Overall Injury Rsk to Dfferent Drvers: Combnng Exposure, Frequency, and Severty Models Young-Jun Kweon Graduate Student Reseacher The Unversty of Texas at Austn fre264@mal.utexas.edu and Kara M. Kockelman Clare Boothe Luce Assstant Professor of Cvl Engneerng The Unversty of Texas at Austn kkockelm@mal.utexas.edu (Correspondng Author) The Unversty of Texas at Austn 6.9 E. Cockrell Jr. Hall Austn, TX 78712-1076 Phone: 512-471-0210 FAX: 512-475-8744 The followng paper s a pre-prnt and the fnal publcaton can be found n Accdent Analyss and Preventon 35 (3):414-450, 2003. Presented at the 81 st Annual Meetng of the Transportaton Research Board, January 2002 ABSTRACT Traffc crash rsk assessments should ncorporate approprate exposure data. However, exstng U.S. natonwde crash data sets, the NASS General Estmates System (GES) and the Fatalty Analyss Reportng System (FARS), do not contan nformaton on drver or vehcle exposure. In order to obtan approprate exposure data, ths work estmates vehcle mles drven (VMD) by dfferent drvers usng the Natonwde Personal Transportaton Survey (NPTS). These results are combned wth annual crash rates and njury severty nformaton from the GES for a comprehensve assessment of overall rsk to dfferent drvers across vehcle classes. Data are dstngushed by drver age, gender, vehcle type, crash type (rollover versus non-rollover), and njury severty. After correctng for crash exposure to drvers, results ndcate that young drvers are far more crash prone than older drvers (per vehcle mle drven) and that
drvers of sports utlty vehcles (SUVs) and pckups are more lkely to be nvolved n rollover crashes than those drvng passenger cars. Although the results suggest that drvers of SUVs are generally much less crash prone than drvers of passenger cars, the rollover propensty of SUVs and the severty of that crash type offset the ncdent benefts for the younger drvers. KEY WORDS Crash rsk, crash exposure, crash frequency, crash severty, sport utlty vehcles, lght-duty trucks
INTRODUCTION Rsk assessment of road users has been conducted n many ways, ncludng estmaton of crash rates by road type, njury severty by crash type, and frequency of speedng volatons. The focus of the assessment may be on facltes, vehcles or travelers. Polcy makers and roadway desgn engneers act to mprove road safety by applyng the knowledge ganed n such studes. Estmatng crash rates s one of the most common ways to assess the rsk of road users or road facltes. Rate calculaton requres dvson of crash counts (.e., crash frequency) by some measure of exposure (e.g., vehcle mles traveled [VMT]). As Hauer (1995) has noted, such normalzaton equalzes for dfferences n ntensty of use, makng safety comparsons more meanngful, and t helps dentfy dfferences between dfferent populatons characterstc crash rates as a clue to causal factors. As Evans (1991) and others have noted, one cannot draw relable conclusons on safety ssues wthout exposure nformaton. Unfortunately, very few data sets provde adequate exposure nformaton. However, several researchers have obtaned surveys and/or estmates of such exposure. These are dscussed here now. Lourens et al. (1999) categorzed the car drvers nto fve subgroups by annual mleage drven. They estmated crashes as a functon of annual mleage nteracted wth gender, age, educaton level, and frequency of fnes (or volatons). After ths mplct correcton for annual mleage, the effects of gender and educaton level were found to not be statstcally sgnfcant predctors of crash nvolvement. Young drvers exhbted the hghest crash rates, and traffc volatons were mportant predctors. Hu et al. (1998) also controlled for drvng dstance, but they focused on the medcal condton of older drvers. They estmated that a gender effect for
ths age group of drvers was statstcally nsgnfcant. Such results would have been hdden from the modelers had drvng exposure not be recognzed. Usng a survey data of Ontaro lcensed drvers, Chpman et al. (1992) estmated drvng tme exposure and drvng dstance exposure, and they took the rato of these to produce an average drvng speed measure. All data were stratfed by age (sx levels), gender, and regon (three levels); and three exposure measures were compared among the stratfed subgroups. They argued that the fatal crashes should be analyzed separately from other crash types snce ther rates and nvolved factors are so dstnctve, and they recognzed that average drvng speed probably relates to crash severty. The men n ther data set drove 56% more dstance than the women, but they only spent 35% more tme drvng than the women (suggestng hgher speeds for men, and thus more dangerous exposure for men). As expected, teenage drvers (.e., those under the age of 20) were found to be less exposed (about 23% less, n dstance and n tme) than the data set s mddle-aged drvers (ages 25-59). And older drvers (age 60-69) drove about 33% less dstance and 19% less tme than the mddle-aged drvers. Davs and Gao (1993) tred to verfy the assumpton of random selecton of crash vctms, usng nduced exposure methods (where one examnes ratos of cross-classfed counts for hghrsk populatons and roadways). They parameterzed relatonshps between nduced exposure and contngency tables/cross-tabulatons and then estmated the ratos of crash rates for dfferent drver cohorts (e.g., male versus female, and mddle-aged versus older drvers), based on an assumpton of asymptotcally normally dstrbuted crash counts. An emprcal Bayes method was used to spot the dfference between crash rates of drver cohorts between two roadways. Through the contngency tables, they found that older drvers (aged 56 and over) were more lkely to be nvolved n crashes when traversng certan roadways. Usng Lyles et al. s data
(1991) for crash rates, they found male drvers to be 40% more crash prone than female drvers. DeYoung et al. (1997) used a quas-nduced exposure method (whch s smlar to the nduced method but does not correct for populaton representaton) to estmate the exposure and fatal crash rates of suspended/unlcensed (S/R) drvers usng data on two-vehcle crashes n the 1987-1992 Fatalty Analyss Reportng System (FARS) data set. As t turned out, the quas-nduced exposure method dd not predct the number of S/R and unlcensed drvers very well, n part because the purpose of ths method s to estmate crash nvolvement rates, rather than the number of specfc road users. Usng polce reports from n Western Australa, Ryan et al. (1998) studed the relatonshp between crash rsk and drver age. Ther fndngs suggested that females exhbt hgher crash nvolvement rates, across all age groups, a result often nconsstent wth common perceptons, largely due to the neglect of drvng exposure across genders n popular statstcs. Drvers under the age of 20 were the most lkely to be crash-nvolved, and drvers under age 25 exhbted very hgh rates as well. Age also exhbted a postve statstcally sgnfcant relaton to drver njury severty. Doherty et al. (1998) also found that drvers under age 20 were more lkely to be crash-nvolved than all other age groups. Abdel-Aty et al. (1998) used a categorcal method wth 1994 and 1995 Florda accdent databases to analyze the relatonshp between age and crash rsk. Ther results ndcated that young drvers (aged 25 and under) and older drvers (over age 64) were more lkely to be crash-nvolved, overall, but mddle-aged drvers were more lkely to be nvolved n crashes whch nvolve alcohol or occur durng rush hours. They also noted that older drvers are more lkely to de n crashes, snce they are relatvely physcally weak.
