Introduction Results DiscussionMethods
An Analysis of the
Iowa Child Passenger Safety Survey
Based on
Generalized Linear M...
Introduction Results Discussion Background Restraints Study DesignMethods
Children and Motor Vehicle Accidents
• According...
Introduction Results Discussion Background Restraints Study DesignMethods
• Child safety seats reduce the risk of death by...
Introduction Results Discussion Background Restraints Study DesignMethods
• In 2001, the National Safe Kids Coalition grad...
Introduction Results Discussion Background Restraints Study DesignMethods
• To measure compliance with the law and to dire...
Introduction Results Discussion Background Restraints Study DesignMethods
• In 2004, the IPRC redesigned the survey in
con...
Introduction Results Discussion Background Restraints Study DesignMethods
• The new data collection protocol requires the ...
Introduction Results Discussion Background Restraints Study DesignMethods
Iowa Law
Requirements of the current Iowa law:
...
Introduction Results Discussion Background Restraints Study DesignMethods
Rear-Facing Safety Seat
From birth up to 1 year ...
Introduction Results Discussion Background Restraints Study DesignMethods
Front-Facing Safety Seat
From 1 through 5 years ...
Introduction Results Discussion Background Restraints Study DesignMethods
Booster Seat / Seat Belt
From 6 through 10 years...
Introduction Results Discussion Background Restraints Study DesignMethods
• Two major problems with restraint use:
 Many ...
Introduction Results Discussion Background Restraints Study DesignMethods
Use of Restraint Devices (2005-2007)
Device
Prop...
Introduction Results Discussion Background Restraints Study DesignMethods
Sampling for IPRC Study
• The survey data is com...
Introduction Results Discussion Background Restraints Study DesignMethods
Sampling for IPRC Study
Population Range Categor...
Introduction Results Discussion Background Restraints Study DesignMethods
IPRC Study Sites
Map of Study Sites
Introduction Results Discussion Background Restraints Study DesignMethods
Data Structure
Response variable: proper restrai...
Introduction Results Discussion Background Restraints Study DesignMethods
Data Structure
Variable Variable Type Levels
Age...
Introduction Results Discussion GLMM PROC GLIMMIXSpatial CovarianceMethods
Data Structure and Model
• We model the respons...
Introduction Results Discussion GLMM PROC GLIMMIXSpatial CovarianceMethods
Spatial Correlation
Residual mean based on fitt...
Introduction Results Discussion GLMM PROC GLIMMIXSpatial CovarianceMethods
GLMM Structure
 Distribution: Binomial
• Respo...
Introduction Results Discussion GLMM Spatial CovarianceMethods PROC GLIMMIX
Random Effect Covariance
• The random effect i...
Introduction Results Discussion GLMM Spatial CovarianceMethods PROC GLIMMIX
Spatial Variance-Covariance Structure
2 2 2 2 ...
Introduction Results Discussion GLMM Spatial CovarianceMethods PROC GLIMMIX
GLMM Structure and GLIMMIX Code
 
| ~ Binomi...
Introduction Results DiscussionMethods Random Effect Fixed Effects
Spatial Random Effect
• Euclidean distance is calculate...
Introduction Results DiscussionMethods Random Effect Fixed Effects
Spatial Random Effect
The output suggests that a minor ...
Introduction Results Discussion Random Effect Fixed EffectsMethods
The data shows an increase in the use of proper
restrai...
Introduction Results Discussion Random Effect Fixed EffectsMethods
96.57%
70.73%
79.47%
3.43%
29.27%
20.53%
0%
10%
20%
30%...
Introduction Results Discussion Random Effect Fixed EffectsMethods
Proper Restraint Use vs. Driver Belted Status
2005-2007...
Introduction Results Discussion Random Effect Fixed EffectsMethods
72.98%
78.09% 75.73% 80.71%
27.02%
21.91% 24.27% 19.29%...
Introduction Results Discussion Random Effect Fixed EffectsMethods
57.78%
71.19%
85.38%
42.22%
28.81%
14.62%
0%
10%
20%
30...
Introduction Results Discussion Random Effect Fixed EffectsMethods
Fixed Effects Estimates from GLMM Fit
Variables Categor...
Introduction Results DiscussionMethods
Conclusions
• The data exhibits some degree of spatial correlation.
• In the multiv...
Introduction Results DiscussionMethods
Conclusions
• Drivers are most cautious with infants (age 0 to 1).
 The odds of an...
Introduction Results DiscussionMethods
Conclusions
• Drivers who are belted are more likely to use proper
restraints for t...
