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Accident Analysis and Prevention 40 (2008) 835–839

Brief communication

Modeling motor vehicle crashes for street racersusing zero-inflated models

Zhuo Li a,1, Stacey Knight b,c, Lawrence J. Cook b,c, Lisa K. Hyde b,c,Richard Holubkov b, Lenora M. Olson b,c,∗

a Department of Family and Preventive Medicine, University of Utah,375 Chipeta Way, Salt Lake City, UT 84108, USA

b Division of Pediatric Critical Care, Department of Pediatrics, University of Utah School of Medicine,295 Chipeta Way, Salt Lake City, UT 84108, USA

c Intermountain Injury Control Research Center, Department of Pediatrics, University of Utah School of Medicine,295 Chipeta Way, Salt Lake City, UT 84108, USA

Received 5 May 2007; accepted 7 September 2007

bstract

Motor vehicle crashes are a leading cause of death for young people in the United States. Assessing which drivers are at a high risk of experiencingcrash is important for the implementation of traffic regulations. Illegal street racing has been associated with a high rate of motor vehicle crashes.

n this study, we link Utah statewide driver license citations and motor vehicle crash data to evaluate the rate of crashes for drivers with street racingitations relative to other drivers. Using a zero-inflated negative binomial model we found that drivers with no citations are approximately three

imes more likely to be at zero risk of a crash compared to drivers with street racing citations. Moreover, among drivers at non-negligible risk ofrash, cited street racers are more likely to be involved in a crash compared to drivers without citations or those cited for violations other than streetacing. However, drivers with increased numbers of non-street-racing citations experience crash risks approaching those of the cited street racers.

2007 Elsevier Ltd. All rights reserved.

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eywords: Motor vehicle crash; Street racing; Zero-inflated model; Citation; C

. Introduction

Motor vehicle crashes are among the leading causes of deathn the United States, especially for those between the ages of–33 years (NHTSA, 2005). A growing area of interest andesearch in motor vehicle safety is illegal street racing whichay be associated with an increased risk of experiencing a motor

ehicle crash. Illegal street racing can refer to either an illegallyrganized event with spectators and marked distances on pub-

ic roadways, or illegal spontaneous racing with another car onublic roadways. While street racing is a contributing factoro less than 1% of fatal crashes in the United States, the mor-

∗ Corresponding author at: University of Utah School of Medicine, Depart-ent of Pediatrics, 295 Chipeta Way, Salt Lake City, UT 84108, USA.el.: +1 801 585 9160; fax: +1 801 581 8686.

E-mail address: Lenora.Olson@hsc.utah.edu (L.M. Olson).1 Present address: Biostatistics Division, Mayo Clinic, 200 First Street SW,ochester, MN 55902, USA.

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idity and mortality associated with street racing appears to ben increasing problem in many cities and towns (Knight et al.,004). According to nation-wide statistics, 49 people are injuredor every 1000 who participate in illegal street racing (NHTSA,005). However, most studies examining street racing have notssessed a driver’s risk of being involved in a motor vehiclerash. We used Utah statewide driver license citations and motorehicle crash data to compare drivers with street racing citationso drivers with no citations and drivers with non-street racingitations in order to examine the influence of street racing onhe rates of motor vehicle crashes. The ability to determine if ariver’s behavior is associated with an increased risk of a motorehicle crash is important for the implementation and modifica-ion of traffic rules, regulations, and prevention activities.

. Methods

This study was conducted using linked data from the Utahtatewide driver license citation database and the Utah statewide

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36 Z. Li et al. / Accident Analysis

otor vehicle crash data from 1992 to 2002. The University oftah School Of Medicine Institutional Review Board approved

his study.

.1. Data

The driver license citation data were obtained from the Utahepartment of Public Safety, Drivers License Division. This file

ontains demographic information and driving citations for alltah licensees during the study period. The motor vehicle crashata were obtained from the Utah Department of Transportation,ivision of Traffic and Safety. This file contains information on

eported motor vehicle crashes occurring on public roadwaysith at least one injury or fatality or at least $1000 in propertyamage.

These two databases were probabilistically linked. Proba-ilistic linkage uses variables common in two databases toetermine whether a pair of records refers to the same personnd event based on the cumulative agreement and disagreementf field values. CODES 2000 linkage software (Strategic Match-ng, Inc., Morrisonville, NY) was used to probabilistically linkhe two databases. The matching variables were driver name,ate of birth, gender, and driver license number. The resultingnalysis data set contained 1,603,305 observations, with casesxcluded if they had missing data on variables of interest (e.g.,ge at entry or gender).