Whle the lterature has uncovered a number of exposure dfferences across drver types, essentally no such research has consdered the type of passenger vehcles beng drven. Yet one may expect that passenger cars, vans, pckups, and sport utlty vehcles (SUVs) perform very dfferently, n addton to havng varyng crash exposures. One partcularly severe crash type s that nvolvng a rollover. The Natonal Hghway Traffc Safety Admnstraton (NHTSA) has found that the relatonshp between rollover rsk and Statc Stablty Factor (SSF) (defned as a half the wdth of a vehcle dvded by the heght of ts center of gravty) s negatve. Ths s as expected: less stable vehcles (.e., those wth a lower SSF) nclude SUVs and pckups, and these are often perceved as more lkely to roll over n sngle-vehcle crashes. The average SSF of the 100 vehcle models studed by NHTSA (2000) were 1.400 for passenger cars, 1.153 for vans, 1.087 for SUVs, and 1.170 for pckups. In controllng for exposure dfferences, ths work s able to rgorously examne whether rollover crash rate dfferences exst across vehcle (and drver) types. Ths research has made use of large U.S. data sets to provde robust estmates of crash rates by crash category, drver characterstcs, and vehcle type. It also merges these results wth crashseverty model estmates (as provded by Kockelman and Kweon [2001]) to estmate the probablty of severe njures and death to the dfferent drver-vehcle cohorts, over 50,000 mles of drvng. Such estmates are very valuable for publc polcy and drver assessments of drvng rsks. THE DATA SETS The 1995 Natonwde Personal Travel Survey (NPTS) and the General Estmates System (GES) data sets were used for ths study. The NPTS data have been collected roughly every fve years, but the 1995 NPTS data are the most recently avalable at ths tme. 1 And, although the
GES data s collected annually (the most recently avalable one n 1999), the 1995 data were used here, n order to correspond to the NPTS data. 1995 NPTS Data The NPTS data set s the naton s best sngle course of a daly trps nventory. The 1995 dataset ncludes 42,033 households, 95,360 persons, and 75,217 vehcles. There are sx physcally separate fles assocated n the 1995 NPTS dataset, and four conceptually dfferent levels (household, person, vehcle, and travel day) n the dataset. These separate fles were approprately combned wth weghtng factors to match ths study s purposes. Applyng approprate weghtng factors s requste for all analysts who ntend to use survey data correctly. In the NPTS 1995 data set, households were over-sampled n add-on areas such as New York, Massachusetts and Oklahoma. There are four dfferent weghts for the dfferent levels of analyss; these are household weghts, person weghts, travel day weghts, and travel perod weghts. Snce the purpose of usng the NPTS data n ths work was acquston of drvers travel dstances, travel day weghts were used when combnng the fles. 1995 GES Data The Natonal Automotve Samplng System (NASS) General Estmates System (GES) dataset, brefly the GES data, has been collected every year from 1988. The GES data are ntended to be a natonally representatve probablty sample from the annual estmated 6.4 mllon polce accdent reports n the Unted States. The GES ncludes all types of crashes, ncludng fatal crashes, njury crashes, and property-damage-only crashes. The 1995 GES data nclude 53,749 crashes, 95,803 vehcles, 140,512 persons, and 95,477 drvers. Whle these 53,749 crashes are.8% of the (estmated) U.S. total n 1995, and each GES crash observaton
comes wth a natonal weghtng factor. These were used to scale up the GES crash counts to a U.S. total (as shown n Table 2). Extractng Necessary Informaton from the 1995 NPTS and GES Snce both the NPTS and GES datasets have several separate fles, there was some work nvolved n mergng and aggregatng ther data fles. The person-level, vehcle-level, and travelday-level fles n the 1995 NPTS dataset were merged usng travel-day weght factors (snce VMT estmates were needed). The merged data fle was ntally categorzed across 48 cohorts (by age, gender, and vehcle type). Unfortunately, suffcent nformaton on observatons nvolvng unknown and other vehcle types was not avalable, necesstatng the removal of 12 cohorts. And the NPTS data set does not cover commercal vehcle operatons, so the 6 cohorts nvolvng heavy- and medum-duty trucks were removed. The remanng 30 cohort categores are defned by vehcle type, gender, and age. The 5 avalable vehcle types are those of passenger car, SUV, mnvan (MVAN) 2, pckup (PU), and motorcycle (MC). SUVs are conventonally defned as lght-duty vehcles that meet several clearance requrements (for off-road use) 3. In the NPTS and GES data sets, pckup trucks are defned as a lght conventonal truck of pckup style cab weghng less than 10,000 lbs (wth maxmum payload). The three age dvsons are comprsed of young drvers (.e., those less than 20 years of age), mddle-aged drvers (.e., those from 20 through 60 years of age), and older drvers (.e., those over age 60). Snce ths nvestgaton s focus s on drver exposure and nvolvement, only trps records cases where the traveler was drvng were extracted. The travel mles were then aggregated n these same categores, to provde an estmate of annual vehcle mles drven (VMD) for the natonal cohort. These numbers are provded n Table 1.
