influence proper restraint use.
• Evaluate compliance with the new regulation by comparing the results of years 2005, 2006, and 2007.– Is there any improvement?
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Introduction Results Conclusions Background Restraints Study DesignMethods
Study Design
• Conducted by University of Iowa Injury Prevention Research Center. (UI-IPRC)
• Based on collecting samples from 36 Iowan communities (sites).– Site population sizes from 1,000 to 200,000;
classified by four levels.
Population level Category
1,000-2,499 Rural
2,500-9,999 Town
10,000-49,999 Suburban
50,000+ Urban
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Introduction Results Conclusions Background Restraints Study DesignMethods
Study Area
All observations within each site share same latitude and longitude coordinates.
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Introduction Results Conclusions Background Restraints Study DesignMethods
Data Structure
Driver Belted No Yes
Urban/Rural Rural Town Suburban Urban
Year 2005 2006 2007
Vehicle Type Small Medium Large
9093 observations in 2005-2007 survey
Variables collected and used in survey analysis
Age Level 1: ≤1 2: 2-5 1: ≤1 2: 2-5 3: 6-10
Restraint TypeNot rear facing
SSBelted
Rear facing
SS
SSBooster
Belted
Proper Restraint Use No Yes
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Introduction Results Conclusions GLMM PROC GLIMMIXSpatial CovarianceMethods
Spatial CorrelationResidual mean based on fitted GLM without consideration of
urban/rural covariate
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Introduction Results Conclusions GLMM PROC GLIMMIXSpatial CovarianceMethods
Generalized Linear Mixed Model
– Distribution: Bernoulli (Binary)• Proper restraint use
– Link: Logit– Fixed effects:
• Control for Driver belted, Age level, Year, Vehicle type
– Random effect:• Site location
GLMM model ( | ) by
Link function: = ( )
E y
g X Z
var( ) 'Z Z
• Modeling for this analysis
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Introduction Results Conclusions GLMM Spatial CovarianceMethods PROC GLIMMIX
Random Effect Covariance
• Spatial random effect will be considered in our model– account for between site correlation
• Covariance assumption– Isotropic exponential spatial covariance structure is
assumed.– First law of cognitive geography: closer sites tend to be more
similar. The covariance between two observations is:
The covariance decreases with the increase of the Euclidean distance between two observations:
2
1
k
ij i j mi mjm
d c c c c
ijd
2ij where exp ij
ij
d
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Introduction Results Conclusions GLMM Spatial CovarianceMethods PROC GLIMMIX
Spatial Variance-Covariance Structure
2 2 2 2 2 2 2 2 212 12 12 13 13 13
2 2 2 2 2 2 2 2 212 12 12 13 13 13
2 2 2 2 2 2 2 2 212 12 12 13 13 13
2 2 2 2 221 21 21
2 2 2 221 21 21
2 2 2 221 21 21
2 2 2 223 23 23
2 2 2 2 223 23 23
2 2 2 2 223 23 23
2 2 2
2 2 2
2 2 2
Site 1
Site 2
Site 3
Site 1 Site 2 Site 3
var( ) 'Z Z
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Introduction Results Conclusions GLMM Spatial CovarianceMethods PROC GLIMMIX
GLMM Structure and GLIMMIX Code
| ~ ,
GLMM: |
y dist R
g y X Z
proc glimmix; class variables; model <resp>=<fixed effects> / dist= link= ; random <random effects> / <options>;run;
Type=sp(exp) (lat long) V=1;
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Introduction Results ConclusionsMethods
Random Effect
• Euclidean distance is calculated using latitude and longitude.
• Covariance parameter estimates:
• The effective range is the distance beyond which the correlations fall below 0.05. It is estimated by:
2ˆ 0.09574 ˆ 0.2621
ˆ3 0.7863
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Introduction Results ConclusionsMethods
Random EffectThe output suggests spatial correlation exists between sites within a certain distance. For example:
2 20.36; =0.249; exp 0.024ijij ij ij
dd
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Introduction Results ConclusionsMethods
Fixed EffectsSignificant odds ratios:
Variables Category Odds Ratios
Driver belted No to yes 0.107
Age level Less than 1 to 6-10 7.78
2-5 to 6-10 0.497
Vehicle size Large to small 3.119
Middle to small 1.503
Year 2005 to 2007 0.464
2006 to 2007 0.675
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Introduction Results ConclusionsMethods
Comparison Among 2005, 2006, and 2007 Surveys
The data shows progress in increasing the proper restraint use for child passengers.
2005 2006 200760%
65%
70%
75%
80%
85%
0.710724827812398
0.782853359814631
0.832558139534884
Properly restrained percentage
Properly restrained
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Introduction Results ConclusionsMethods
Conclusions• Spatial correlation/clustering pattern does exist in the
data.
• Cautious drivers pay more attention to the safety of their child passengers.