Study variables and definitions:Drivers were divided into three categories: drivers with no

itations (non-cited drivers), drivers with citations not related totreet racing (non-racing cited drivers), and drivers with streetacing citations (racing cited drivers). Citation type was catego-ized based on the citation information obtained from the Drivericense Division database. In addition to the classification of theitation types, the total citation events were also calculated byounting the number of times at least one citation was issued to ariver during the study period (e.g., if two citations were issuedn the same date, it is counted as a single citation event). Covari-tes used in the study were (1) driver’s age at entry, which isefined as the age of a Utah driver when he/she entered the study1 January 1992, or date license first issued if later); (2) driver’sex; and (3) licensing area (urban vs. rural), categorized basedn the county of residence from the drivers license file (USDA,003).

The main outcome of interest was the crash rate which wasetermined by dividing the total number of crashes during thetudy period by the number of driving days for each driver. Theriving days were calculated as the difference in days betweenhe time a driver entered the study (1 January 1992 or date licenserst issued if later) and the time the study ended (31 December002).

.2. Statistical analysis

We first examined the distributions of the driver character-stics and the covariates using both univariate and bivariatenalyses. Then, we assessed four different generalized lin-ar models to fit the data: Poisson, negative binomial (NB),

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revention 40 (2008) 835–839

ero-inflated Poisson (ZIP), and zero-inflated negative binomialZINB). Traditionally, the Poisson distribution is appropriateor modeling count data, such as the number of motor vehiclerashes. However, since the number of people not experienc-ng a crash was far greater than people experiencing a crash,he motor vehicle crash data have more zero events than can beccounted for by the Poisson distribution. Zero-inflated mod-ls are used when excess zeros result in a bimodal distribution.his bimodal distribution is a mixture of a mass of extra zerosnd a mass that has a Poisson or negative binomial distribu-ion (Cheung, 2002). The mass of extra zeros can be thoughtf as two subgroups of drivers: (1) drivers whom due to someharacteristic could not have crashed during the study periodnd (2) drivers that could have crashed but did not crash or didot have a reportable crash. Several motor vehicle crash studiesave used zero-inflated models and negative binomial modelsKumara and Chin, 2003; Lee et al., 2002; Lee and Mannering,002; Qin et al., 2004).

The zero-inflated models have two parts: the zero-inflated andhe Poisson or negative binomial depending if a ZINB or a ZIP

odel is used. The zero-inflated part estimates the probabilityhat a group of drivers is in the “true zero state” by estimating how

uch more likely one group is to have an excess of drivers with-ut crashes compared to another group. The Poisson or negativeinomial coefficients estimate the rate of crashes, conditionedn the group of drivers not being in the “true zero state”. Theseoefficients are reported using relative risk. The two parts ofhe zero-inflated model need to be considered together whenssessing the association between the independent and depen-ent variable in the model.

Model goodness of fit was examined by the log likelihoodsing the Akaike information criterion (AIC) (Akaike, 1974;urnham and Anderson, 2002), and the Bayesian informationriterion (BIC) (McQuarrie and Tsai, 1998). The likelihood ratioest was used to compare the Poisson model and NB modelAgresti, 2002; Arminger and Clogg, 1995), and the ZIP andINB models. For the zero-inflated models, goodness of fit wasssessed using the method of Vuong (Vuong, 1998).

The dependent variable in each model is the rate of crashesor a driver, defined as the total number of crashes for the driverivided by his/her driving days (crashes per 1000 days) duringhe study period. The independent variables modeled were cita-ion type (categorized as none, one non-racing citation event, twoon-racing citation events, three non-racing citation events, fourr more non-racing citation events, at least one racing citationvent), age group (categorized as 15–19 years, 20–24 years, 25ears or older), gender (female, male) and area where licenseas issued (categorized as rural or urban). All independentariables were chosen a priori. Programming was done usingROC NLMIXED in SAS 9.0. Statistical significance was sett α = 0.05, and 95% confidence intervals were used.

. Results

There were 1,603,305 drivers licensed and 597,894 crashesuring the study period. The average number of crashes per000 driving days for all drivers was 0.16. Approximately

Z. Li et al. / Accident Analysis and Prevention 40 (2008) 835–839 837

Table 1Characteristics of study population, Utah, 1992–2002 (N = 1,603,305)

Number of drivers, N (%) Crashes/1000 days

Age at entry15–19 years 378,476 (23.6%) 0.2820–24 years 232,218 (14.5%) 0.18≥25 years 992,611 (61.9%) 0.12

GenderMale 856,185 (53.4%) 0.19Female 747,120 (46.6%) 0.14

Licensing areaRural 260,990 (16.3%) 0.13Urban 1,342,315 (83.7%) 0.18

Citation typeNone 901,448 (56.2%) 0.10Non-racing 698,585 (43.6%) 0.26Racing 3,272 (0.2%) 0.70

Number of citations0 901,448 (56.2%) 0.101 335,373 (20.9%) 0.222 153,860 (9.6%) 0.25

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Table 3Summary of the odds ratios and relative risks from the ZINB model