Three fles n the 1995 GES data were merged nto a sngle drver-level fles; these are the vehcle, crash, and person fles. And the natonal weght factors were appled to each, to reflect samplng bases. Imputed varables were used for all three factors where data were mssng, whch occurred n 4.5% of records for the case of age, 2.9% for the case of gender, and 2.2% for the case of vehcle body type. (All records were retaned to permt a better estmate of the total, populaton counts.) The categorzaton and aggregaton of the weghted number of crashes produced the fnal crash frequency data for the 30 cohorts; these counts are provded n Table 2. Crash counts were dvded by VMDs n each of the cohorts for all crash types and rollover crashes; these crash rate values are provded n Tables 3 and 4. Before presentng the results of ths work, t should be noted that, f the weghted NPTS records do not capture total use of passenger cars, SUVs, pckups, mnvans, and motorcycles n the U.S., Table 3 and 4 s crash rate estmates are expected to be based hgh. For example, the NPTS asks ts sampled households members to report any type of drvng they do (even that drvng whch s part of ther work), but the amount of commercal/heavy-duty-vehcle drvng s clearly based low n the NPTS data set. Ths work s focus s on vehcles drven by households; however, the NPTS s undersamplng of VMD may occur here, to some extent. RESULTS AND DISCUSSION Crash rates of drver-vehcle cohorts are presented and dscussed n ths secton. Crash rates for all types of crashes are dscussed frst; these are followed by an examnaton of rollover and non-rollover crash rates. Vehcle Mles Drven (VMD) and Annual Crash Counts Estmates of vehcle mles drven (for the year 1995, usng the NPTS data set) are presented n Table 1, and estmates of annual crash counts (for the year 1995, usng the GES data
set) are provded n Table 2. No observatons of motorcycle (MC) drvng were made n the NPTS data set for two of the gender-age cohorts (though these were observed n crashes); thus, there are some mssng cells n Table 1 (and n the resultng crash-rate tables). As evdenced n Table 1, the total number of mles drven by young males s 46% more than that drven by young females. The same gap, n percentage terms, s vsble for mddle-age males and females, but wdens to 94% for older persons. Ths wdenng may be attrbuted to cultural norms of the past, when such persons came of drvng age. In the category of pckup trucks (PU), men drve much more than women, loggng 6 to 13 tmes more mles across the three age categores. In the mddle-age drver cohorts, there s not much dfference n total vehcle mles drven between men and women of passenger cars (PCs) or mnvans (MVANs). However, ths does not mean that women and men ownng such vehcles drve smlar dstances: men, on average, drve more because many of them are drvng other vehcle types. Clamng almost 50% of the total VMD, the mddle-age male cohort clearly drves the most. Table 2 provdes the annual crash counts (usng 1995 data) for 30 age-gender-vehcle cohorts. Young and mddle-aged male drvers experence almost 60% more vehcle crashes than female drvers. In the case of older drvers, the relatve dfference n the number of crashes rses to 70% but ths s aganst a 100% ncrease n exposure, as evdenced n Table 1. In terms of the numbers of SUV-nvolved crashes, there are consderable dfferences between male and female drvers for each age cohort; and these dfferences become larger n crashes of pckup (PU) trucks. But the absolute numbers of vehcle crashes cannot provde sold evdence of safety problems assocated wth road users. An apprecaton of relatve crash frequences requres recognton of exposure (VMD) data. Ths s done n the followng secton.
Crash Rates, All Crash Types Dvdng Table 2 s cell values by those of Table 1 yelds Table 3 s estmates of crash rates. Usng Table 3, an exposure-adjusted comparson of crash frequency or rsk s now possble, between cohorts of nterest. Over all vehcle types, there are no substantal dfferences between the general crash rates for male and female drvers n the same age cohort. Young and mddle-aged men are slghtly more nvolved than ther female counterparts, but older women are slghtly more nvolved than older men. The addtonal drvng experence (as evdent n VMD) does not make male drvers less crash-nvolved; however, male drvers may be drvng n more dangerous envronments (e.g., when dark and rany or at hgh speeds). And women may recognze ther relatve lack of drvng experence, takng extra precautons. Ths may be true across vehcle types as well, resultng n a degree of ncomparablty across cohorts and cases. Dfferences of nterest also can be found across vehcle types n Table 3. Males are more crash-nvolved than females when drvng passenger cars, but not when drvng lght-duty trucks (.e., SUVs, pckups, and mnvans). And drvers of passenger cars are more crash-nvolved than those drvng lght-duty trucks. They are more than twce as crash-nvolved as drvers of SUVs! Possble explanatons for part of such strkng dstnctons nclude the followng: lght-duty truck (LDT) drvers may drve dfferently (e.g., more slowly) and/or be more rsk averse; LDT drvers may be less lkely to report crashes (e.g., n rural areas or wth mnor property damage); they may drve on less congested and/or safer roads durng better condtons; they also may have better sght dstances or more stable vehcles. Such data dstnctons are generally not avalable n both the NPTS and GES data sets, but they are of nterest to polcy makers and drvers. (As an example of such work, Kockelman and Yong s [2001] multvarate models found that, ceters