• Drivers are more careful with the youngest children.• Drivers ignore or don’t fully understand what is proper
restraint use for children age 2 to 5 years.• Vehicle type is a potential risk factor.
• There is a statistically significant improvement in proper restraint use from 2005 to 2007.
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Introduction Methods Results Conclusions
Acknowledgement
• Dr. Joseph Cavanaugh• John Lundell• Lucas Bohnett• Jing Xu• All others who have helped this project
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Introduction Methods Results Conclusions
Thank you!!
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Introduction Methods Results Conclusions
Proper Use of Restraint Devices (2005-2007)
Y2005-Y2007Restraint
Device
Properly Restraint (No/Yes/Total)
Age levelsTotal
Age 0-1 Age 2-5 Age 6-10
Propriety Propriety Propriety
No Yes Total No Yes Total No Yes Total No Yes Total
Belted 0 0 0 766 0 766 0 2936 2936 766 2936 3702
Booster 6 0 6 0 1220 1220 0 311 311 6 1531 1537
CSS 17 957 974 0 1591 1591 0 23 23 17 2571 2588
No 11 0 11 397 0 397 845 0 845 1253 0 1253
Total /Missing 34 957
991/2
227 28113974/
2845 3270
4115/ 9
2042 70389080/
13
Two major sources of inappropriate restraints• Use of safety belt on children between age 2 and 5 (766/2042 =
37.5%)• Not using safety belt (1253/2042 = 61.36%)
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Introduction Methods Results Conclusions
Driver belted: yes Driver belted: no0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
83.97%
36.67%
16.03%
63.33%
Not properly restained
Properly restrained
Proper Restraint vs. Driver Belted Status
AssociationX2 = 1363.26d. f. = 2p-value < .0001
Year 2005-2007
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Introduction Methods Results Conclusions
0-1 2-5 6-100%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
96.57%
70.73%79.47%
3.43%
29.27%20.53%
Not Properly Restrained
Properly Restrained
Proper Restraint Use by Age Level
Year 2005-2007
AssociationX2 = 320.189d. f. = 2p-value < .0001
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Introduction Methods Results Conclusions
Restraint Use by Age Level
0-1 2-5 6-100%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
98.89%90.01%
79.47%
1.11%9.99%
20.53% Not re-straint
Age_level
AssociationX2 = 339.56d. f. = 2p-value < .0001
Year 2005-2007
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Introduction Methods Results Conclusions
Small Midum Large0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
57.78%71.19%
85.38%
42.22%28.81%
14.62% Not Properly Restrained
Properly Restrained
Proper Restraint Use by Vehicle Type
AssociationX2 = 334.64.07d. f. = 2p-value < .0001
Year 2005-2007
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Introduction Methods Results Conclusions
Rural Town SubUrban Urban0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
72.98% 78.09% 75.73% 80.71%
27.02% 21.91% 24.27% 19.29% Not Properly RestrainedProperly Restrained
Proper Restraint Use by Urban/Rural
AssociationX2 = 45.15d. f. = 3p-value < .0001
Year 2005-2007
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Introduction Methods Results Conclusions
Rural areas Small town core Larger town core Metro_area high commuting
Metro_area core0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
79.62%70.72%
76.32% 78.07% 80.98%
20.38%29.28%
23.68% 21.93% 19.02%
Not Properly Restrained
Properly Restrained
Proper Restraint Use by RUCA
Higher usage in heavier traffic areas except rural areas
AssociationX2 = 73.73d. f. = 4p-value < .0001
Year 2005-2007
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Introduction Methods Results Conclusions
Population Classification by RUCAYear 2005-2007
RUCA
Col Pct Rural areas Small town core Larger town coreMetro_area
high commuting Metro_area core Total
Rural 749 301 600 0 150 1800
29.27 15.98 36.43 0 5.71
Town 452 683 0 0 674 1809
17.66 36.25 0 0 25.65
SubUrban 593 900 300 0 300 2093
23.17 47.77 18.21 0 11.42
Urban 765 0 747 375 1504 3391
29.89 0 45.36 100 57.23
Total 2559 1884 1647 375 2628 9093
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Introduction Methods Results Conclusions
Proper Use of Restraint Devices (2005)
Two major sources of inappropriate restraintsUse of safety belt on children between age 2 and 5 (331/882 = 37.5%)Not using safety belt (549/882 = 62.2%)
Y2005Restraint
Device
Properly Restraint (No/Yes/Total)
Age levelsTotal
Age 0-1 Age 2-5 Age 6-10
Propriety Propriety Propriety
NoYes
Total
No Yes Total No Yes Total No Yes Total
Belted 0 0 0 331 0 331 0 903 903 331 903 1234
Booster 1 0 1 0 274 274 0 52 52 1 326 327
CSS 1329