Zero-inflateda oddsratio (95% CI)

Negative binomialb

relative risk (95% CI)

None vs. racing 3.13 (2.57, 3.80) 0.31 (0.30, 0.32)1 non-racing vs. racing 0.51 (0.41, 0.63) 0.43 (0.42, 0.45)2 non-racing vs. racing 0.51 (0.41, 0.63) 0.57 (0.54, 0.59)3 non-racing vs. racing 0.41 (0.33, 0.51) 0.65 (0.63, 0.68)≥4 non-racing vs. racing 0.38 (0.30, 0.47) 0.85 (0.82, 0.89)Age 15–19 vs. ≥25 0.75 (0.72, 0.78) 1.46 (1.45, 1.47)Age 20–24 vs. ≥25 1.09 (1.05, 1.14) 1.03 (1.02, 1.04)Male vs. female 0.84 (0.82, 0.85) 1.03 (1.02, 1.04)Rural vs. urban 1.14 (1.10, 1.18) 0.78 (0.77, 0.79)

a The zero-inflated part of the model reported the increased/decreased oddsof the group have an excess number in the “true zero state” or drivers withoutc

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hree-quarters (72%) of the drivers experienced zero reportedrashes and approximately one quarter had multiple citations.able 1 shows the characteristics of the study population.eenage drivers, who accounted for one quarter of the drivers,ad the highest crash rate (0.28) among all drivers. While therivers were evenly distributed with respect to gender, malesad a higher rate of crashes per 1000 driving days than femalerivers (0.19 vs. 0.14). The majority of drivers were licensedn urban areas, and the crash rate was higher for the driversicensed in urban areas compared to rural areas (0.18 vs. 0.13).pproximately 0.2% of all drivers received at least one street

acing citation during the study period. Drivers with a street

acing citation had a higher crash rate (0.70) compared torivers who received no citations (0.10) or received non-racingitations (0.26). However, these rates were not adjusted forther covariates such as gender and age of driver.

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able 2arameter estimation for the four regression models

arameter interpretation Poisson (S.E.) N

ntercept −1.32 (0.018) −1one vs. racing −1.54 (0.018) −1non-racing vs racing −0.75 (0.018) −0non-racing vs. racing −0.48 (0.018) −0non-racing vs. racing −0.33 (0.018) −0or more non-racing vs. racing −0.06 (0.018) −0ge 15–19 vs. ≥25 0.45 (0.003) 0ge 20–24 vs. ≥25 0.03 (0.004) 0ale vs. female 0.07 (0.003) 0ural vs. urban −0.28 (0.004) −0

ll estimates are significant at a 0.05 significance level. According to the likelihoodoisson model (P < 0.0001) and the ZINB is significantly better than the ZIP (P < 0.0B model with ZINB model found that both zero-inflated models are highly significa

he best fit to these data based on these statistical results.

rashes.b The negative binomial part of the model represents the risk of a crash.

Poisson, NB, ZIP and ZINB models were fit to our data ando adjust for the covariates. The resulting parameter estimatesre shown in Table 2. The results from the four models wereimilar. However, goodness-of-fit testing showed that the ZINBodel provided the best model fit.We used results from the ZINB model in Table 3. The group

ith no citations had three times more drivers without crasheshan would be expected compared to the racing citation groupOR = 3.13; 95% CI: 2.57, 3.80). The negative binomial portionf the model showed that the relative risk of a crash was loweror the drivers with no citations compared to the racing citationroup (RR = 0.31, 95% CI: 0.30, 0.32). The groups with at leastne non-racing citation were less likely than expected to haven excess of drivers without crashes compared to the racing cita-ion group. For example, the group with four or more non-racingitations had a decreased number of drivers without crasheshan would be expected compared to the racing citation groupOR = 0.38; 95% CI: 0.30; 0.47). However, the negative binom-nal portion of the model showed that the relative risk of a crash

or the drivers with non-racing citations was lower compared tohe drivers with racing citations. Fig. 1 shows that as the num-er of non-racing citations increased, the relative risk of a crashpproaches that of the group with racing citations. Compared

B (S.E.) ZIP (S.E.) ZINB (S.E.)