Introduction Results DiscussionMethods
Limitations
• Within-vehicle correlations, which could not be
modeled due to the li...
Introduction Methods Results Discussion
Acknowledgements
• John Lundell
• Eric Chen
• Jing Xu
Introduction Methods Results Discussion
Thank you!
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A Spatial Analysis of the Iowa Child Passenger Safety Survey Based ...

  1. 1. Introduction Results DiscussionMethods An Analysis of the Iowa Child Passenger Safety Survey Based on Generalized Linear Mixed Models Joseph Cavanaugh and Eric Chen Department of Biostatistics The University of Iowa New York State Psychiatric Institute Columbia University February 26, 2009
  2. 2. Introduction Results Discussion Background Restraints Study DesignMethods Children and Motor Vehicle Accidents • According to the National Safe Kids Coalition, motor vehicle accidents are the leading cause of death in the United States among children from 3 to 14 years of age. • In Iowa, approximately 40 children each year are killed in motor vehicle accidents, one every 9 days. (Iowa Department of Public Safety, 2004)
  3. 3. Introduction Results Discussion Background Restraints Study DesignMethods • Child safety seats reduce the risk of death by 71% for infants, and by 54% for children aged 1 to 4 years. (National Highway Traffic Safety Administration, 2005) • For children aged 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 available to keep children safe in motor vehicles. Children and Motor Vehicle Accidents
  4. 4. Introduction Results Discussion Background Restraints Study DesignMethods • In 2001, the National Safe Kids Coalition graded each state’s child restraint law. Iowa received an "F", ranking 46 out of 51 (50 states and the District of Columbia). • In July of 2004, Iowa’s Child Restraint Law was strengthened based on recommendations from the National Highway Traffic Safety Administration and the American Academy of Pediatrics. • The revised law included an 18-month education phase prior to full enforcement of the new requirements. Iowa History
  5. 5. Introduction Results Discussion Background Restraints Study DesignMethods • To measure compliance with the law and to direct educational efforts, observational restraint usage surveys have been conducted annually since 1988. • These child passenger safety surveys are funded by the Governor’s Traffic Safety Bureau (GTSB). • The GTSB has contracted with the University of Iowa Injury Prevention Research Center (IPRC) to conduct the surveys since 1996. Iowa History
  6. 6. Introduction Results Discussion Background Restraints Study DesignMethods • In 2004, the IPRC redesigned the survey in conjunction with the implementation of the new law. • The sampled communities, and targeted sample sizes within these communities, were selected so that the sample would resemble the state population in terms of its rural and urban composition. • The annual targeted sample size was set at 3,000. • The data is collected by three trained surveyors. IRPC Child Passenger Safety Survey
  7. 7. Introduction Results Discussion Background Restraints Study DesignMethods • The new data collection protocol requires the surveyor to approach the driver in the parking lot of a convenience store and to ask for his/her participation.  A card is given to the driver explaining the study.  The driver is asked the age of each child.  The restraint status of each child is directly observed.  The restraint status of the driver (belted / not belted) and the vehicle type (truck, car, van, SUV) are also recorded.  No identifying information (e.g., names, license plate numbers) is collected. • An annual report summarizing the survey results is presented to the Iowa state legislature. IPRC Child Passenger Safety Survey
  8. 8. Introduction Results Discussion Background Restraints Study DesignMethods Iowa Law Requirements of the current Iowa law:  Children must ride in an appropriate rear- facing child safety seat until one year of age and at least 20 pounds.  Children must ride in a child safety seat or a booster seat through the age of 5 years.  Children ages 6 through 10 must ride in a booster seat or use a seat belt.
  9. 9. Introduction Results Discussion Background Restraints Study DesignMethods Rear-Facing Safety Seat From birth up to 1 year old, the child should be put in a rear-facing safety seat.
  10. 10. Introduction Results Discussion Background Restraints Study DesignMethods Front-Facing Safety Seat From 1 through 5 years old, the child should be put in a safety seat or a booster seat.
  11. 11. Introduction Results Discussion Background Restraints Study DesignMethods Booster Seat / Seat Belt From 6 through 10 years old, the child should be put in a booster seat or restrained with a seat belt.