330 0 602 602 0 7 7 1 938 939
No 3 0 3 225 0 225 321 0 321 549 0 549
Total /Missing
5329
334/1
556 8761432/
1321 962
1283/ 4
882 21673049/
6
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Introduction Methods Results Conclusions
Proper Use of Restraint Devices (2006)Two major sources of inappropriate restraintsUse of safety belt on children between age 1 and 5 (265/656 = 40.4%)Not using safety belt (381/656 = 58.1%)
Y2006Restraint
Device
Properly Restraint (No/Yes/Total)
Age levelsTotal
Age 0-1 Age 2-5 Age 6-10
Propriety Propriety Propriety
No Yes Total No Yes Total No Yes Total No Yes Total
Belted 0 0 0 265 0 265 0 1042 1042 265 1042 1307
Booster 4 0 4 0 564 564 0 106 106 4 670 674
CSS 6 249 255 0 401 401 0 3 3 6 653 659
No 5 0 5 115 0 115 261 0 261 381 0 381
Total /Missing 15 249 264 380 965
1345/1
261 11511412/
4656 2365
3021/5
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Introduction Methods Results Conclusions
Proper Use of Restraint Devices (2007)
Y2007Restraint
Device
Properly Restraint (No/Yes/Total)
Age levelsTotal
Age 0-1 Age 2-5 Age 6-10
Propriety Propriety Propriety
No Yes Total No Yes Total No Yes Total No Yes Total
Belted 0 0 0 170 0 170 0 991 991 170 991 1161
Booster 1 0 1 0 382 382 0 153 153 1 535 536
CSS 10 379 389 0 588 588 0 13 13 10 980 990
No 3 0 3 57 0 57 263 0 263 323 0 323
Total /Missing 14 379
393/1
227 970 1197 263 11571420/
1504 2506
3010/2
Two major sources of inappropriate restraintsUse of safety belt on children between age 1 and 5 (170/504 = 33.7%)Not using safety belt (323/504 = 64.1%)
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Introduction Methods Results Conclusions
Generalized Linear Mixed Model
• General Model considerations– A Model is a description of the components of an
observation
• observation = systematic + random• Alternative: random = design components +
remaining variation• “All models are wrong but some are useful” –
G.E.P Box
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Introduction Results Conclusions GLMM Spatial CovarianceMethods PROC GLIMMIX
Variance-Covariance Structure
2 2 2 2 2 21 12 12 12
2 2 2 2 2 22 12 12 12
2 2 2 2 2 23 12 12 12
2 2 2 2 2 221 21 21 4
2 2 2 2 2 221 21 21 5
2 2 2 2 2 221 21 21 6
( )
( )
( )
( )
( )
( )
v
v
v
v
v
v
Site 1
Site 2
Site 1 Site 2
( ) var( ) ' ; iVar y Z Z R R diag v
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Introduction Methods Results Conclusions
GLMM Estimation
1 12 2
12
GLMM is model of ( | )
Link form: ( | )
Inverse link form: ( | ) = ( )
More general expression of distribution of |
|
( ) is "working correlation matrix"
E
i
E y u
g E y u X Zu
E y u h X Zu
y u
Var y u R R AR
R diag V A
stimation: as with LMM, may choose to focus on
1. only GLS equations in LMM;
Generalized Estimating Equations with GLMM
2. and several approachesu
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Introduction Methods Results Conclusions
Pickup Pickup club cab
Car SUV Van0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
57.78%73.06% 70.90%
83.23% 86.58%
42.22%26.94% 29.10%
16.77% 13.42% Not Properly RestrainedProperly Restrained
Proper Restraint Use by Vehicle Type
Year 2005-2007
AssociationX2 = 342.46d. f. = 4p-value < .0001
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Introduction Methods Results Conclusions
Limitation of the survey data and future considerations
• Multiple children in one vehicle may introduce correlation
• There appears spatial correlation and clustering in directional pattern. More sophisticated spatial analysis method could be involved to investigated the direction clustering pattern -- Kriging.
• we clearly need to increase our efforts to educate parents about what is the proper restraint device, especially for young children age from 2 to 5.
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Introduction Methods Results Conclusions
References
• CDC. Web-based Injury Statistics Query and Reporting System [online]. (). National Center for Injury Prevention and Control, Centers for Disease Control and Prevention (producer). Available from URL: www.cdc.gov/ncipc/wisqars. [2006 Dec 8].
• Department of Transportation (US), National Highway Traffic Safety Administration (NHTSA), Traffic Safety Facts 2005: Children. Washington (DC): NHTSA; 2006. Available from URL: http://www-nrd.nhtsa.dot.gov/pdf/nrd-30/NCSA/TSF2005/810618.pdf.
• Durbin DR, Elliott MR, Winston FK. Belt-positioning booster seats and reduction in risk of injury among children in vehicle crashes. JAMA 2003;289(14):2835–40.
• Iowa Department of Public Safety , Child Restraint Fact Sheet http://www.dps.state.ia.us/commis/gtsb/fact-2childrestraint.pdf