parbus, larger, wealther households n lower-densty areas purchased more SUVs than other households. Smaller, less wealthy households n low-densty areas were more lkely to purchase pckups.) Table 3 clearly also suggests that younger drvers are extremely nvolved n crashes (relatve to ther drvng dstances). Ths relatve dstncton between age groups (computed as the rato of rates) s most acute for young drvers of SUVs and mnvans. Motorcycle drvng s a class of ts own: ts drvers overall crash-rate estmates exceed those of other cohorts by four to ffteen tmes. Whle lmted sample szes make ths cohort s estmates relatvely varable, the trends are not nconsstent wth expectatons. It should be noted that Table 2 s counts and Table 3 s rates nclude all crash types (e.g., head-on, rear-end, and rollover). Thus, they provde a rather general estmate of crash nvolvement and rsks. Dfferent crash types are more serous than others, as are the actons and responses of dfferent drver types and ther vehcles. The followng examnatons and ther assocated tables make such dstnctons. Rollover and Non-rollover Crash Rates A common percepton of lght-duty trucks s that they are more lkely to roll over. And rollovers are extremely hgh-rsk crashes for death and severe njury (see, e.g., Kockelman and Kweon [2001]). As addressed n ths paper s lterature revew, the statc stablty factors (SSFs) of LDTs are estmated to average 16.5 to 22.4 percent lower than those of passenger cars (NHTSA 2000). And SSFs tend to relate negatvely to rollover rsk. For these reasons, rollover and non-rollover crash rates are examned here, separately. Table 4 provdes estmates of rollover crash rates. As expected, SUV and pckup drvers are more lkely to experence a rollover crash than ther passenger-car- and mnvan-drvng
counterparts. As one would also expect (gven Table 2 s results), younger drvers are the most nvolved n such crashes, and the magntudes of dfference are heghtened relatve to ther over-nvolvement n crashes of all types (shown n Table 3). Ther rollover crash rates are over sx tmes those of mddle-aged drvers; n contrast, when consderng all crash types, ths dfference was less than a factor of four. SUV drvng offers the hghest rollover rates for young males, but pckup drvng offers the hghest rates for young females. Whle crash rates are an excellent ndcator of crash nvolvement, they do not provde a very strong apprecaton of crash severty. The probabltes of drver njury and death n such crashes are examned now, provdng a better sense of crash costs to drvers. Overall Injury Severty Probabltes When assessng the drvng rsks of dfferent drvers and vehcles, one may be most nterested n the severty of the crash. If a type of vehcle performs very poorly n crashes, t may not matter much f t s not hghly crash-nvolved (per mle drven); many people wll not care to buy t and regulators may choose to restrct ts sale. If a partcular drver type survves crashes very well, such drvers are less lkely to worry about havng hgher crash nvolvement rates. The provson of probablty estmates for dfferent drvers and vehcle types offers useful comparsons n ths regard; such values encapsulate a varety of factors, gvng a more comprehensve value to crash rsks. The results n ths secton are based on the crash rates estmated above and the drvernjury-severty models estmated by Kockelman and Kweon (2001) usng ordered-probt models to predct four crash-severty levels (.e., no njury to drver, not-severe njury, severe njury, and fatalty). 4
Crash nvolvement rates and severe-njury and fatal-crash probabltes for each cohort are estmated assumng 50,000 mles of drvng. Ths amount of drvng represents on the order of fve years drvng for many drvers, but many more years drvng for most young and older drvers. The calculatons also assume that crash counts for ndvdual drvers follow a Posson dstrbuton, wth rates equal to those shown n Tables 3 and 4. The Posson dstrbuton can arse from a memoryless property of duratons between crashes; such an assumpton effectvely mples that a drver s crash rsk s unform at all tmes. The Posson dstrbuton s qute common for crash-rate analyss (Evans 1991; Hauer 1997). However, t does mply that the varance of crash-nvolvement counts (from the sum of ndependent Posson varables) equals ther mean (wthn a specfc cohort, as appled here). Snce data on specfc drvers crash hstores are not generally avalable (and are not n the GES data set), ths assumpton s not tested here. The overall crash njury severty probablty for each cohort s obtaned by multplyng total Posson-based crash nvolvement probabltes wth the probabltes of varous njury severty levels. All probabltes are calculated for the case of rollover and non-rollover crash types across 24 cohorts. Motorcycle (MC) crash probabltes are excluded here, snce these were not estmated separately n Kockelman and Kweon s models (2001). However, t s expected that severe njury and fatal crash probabltes would be very hgh for ths class of drver. Overall severty crash rates are provded n Table 5 through 12, based on the followng equaton: c ( CrashType c Crash) Rate = TotalRate Pr (1)
where s an age-gender-vehcle cohort and c s the crash type. The probablty of njury severty condtoned on a crash occurred s calculated usng the ordered-probt model results and ts formula s shown n Eq. (3). The fgures provde crash rates for four dfferent njury severty no njury, non-severe njury, severe njury, and fatal njury n rollover and non-rollover cases. To acknowledge the fact that drvers may be nvolved n more than one crash of certan types, probabltes nclude the possblty of two and three crash events of each type, rather than just the probablty of exactly one event. The followng set of equatons llustrate the type of equatons used to calculate overall njury probabltes of the drver cohorts: - e λ x * λ P ( x; λ ) = x! (2) where x s the number of crashes experenced, and λ s the rate of crash nvolvement (for every 50,000 mles drven). Eq. (2) assumes a Posson process for crash nvolvement. Once a crash has occurred, the ordered-probt probabltes rely on the followng set of equatons: P P P P ( 0) () 1 ( 2) () 3 = Pr(No Injury A crash occurred) = Pr( T = Pr( ε ψ X β ) = Φ( ψ X β ) = = Pr( T = Φ = = 1 Φ = 0) = Pr( T = 1) = Φ ( ψ X β ) Φ( ψ X β ) ( ψ X β ) Φ( ψ X β ) ( ψ X β ) * ψ ) = Pr( X β + ε ψ ) = Pr(Severe Injury A crash occurred) 2 Pr( Fatal Injury 2 1 Pr( Not Severe Injury 1 1 0 1 A crash occurred) A crash occurred) 0 0 (3) where T s the observed, dscrete njury level for drver/vehcle cohort, severty level, and * T s the latent njury ψ n s an ordered probt s (latent) threshold between njury severty levels n and n+1. (For example, ψ 2 ndcates a shft from severe njury to fatalty.)