  12. 12. Introduction Results Discussion Background Restraints Study DesignMethods • Two major problems with restraint use:  Many children are unrestrained, especially children from 6 through 10 years old.  Many toddlers (1 through 5 years old) are restrained with a seat belt as opposed to a booster or safety seat. Problems with Restraint Use
  13. 13. Introduction Results Discussion Background Restraints Study DesignMethods Use of Restraint Devices (2005-2007) Device Properly Restrained (No/Yes/Total) Age Levels Total Age 0 to 1 Age 1 through 5 Age 6 through 10 Compliant Compliant Compliant 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 None 11 0 11 397 0 397 845 0 845 1253 0 1253 Total 34 957 991 1163 2811 3974 845 3270 4115 2042 7038 9080 Of the 2042 improperly restrained children, • 37.5% (766/2042) were children from 1 through 5 years old who were wearing a safety belt, • 61.4% (1253/2042) were unrestrained.
  14. 14. Introduction Results Discussion Background Restraints Study DesignMethods Sampling for IPRC Study • The survey data is compiled by collecting samples from 36 Iowan communities or sites. • The sampled sites, and targeted sample sizes within these sites, were selected so that the sample would resemble the distribution of the state population over four urban / rural strata. Population Range Category Iowa Population 1,000-2,499 Rural 21% 2,500-9,999 Town 21% 10,000-49,999 Suburban 23% 50,000+ Urban 35%
  15. 15. Introduction Results Discussion Background Restraints Study DesignMethods Sampling for IPRC Study Population Range Category Number of Sampled Sites Targeted Sample Size 1,000-2,499 Rural 12 50 2,500-9,999 Town 8 75 10,000-49,999 Suburban 7 100 50,000+ Urban 9 125
  16. 16. Introduction Results Discussion Background Restraints Study DesignMethods IPRC Study Sites Map of Study Sites
  17. 17. Introduction Results Discussion Background Restraints Study DesignMethods Data Structure Response variable: proper restraint use (binary) Age 0 up to 1 infant 1 through 5 toddler 6 through 10 young child Restraint Type Rear- facing CSS CSS Booster Belted Proper Restraint Use Yes
  18. 18. Introduction Results Discussion Background Restraints Study DesignMethods Data Structure Variable Variable Type Levels Age Ordinal Infant (0 to 1 year), Toddler (1 through 5 years), Young Child (6 through 10 years) Driver Belted Binary No, Yes Urban / Rural Ordinal Rural, Town, Suburban, Urban Vehicle Size Ordinal Small, Medium, Large Year Ordinal 2005, 2006, 2007 Independent variables
  19. 19. Introduction Results Discussion GLMM PROC GLIMMIXSpatial CovarianceMethods Data Structure and Model • We model the response variable as a function of the explanatory variables using the framework of generalized linear mixed models (GLMM). • Our model is formulated to account for two sources of correlation.  Correlation among responses collected within the same site.  Spatial correlation between sites based on the proximity between the sites. • An important source of correlation that could not be modeled (since the data was not collected) is the correlation among responses collected within the same vehicle.
  20. 20. Introduction Results Discussion GLMM PROC GLIMMIXSpatial CovarianceMethods Spatial Correlation Residual mean based on fitted generalized linear model (without inclusion of urban/rural covariate)
  21. 21. Introduction Results Discussion GLMM PROC GLIMMIXSpatial CovarianceMethods GLMM Structure  Distribution: Binomial • Response: proper restraint use  Link: Logit  Fixed effects: • Based on explanatory variables  Random effect: • Based on site location ( | ) , where ( ) E y g X Z           var( ) var( ) 'Z Z  Components of GLMM:
  22. 22. Introduction Results Discussion GLMM Spatial CovarianceMethods PROC GLIMMIX Random Effect Covariance • The random effect included in the GLMM accounts for within and between site correlations. • An isotropic exponential spatial covariance structure is assumed for the random effect.  The covariance between two sites is given by where is the Euclidean distance between the sites.  Note that the covariance decreases as the distance between sites increases.  The effective range, corresponds to the distance beyond which the correlations fall below 0.05. ijd 2 ij  where exp ij ij d          3 ,
  23. 23. Introduction Results Discussion GLMM Spatial CovarianceMethods PROC GLIMMIX Spatial Variance-Covariance Structure 2 2 2 2 2 2 2 2 2 12 12 12 13 13 13 2 2 2 2 2 2 2 2 2 12 12 12 13 13 13 2 2 2 2 2 2 2 2 2 12 12 12 13 13 13 2 2 2 2 2 21 21 21 2 2 2 2 21 21 21 2 2 2 2 21 21 21                                                                     2 2 2 2 23 23 23 2 2 2 2 2 23 23 23 2 2 2 2 2 23 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
