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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
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)
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
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
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
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.
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.
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.
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
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?
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
Introduction Results Conclusions Background Restraints Study DesignMethods
Study Area
All observations within each site share same latitude and longitude coordinates.
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
Introduction Results Conclusions GLMM PROC GLIMMIXSpatial CovarianceMethods
Spatial CorrelationResidual mean based on fitted GLM without consideration of
urban/rural covariate
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
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
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
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;
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
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
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
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
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.
Introduction Methods Results Conclusions
Acknowledgement
• Dr. Joseph Cavanaugh• John Lundell• Lucas Bohnett• Jing Xu• All others who have helped this project
Introduction Methods Results Conclusions
Thank you!!
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%)
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
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
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
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
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
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
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
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
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
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%)
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
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
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
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
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.
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