Drvers can experence more than one crash of a gven type (except fatal crashes, sans rencarnaton). Computaton of overall rates of crash nvolvement that a drver experences on average durng a 50,000 mles drvng perod are relatvely smple, as llustrated by Eq. (1). For probabltes, however, varous equatons combnng multnomal outcomes wth Posson rates must be appled. The overall njury severty probabltes are presented for severe njury and fatal crashes n more than one crash cases. In order to permt the possblty of dfferent levels of njury severtes n each crash, the multnomal (MN) probablty condtoned on Posson s used. The MN probablty s assocated wth combo occurrences and can be wrtten as: MN probablty = j C X! X! j j C p X j j (4) where j s the crash type (such as one causng severe drver njury), C s a set of ncdences of dfferent types, X s the total number of occurrences experenced by the drver durng that drvng perod (of 50,000 mles), X j s the number of crash-type j occurrences, and p j s the probablty of crash type j s occurrence. As an example of ths approach, f a drver experences a total of three crashes, where one s severe and two are no njury, the probablty of ths example s the followng: 3! 1 2 MN probablty ( 1s severe & 2 nvolve nonjury) = p severe p no njury (5) 1! 2! The probablty that a drver sustans a severe njury durng the drvng perod of nterest s the summaton of all non-fatal crash combnatons n a seres of crashes. Ths probablty s presented n Table 13. The combnatons nclude: one crash wth severe njury; two crashes, one wth severe njury and the other wth no or not-severe njury; two crashes, both wth severe
njury; three crashes, wth severe njury n one and less-then-severe njury n the other two crashes; three crashes, wth severe njury n two and less-than-severe n the other; three crashes, wth severe njury n all three crashes; and so on. The resultng probablty can be expressed as the followng: Prob(Crash at least once & at least 1crash s severe but none s = + p + p * 1! p (1) p 1! * * (2) 2! 2! p (3) 3! (3) p 2! 1! (3) 1 + p 2 * + p 2 (3) [1 p 2! (2) p 1! 1! * 3! (3) p 1! 2! (3) p 1 (3) [1 p 1 (3) [1 p (4)] 1 + p * (3) p (3) p (3) 3! 3! (4)] p (4)] (3) 3 worse) 2 +... (6) A geometrc dstrbuton, rather than a multnomal, s appled n the case of a drver s experencng a fatal crash snce ths type of crash must occur last n any sequence of possble crashes. These probabltes are provded n Table 14. The fatal njury severty probablty durng any perod (e.g., the drver s lfetme) can be wrtten as: Prob(Crashes & only the last one s fatal) = p (1) p (4) + p (2) p (4)[1 p (4)] + p (3) p (4)[1 p (4)] +... * * * 2 { } * x 1 p ( x) p (4) 1 p (4) x= 1 = (7) Thus, the above set of equatons brngs together crash nvolvement and crash severty probabltes. Tables 5 and 6 provde estmates of rollover and non-rollover crash rates where the drver s not njured. These suggest that non-rollover, non-njury drver experences are roughly 134 tmes more probable (usng the average rato of probabltes) than rollover, non-njury
experences. For purposes of comparson (and usng results n subsequent tables), the average rato of rates drops to 40, 15, and 6 when non-severe njury, severe njury, and fatal crashes are consdered. Clearly, non-rollover crashes are much more lkely than rollover crashes, but the probablty of severe njury and death n a rollover crash s much hgher. As antcpated, Tables 5 and 6 confrm that young drvers are at relatvely hgh rsk for crashes. Females are estmated to be at lower rsk for these two types of non-njury crash than males, for most vehcle types (and assumng 50,000 mles of drvng). Females are at greatest rsk for non-njury rollover crashes when drvng SUVs and pckups, and for non-rollovers when drvng passenger cars. In general, a female s probablty of experencng a non-njury rollover crash s less than that of males, but not when drvng a pckup or mnvan. Whle crashes of all types are costly and emotonally, f not physcally, panful, polcy makers and drvers maybe often most nterested n the probabltes of crashng and sustanng some sort of njury. Tables 7 and 8 present the rate estmates for non-severe njury crashes for drvers (per 50,000 mles drven); Tables 9 and 10 correspond to severe drver njures, and Tables 11 and 12 present drver death rates. In all cases non-rollover crashes are more lkely than rollover crashes, and, n most cases, ths dfference s by an order of magntude. Yet the probabltes of such crashes are generally low. For example, a mddle-aged woman exhbts a deadly crash rate of 0.048, per 50,000 mles of drvng a passenger car. Ths s even lower f she s drvng a lght-duty truck. Of course, f she often also s a passenger, her rsk of njury whle travelng wll rse (per tme perod). Accordng to Table 7, rollover crashes are more prevalent when drvng an SUV than a passenger car. Female drvers are more lkely to receve non-severe njures than males n a
pckup or mnvan. In case of a rollover crash, female drvers are more apt to experence ths type of crash n an SUV by all ages, and a passenger car by md-aged or old drvers. Table 8 suggests that passenger car drvers experence non-rollover crashes and sustan a non-severe njury more often than other vehcle drvers, except for young female (for her, a pckup s the most). And females are more lkely to experence ths type of crash than males n md- or old age. Ths result s n general contrast to the results of Table 6, where men were at greater rsk (of non-njury crashes). It may be that women are more lkely to report to polce offcers that they have sustaned a (non-severe) njury, or t may be that they njure more easly. It may also be that the types of crash n whch they are nvolved dffer; these detals are not present n aggregate data lke those presented here. Tables 9 and 10 descrbe rsks for sustanng severe njures durng 50,000 mles of drvng. Young and older men appear to be at lower rsk for ths than women are except whle drvng a passenger car. It may be that females are less often wearng seatbelts or more lkely to sustan a severe njury, for the same ntensty of crash. However, n general, females are somewhat more crash-nvolved, for the same travel dstance; ther crash rates are hgher than those of males n 11 of the 13 avalable cohort comparsons shown n Table 3. To get a sense of the magntudes of rsk, one may observe that the severe-njury crash rate that a mddle-aged woman drvng a passenger car 50,000 mles wll experence s about 0.613. Fortunately, the rates for death are roughly an order of magntude lower, partcularly for non-rollover crashes, as shown n Tables 11 and 12. The dfferences n rates between rollover and non-rollover are reduced as the severty level s ncreased, snce rollovers are very severe crashes (see, e.g., Kockelman and Kweon