  24. 24. Introduction Results Discussion GLMM Spatial CovarianceMethods PROC GLIMMIX GLMM Structure and GLIMMIX Code   | ~ Binomial GLMM: y g X Z      proc glimmix; class variables; model <resp> = <fixed effects> / dist= link= ; random <random effects> / <options>; run; Type=sp(exp) (lat long);
  25. 25. Introduction Results DiscussionMethods Random Effect Fixed Effects Spatial Random Effect • Euclidean distance is calculated using latitude and longitude. • Covariance parameter estimates: • The effective range is estimated by 2 ˆ 0.09574  ˆ 0.2621  ˆ3 0.7863 
  26. 26. Introduction Results DiscussionMethods Random Effect Fixed Effects Spatial Random Effect The output suggests that a minor degree of spatial correlation exists between nearby sites. 2 2 ˆ ˆˆ ˆ0.36; =0.249; exp 0.024ˆ ij ij ij ij d d                 
  27. 27. Introduction Results Discussion Random Effect Fixed EffectsMethods The data shows an increase in the use of proper restraints for child passengers. Proper Restraint Use by Year 0.71 0.78 0.83 64% 66% 68% 70% 72% 74% 76% 78% 80% 82% 84% 86% 2005 2006 2007 Properly restrained percentage
  28. 28. Introduction Results Discussion Random Effect Fixed EffectsMethods 96.57% 70.73% 79.47% 3.43% 29.27% 20.53% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Infant Toddler Young Child Not Properly Restrained Properly Restrained Proper Restraint Use by Age Level 2005-2007
  29. 29. Introduction Results Discussion Random Effect Fixed EffectsMethods Proper Restraint Use vs. Driver Belted Status 2005-2007 83.97% 36.67% 16.03% 63.33% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Driver belted: yes Driver belted: no Not Properly Restrained Properly Restrained
  30. 30. Introduction Results Discussion Random Effect Fixed EffectsMethods 72.98% 78.09% 75.73% 80.71% 27.02% 21.91% 24.27% 19.29% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Rural Town Suburban Urban Not Properly Restrained Properly Restrained Proper Restraint Use by Urban/Rural Status 2005-2007
  31. 31. Introduction Results Discussion Random Effect Fixed EffectsMethods 57.78% 71.19% 85.38% 42.22% 28.81% 14.62% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Small Medium Large Not Properly Restrained Properly Restrained Proper Restraint Use by Vehicle Size Year 2005-2007
  32. 32. Introduction Results Discussion Random Effect Fixed EffectsMethods Fixed Effects Estimates from GLMM Fit Variables Category Odds Ratio Age Level Infant vs Young Child 7.780 Toddler vs Young Child 0.497 Driver Belted No vs Yes 0.107 Vehicle Size Large vs Small 3.119 Middle vs Small 1.503 Year 2005 vs 2007 0.464 2006 vs 2007 0.675 Significant odds ratios:
  33. 33. Introduction Results DiscussionMethods Conclusions • The data exhibits some degree of spatial correlation. • In the multivariable model, rural/urban status is not statistically significant. • Compliance with the restraint laws has been increasing; the increases are both statistically significant and of practical importance.
  34. 34. Introduction Results DiscussionMethods Conclusions • Drivers are most cautious with infants (age 0 to 1).  The odds of an infant being properly restrained are about 8 times as great as the odds of a young child (aged 6 through 10) being properly restrained. • For toddlers (age 1 through 5), restraint laws are not fully understood.  The odds of a toddler being properly restrained are half as great as the odds of a young child (aged 6 through 10) being properly restrained.
  35. 35. Introduction Results DiscussionMethods Conclusions • Drivers who are belted are more likely to use proper restraints for their children.  If the driver is belted, the odds of a child passenger being properly restrained are about 8 times as high as the odds if the driver is not belted. • The larger the cab size of the vehicle, the more likely that child passengers are to be properly restrained.  For vehicles with large cabs, the odds of a child passenger being properly restrained are about 3 times as high as the odds for vehicles with small cabs.  For vehicles with medium cabs, the odds of a child passenger being properly restrained are about 1.5 times as high as the odds for vehicles with small cabs.
  36. 36. Introduction Results DiscussionMethods Limitations • Within-vehicle correlations, which could not be modeled due to the limitations of the data, may be important. • For the surveyors, no data has been collected which would allow an assessment of validity or inter-rater reliability.
  37. 37. Introduction Methods Results Discussion Acknowledgements • John Lundell • Eric Chen • Jing Xu
  38. 38. Introduction Methods Results Discussion Thank you!
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