.34 (0.021) −1.10 (0.023) −1.07 (0.022)

.53 (0.021) −1.08 (0.023) −1.17 (0.023)

.74 (0.021) −0.75 (0.023) −0.84 (0.023)

.47 (0.021) −0.48 (0.023) −0.57 (0.023)

.32 (0.021) −0.34 (0.023) −0.43 (0.023)

.05 (0.021) −0.09 (0.022) −0.16 (0.022)

.48 (0.003) 0.37 (0.004) 0.38 (0.004)

.04 (0.004) 0.03 (0.006) 0.03 (0.006)

.07 (0.003) 0.04 (0.004) 0.03 (0.004)

.28 (0.004) −0.24 (0.005) −0.25 (0.006)

ratio test, the NB model provides a significantly better fit to the data than the001). The Vuong test results comparing the Poisson model with ZIP model andntly better (P < 0.0001). Therefore, we can conclude that ZINB model provides

838 Z. Li et al. / Accident Analysis and P

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ig. 1. Relative risk of motor vehicle drivers without racing citations comparedo drivers with racing citations, Utah, 1992–2002 (N = 1,603,305).

o the group with a racing citation, the relative risk of havingcrash was 0.43 (95% CI: 0.42, 0.45) for the group with one

on-racing citation. The relative risk increased to 0.85 (95% CI:.82, 0.89) for the group with four or more non-racing citations.esides the drivers’ citation history, other risk factors such asge and license area impacted the crash occurrence (see Table 3).

. Discussion

Our study showed differences among drivers with respect toitations and motor vehicle crash experiences when we adjustedor covariates using the ZINB model. First, drivers in the groupith no citations were at a decreased odds and rate of being incrash compared to those with a street racing citation. Second,hile the odds of a crash are higher among drivers with non-

acing citations, the rates of crashes are decreased compared tohe racing citation group. This finding held true even when fourr more non-racing citations were issued to a driver. Our findingsuggest that those who street race as evidenced by citations aret an increased risk of experiencing a crash.

We found that drivers with different types of citations haveifferent risk patterns for experiencing a motor vehicle crashndicating that a driver’s driving behavior is associated with anncreased risk of a motor vehicle crash. For example, driversith no citations had higher odds of no crashes and lower ratesf crashes than drivers with street racing citations. Our findingsre consistent with other studies showing that drivers involvedn crashes usually have prior citations and a poor driving historyBrewer et al., 1994; Knight et al., 2004; Stella et al., 2002;

illiams et al., 2006). These findings suggest that drivers whoave no citations are safer drivers as they are probably less likelyo engage in driving behaviors such as speeding and drivinghile impaired that result in a citation and increase the risk of a

rash.We also confirmed that drivers with a street racing citation are

t higher risk of crashes than other highly non-street racing citedrivers. Even as the number of non-racing citations increased,

he risk of a crash for the non-racing drivers did not surpass thoseith a street racing citation. There are several potential reasons

or the rate of crashes experienced by those who receive a streetacing citation. Illegal street racing usually involves speeding

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revention 40 (2008) 835–839

hich has been shown to increase the risk of a motor vehiclerash (Williams et al., 2006). In addition, street racing has beenhown to involve not only speeding, but a younger age group andther known risky driving behaviors including the use of alcoholKnight et al., 2004). These factors probably contribute to theverall increased risk of a crash for individuals that engage intreet racing compared to those with non-racing citations.

Although the study has the strength of having access to thetah statewide driver license citation and motor vehicle crashatabases, the study also has several limitations. First, street rac-ng may be underreported. Because we relied on street racingitations records to obtain information about the drivers whotreet race, some racing behavior may not caught by police ando may not be captured. According to the 2002 National Surveyf Speeding and Unsafe Driving Attitudes and Behaviors con-ucted by NHTSA, about 3% of drivers reported engaging inacing another car (NHTSA, 2003), yet only 0.2% of the driversn our dataset are cited for street racing. Furthermore, the cita-ion issued is determined by the police officer on the scene. It isossible that street racers received non-racing citations such aspeeding. Thus, we may have underestimated the relative riskf a crash for cited racing drivers compared to non-cited racingrivers. Furthermore, when a citation was issued as a result of arash, both the crash and the citation were included in the analy-is. This was done to maximize the number of street racing citedrivers. However, by including both, we may have overestimatedhe risk of a crash for drivers with citations.

Second, we chose to use the ZINB model. It is possible that allhe assumptions for this model were not met especially in regardor the underlying dual-state distribution. Given the empiricalvidence that zero-inflated models are often sufficient to explainhe underlying population heterogeneity (Lee et al., 2002), it

ay still be necessary to develop formal tests to give an infer-nce about dual-state crash distribution. This is probably not aroblem for our study as the ZINB model is usually robust andtable when the underlying assumptions do not hold.

Despite the study limitations, we have demonstrated thatllegal street racing adversely affects motor vehicle crash out-omes. The results from our models confirmed our hypothesishat drivers who received at least one street racing citation expe-ience a higher risk of being in a motor vehicle crash comparedith drivers without any citations, or drivers with several non-

treet-racing citations. Thus, street racers are a high-risk drivingopulation, and traffic safety prevention efforts should be devel-ped that focus on this driving population.

cknowledgements

This work was partially supported by NHTSA Cooperativegreement number DTNH22-03-H-27207. The authors would

ike to thank Amy Donaldson, MS and Heather Keenan, MDMC,hD for their review of the manuscript before submission.

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