[2001]). Unfortunately, young drvers are at relatvely hgh rsk of rollng over (Table 4). The resultng hgh rsk to young drvers s an unfortunate realty. Tables 11 and 12 suggest that female drvers (of all ages), young males, and older male drvers are more lkely to de from a rollover whle drvng an SUV than a passenger car. But passenger car drvers are predcted to be at hgher rsk of death n non-rollover crashes than those n other vehcles. Summng the two tables rates, the most death-prone drver cohort, for 50,000 mles of drvng, nvolves young women drvng SUVs, wth a rate of 0.316 (0.190+0.126). The next more lkely cohorts are young women n passenger cars (at 0.276) and n SUVs (0.252). Why are women are at somewhat greater rsk of dyng (for the same dstance drven)? As suggested before, t may be that women njure more easly for the same ntensty crash; ther somewhat hgher crash nvolvements (as shown n Table 3) do not justfy the ncreases n rates found n Tables 11 and 12, whch typcally are often on the order of two or three tmes more. It also may be that less experence drvng (e.g., young and mddle-aged men drve roughly 50% more than women, as shown n Table 1) translates to poorer response under crash crcumstances. Hgher death rates may also mean that such drvers pay less attenton to drvng or understand vehcle operatons less. Unfortunately, the GES and NPTS data cannot really address these ssues. Drvng smulators or other data sets are necessary. As prevously mentoned, probabltes are provded for severe and fatal njury cases. Table 13 offers estmates of the probablty that drvers receve at least one severe njury durng the course of 50,000 mles of drvng, and Table 14 provdes estmates of the probablty that drvers de durng ths perod (n the last crash, of course). Both cases nvolve crashes of dfferent severty, and all levels need to be added to get the probablty, whch may nclude an nfnte number of crashes. Recognzng that the probablty of experencng fve or more
crashes (n the course of 50,000 mles) s neglgble (for the average drver), the probabltes for multple crashes n Tables 13 and 14 only have been computed for up to four crashes (and all ther vald combnatons). Table 13 ndcates that young drvers are at hgher rsk of recevng severe njures than old or mddle-aged drvers. Female drvers are more lkely to suffer severe njury n crashes than are males (when drvng all vehcle types except for passenger cars). Young and mddle-aged males are more crash-prone when drvng passenger cars than are ther female counterparts. Accordng to these results, a pckup places young female drvers at hgher rsk than a passenger car, and a mnvan s the safest vehcle for a young drver. However, t s relatvely rare for youths to drve mnvan. However, nether of these two drver-vehcle combnatons s very lkely, n practce. Table 14 provdes estmates of the probablty that drvers wll de n the last of a seres of (one or more) crashes that they may experence. Female drvers are at greater rsk than males n SUVs, pckups, and mnvans; but young and mddle-aged males are more vulnerable n passenger cars. Note that these probabltes obscure the nature of the crash; rollover crashes are often fatal, and SUVs and pckups are more lkely to roll than passenger cars. CONCLUSIONS Rsk assessment of road users s an mportant area for nvestgaton. The results of such work permt peoples assessments of ther own and others drvng safety. They are lkely to mpact vehcle ownershp choces and drvng behavors. And they should be present n state and federal dscussons of drvng regulaton of both drvers and ther vehcles. The work presented here llumnates many rsk patterns across drver gender, drver age group, and vehcle type. Here, the computaton of crash rates through parng of NPTS exposure data wth GES crash
data offered valuable nformaton. And the separate consderatons of rollover and nonrollover crashes, as well as crash severty (as related to drver njury), provded addtonal conclusons. These results suggest that polcy makers may fnd t best to lmt the drvng of young persons, through rasng the legal drvng age, applyng drvng curfews, prohbtng freeway drvng, and/or restrctng such drvers to passenger cars. They also ndcated that women are at greater rsk of death from crashes than are men, for every mle drven; ths result suggests that more attenton to female drver educaton and/or female physcal response under crash condtons. And automoble manufacturers may want to mprove vehcle desgn features for hgher-rsk drvers. In contrast, older drvers appear to face relatvely low rsk of crash, for every mle drven. Ths may be due to personal compensaton mechansms, ncludng use of slower speeds, avodance of hgh-speed roadways, and/or avodance of nght-tme drvng condtons. The results also hghlght the need to control for drver exposure. Wthout parng the GES crash data to exposure data, one mght conclude that male drvers are over-nvolved n crashes and young drvers are under-nvolved. In realty, the dfferences are much lower between genders, but severe across age groups. The dfferences across vehcle types are also strkng; lght-duty trucks are more often nvolved n rollovers than are passenger cars, partcularly for younger drvers, older drvers, and female drvers. However, they are substantally less nvolved n other crash types (except, n many cases, when drven by younger drvers). As much as ths work was able to conclude, mportant questons reman unanswered. For example, do drvng condtons dffer across vehcle and drver categores? Do some drvers drve more mles under dangerous (e.g., hgh-speed, rany, or dark) condtons than others? And
are hgh-rsk drvers drvng dfferently because they should (obscurng vehcle-related and other rsk dstnctons)? More extensve surveys of drver behavor and crash hstory would llumnate such nformaton, provdng more equtable comparsons and stronger conclusons. If, for example, mddle-aged SUV drvers are hghly rsk averse and/or drve under uncongested but slow-speed condtons, ther relatvely low crash rates may not make for far comparsons wth the more common cohort of mddle-aged passenger-car drvers. We hope that future work wll llumnate any dstnctons that exst. ACKNOWLEDGEMENTS The authors apprecate the admnstratve support of Annette Perrone and the fnancal support of the Luce Foundaton and the Unversty of Texas s Department of Cvl Engneerng. ENDNOTES 1 The 2001 Natonal Household Travel Survey (NHTS), whch s the combned data set of the NPTS and Amercan Travel Survey (ATS), wll be avalable n late 2002. 2 The NPTS survey queston of basc vehcle type does not dscrmnate between mnvans and cargo vans. Thus, vehcle make and model nformaton had to be matched to mnvan codes to ensure consstency between the crash and use data sets. 3 The specal features enablng off-road use are four-wheel drve and at least four of the followng fve clearance characterstcs: an approach angle of not less than 28 degrees, a breakover angle of not less than 14 degrees; a departure angle of not less than 20 degrees, a runnng clearance of not less than 8 nches, and front and rear axle clearances of not less than 7 nches each. (CFR 40CFR86.084-2) 4 Kockelman and Kweon s (2001) njury severty models were obtaned usng the then most recently avalable crash data, from the 1998 GES. Vehcles and crash characterstcs may have changed somewhat, between 1995 and 1998, affectng the parameter estmates of the severty models, but t makes good sense to use the more recent estmates snce these are more applcable to today s crashes.
