Introduction Results DiscussionMethods

An Analysis of the Iowa Child Passenger Safety Survey

Based on Generalized Linear Mixed Models

Joseph Cavanaugh and Eric ChenDepartment of Biostatistics

The University of Iowa

New York State Psychiatric InstituteColumbia UniversityFebruary 26, 2009

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)

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

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

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

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

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

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.

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.

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.

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.

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

Introduction Results Discussion Background Restraints Study DesignMethods

Use of Restraint Devices (2005-2007)

Device

Properly Restrained (No/Yes/Total)

Age LevelsTotal

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.

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%

Introduction Results Discussion Background Restraints Study DesignMethods

Sampling for IPRC Study

Population Range Category Number of Sampled Sites

Targeted Sample

Size1,000-2,499 Rural 12 502,500-9,999 Town 8 75

10,000-49,999 Suburban 7 10050,000+ Urban 9 125

Introduction Results Discussion Background Restraints Study DesignMethods

IPRC Study SitesMap of Study Sites

Introduction Results Discussion Background Restraints Study DesignMethods

Data Structure

Response variable: proper restraint use (binary)

Age0 up to 1

infant 1 through 5

toddler6 through 10young child

Restraint TypeRear-facing CSS

CSS Booster Belted

Proper Restraint Use Yes

Introduction Results Discussion Background Restraints Study DesignMethods

Data Structure

Variable Variable Type Levels

Age OrdinalInfant (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

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.

Introduction Results Discussion GLMM PROC GLIMMIXSpatial CovarianceMethods

Spatial CorrelationResidual mean based on fitted generalized linear model

(without inclusion of urban/rural covariate)

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 yg X Z

var( ) var( ) 'Z Z

Components of GLMM:

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

2ij where exp ij

ijd

3 ,

Introduction Results Discussion 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 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);

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

2ˆ 0.09574 ˆ 0.2621

ˆ3 0.7863

Introduction Results DiscussionMethods Random Effect Fixed Effects

Spatial Random EffectThe output suggests that a minor degree of spatial correlation exists between nearby sites.

2 2ˆ ˆˆ ˆ0.36; =0.249; exp 0.024ˆij

ij ij ijdd

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

2005 2006 200760%

65%

70%

75%

80%

85%

0.71

0.78

0.83

Properly restrained percentage

Introduction Results Discussion Random Effect Fixed EffectsMethods

Infant Toddler Young Child0%

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

2005-2007

Introduction Results Discussion Random Effect Fixed EffectsMethods

Proper Restraint Use vs. Driver Belted Status

2005-2007

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 Restrained

Properly Restrained

Introduction Results Discussion Random Effect Fixed EffectsMethods

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 Restrained

Properly Restrained

Proper Restraint Use by Urban/Rural Status2005-2007

Introduction Results Discussion Random Effect Fixed EffectsMethods

Small Medium 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 SizeYear 2005-2007

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:

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.

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.

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.

• Vehicle type is a potential risk factor.

• There is a statistically significant improvement in proper restraint use from 2005 to 2007.

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.

Introduction Methods Results Discussion

Acknowledgements

• John Lundell• Eric Chen• Jing Xu

Introduction Methods Results Discussion

Thank you!