REFERENCES Abdel-Aty, M. A., Chen, C. L., Schott, J. R., 1998. An assessment of the effect of drver age on traffc accdent nvolvement usng log-lnear models. Accdent Analyss and Preventon 30 (6), 851-861. Chpman, M. L., MacGregor, C. G., Smley, A. M., and Lee-Gosseln, M., 1992. Tme vs. dstance as measures of exposure n drvng surveys. Accdent Analyss and Preventon, 24 (6) 679-684. Davs, G. A., Gao, Y., 1993. Statstcal methods to support nduced exposure analyses of traffc accdent data. Transportaton Research Record 1401, 43-49. DeYoung, D. J., Peck, R. C., Helander, C. J., 1997. Estmatng the exposure and fatal crash rates of suspended/revoked and unlcensed drvers n Calforna. Accdent Analyss and Preventon 29 (1), 17-23. Doherty, S. T., Andrey, J. C., MacGregor, C., 1998. The stuatonal rsks of young drvers: The nfluence of passengers, tme of day and day of week on accdent rates. Accdent Analyss and Preventon 30 (1), 45-52. Evans, L., 1991. Traffc Safety and the Drver. Van Nostrand and Renhold. Federal Hghway Admnstraton, 1997. User s gude for the publc use data fles: 1995 natonwde personal travel survey. Publcaton# FHWA-PL-98-002. Hauer. E., 1997. Observatonal Before-After Studes In Road Safety. Oxford, Pergamon. Hauer, E., 1995. On exposure and accdent rate. Traffc Engneerng and Control 3 (3), 134-138. Hu, P. S., Trumble, D. A., Foley, D. J., Eberhard, J. W., Wallace, R. B., 1998. Crash rsks of older drvers: A panel data analyss. Accdent Analyss and Preventon 30 (5), 569-581.
Kockelman, K. M., Kweon, Y.-J., 2001. Drver njury severty: An applcaton of ordered probt models. Forthcomng n Accdent Analyss and Preventon. Kockelman, K. M., Zhao, Y., 2001. Behavoral Dstnctons: The use of lght-duty trucks and passenger cars. Journal of Transportaton and Statstcs 3 (3), 47-60. Lourens, P. F., Vssers, J. A. M..M., Jessurun, M., 1999. Annual mleage, drvng volatons, and accdent nvolvement n relaton to drvers sex, age, and level of educaton. Accdent Analyss and Preventon 31 (5), 593-597. Lyles, R., Stamatades, N., Lghthzer, D., 1991. Quas-nduced exposure revsted. Accdent Analyss and Preventon 23, 275-285. Natonal Hghway Traffc Safety Admnstraton, 2000. Consumer Informaton Regulatons; Federal Motor Vehcle Safety Standards; Rollover Preventon. Docket# NHTSA-2000-6859. Natonal Hghway Traffc Safety Admnstraton (No date) NASS GES Analytcal User s Manual 1988 1999 [Onlne]. Avalable: ftp://www.nhtsa.dot.gov/ges/ges_doc/ [2001, June 25]. Ryan, G. A., Legge, M., Rosman, D., 1998. Age related changes n drvers crash rsk and crash type. Accdent Analyss and Preventon 30 (3), 379-387.
Table 1. Annual Vehcle Mles Drven (10 6 mles, 1995) Age Gender PC SUV PU MVAN MC Overall Young 31,506 3,467 11,422 1,034 97 48,426 Md Male 504,795 90,401 230,551 60,032 2,133 917,284 Old 102,513 7,786 28,895 8,243 12 152,917 Young 29,370 1,204 1,650 681 NA 33,119 Md Female 465,469 49,621 40,631 59,370 53 627,506 Old 72,278 1,258 2,253 1,839 NA 78,677 Overall 1,205,931 153,736 315,401 131,199 2,294 1,857,930 Young = Age < 20, Md = Ages from 20 to 60, and Old = Ages > 60 years. PC = Passenger car, SUV = Sport utlty vehcle, PU = Pckup truck, MVAN = Mnvan, and MC = Motorcycle. Table 2. Annual Crash Counts (All Crash Types, 1995) Age Gender PC SUV PU MVAN MC Total Young 719,046 49,404 193,547 12,876 9,431 1,055,020 Md Male 3,165,487 251,589 1,183,520 95,469 49,875 5,502,690 Old 504,866 15,810 128,722 13,296 3,173 724,237 Young 569,590 25,489 44,597 9,200 605 670,192 Md Female 2,846,540 147,951 211,846 111,731 2,540 3,509,659 Old 405,649 4,413 10,373 4,885 24 434,257 Total 8,211,178 494,656 1,772,605 247,458 65,648 11,896,055 Table 3. Crash Rates of Drvers (per 10 6 mles drven, 1995) Age Gender PC SUV PU MVAN MC Overall Young 22.82 14.25 16.95 12.46 97.66 21.79 Md Male 6.27 2.78 5.13 1.59 23.39 6.00 Old 4.92 2.03 4.45 1.61 260.06 4.74 Young 19.39 21.18 27.04 13.51 NA 20.24 Md Female 6.12 2.98 5.21 1.88 48.38 5.59 Old 5.61 3.51 4.60 2.66 NA 5.52 Overall 6.81 3.22 5.62 1.89 28.62 6.40 Table 4. Rollover Crash Rates of Drvers (per 10 6 mle drven, 1995) Age Gender PC SUV PU MVAN MC Overall Young 0.661 1.449 1.028 0.389 72.2 0.987 Md Male 0.105 0.124 0.157 0.024 22.5 0.184 Old 0.029 0.049 0.062 0.028 213.2 0.059 Young 0.516 1.322 1.769 0.577 NA 0.627 Md Female 0.068 0.111 0.224 0.037 39.3 0.084 Old 0.026 0.052 0.087 NA NA 0.030 Total 0.104 0.155 0.196 0.036 26.2 0.162
Table 5. Rate of Rollng Over and Sustanng No Injury (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 0.1657 0.4401 0.3170 0.1131 Md Male 0.0257 0.0369 0.0475 0.0069 Old 0.0073 0.0149 0.0190 0.0082 Young 0.0944 0.3011 0.4103 0.1249 Md Female 0.0120 0.0248 0.0506 0.0078 Old 0.0047 0.0118 0.0201 NA Table 6. Rate of Non-Rollover Crash Involvement and Sustanng No Injury (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 13.62 8.62 10.80 7.96 Md Male 3.74 1.77 3.34 1.02 Old 3.00 1.33 2.97 1.04 Young 9.88 11.63 14.94 7.39 Md Female 3.12 1.66 2.92 1.04 Old 2.91 2.02 2.66 1.51 Table 7. Rate of Rollng Over and Sustanng Non-Severe Injury (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 0.2935 0.6439 0.4563 0.1733 Md Male 0.0465 0.0551 0.0699 0.0108 Old 0.0130 0.0219 0.0275 0.0127 Young 0.2202 0.5828 0.7813 0.2528 Md Female 0.0287 0.0490 0.0985 0.0160 Old 0.0111 0.0229 0.0385 NA Table 8. Rate of Non-rollover Crash Involvement and Sustanng Non-Severe Injury (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 6.984 3.522 4.325 3.438 Md Male 1.970 0.744 1.375 0.453 Old 1.549 0.548 1.200 0.454 Young 6.971 6.615 8.336 4.426 Md Female 2.256 0.969 1.668 0.639 Old 2.069 1.156 1.496 0.912
Table 9. Rate of Rollng Over and Sustanng Severe Injures (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 0.1597 0.2985 0.2087 0.0835 Md Male 0.0257 0.0260 0.0325 0.0053 Old 0.0071 0.0102 0.0127 0.0061 Young 0.1513 0.3415 0.4517 0.1540 Md Female 0.0201 0.0292 0.0580 0.0099 Old 0.0077 0.0135 0.0224 NA Table 10. Rate of Non-Rollover Crash Involvement and Sustanng Severe Injures (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 1.4172 0.6058 0.7334 0.6153 Md Male 0.4074 0.1304 0.2376 0.0827 Old 0.3162 0.0948 0.2046 0.0816 Young 1.7996 1.4494 1.8012 1.0089 Md Female 0.5934 0.2162 0.3672 0.1485 Old 0.5372 0.2547 0.3251 0.2091 Table 11. Rate of Rollng Over and Sustanng a Fatal Injury (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 0.0418 0.0664 0.0458 0.0193 Md Male 0.0069 0.0059 0.0073 0.0013 Old 0.0019 0.0023 0.0028 0.0014 Young 0.0503 0.0964 0.1258 0.0452 Md Female 0.0068 0.0084 0.0164 0.0030 Old 0.0026 0.0038 0.0063 NA Table 12. Rate of Non-Rollover Crash Involvement and Sustanng a Fatal Injury (per 50,000 mles drven) Age Gender PC SUV PU MVAN Young 0.1410 0.0515 0.0616 0.0544 Md Male 0.0413 0.0113 0.0203 0.0074 Old 0.0316 0.0081 0.0173 0.0073 Young 0.2253 0.1551 0.1902 0.1121 Md Female 0.0756 0.0236 0.0395 0.0168 Old 0.0676 0.0274 0.0345 0.0234
Table 13. Probablty of Sustanng at Least One Severe Injury (n One or More Crashes, whle drvng 50,000 mles) Age Gender PC SUV PU MVAN Young 7.144E-02 3.954E-02 4.224E-02 3.288E-02 Md Male 2.105E-02 7.380E-03 1.288E-02 4.558E-03 Old 1.591E-02 5.068E-03 1.059E-02 4.530E-03 Young 6.154E-02 5.336E-02 6.462E-02 3.832E-02 Md Female 2.034E-02 7.801E-03 1.338E-02 5.323E-03 Old 1.807E-02 8.584E-03 1.104E-02 8.056E-03 Table 14. Probablty of Sustanng a Fatal Injury (whle drvng 50,000 mles) Age Gender PC SUV PU MVAN Young 4.617E-03 2.719E-03 2.612E-03 2.273E-03 Md Male 1.881E-03 6.249E-04 1.007E-03 4.128E-04 Old 1.431E-03 4.230E-04 8.164E-04 4.057E-04 Young 4.206E-03 3.105E-03 3.382E-03 2.705E-03 Md Female 1.814E-03 6.531E-04 1.056E-03 4.756E-04 Old 1.599E-03 6.862E-04 8.529E-04 7.346E-04