Journalof Studieson Alcohol, Vol. 52. No. 4. 1991
Alcohol-Related Relative Risk of Fatal Driver Injuries in Relation to Driver Age and Sex* PAUL L. ZADOR,
PH.r•.
InsuranceInstitutefor Highway Safety, 1005 North Glebe Road, Arlington, Virginia 22201
ABSTRACT.
The relative risks of fatal crash involvement at various
bloodalcoholconcentrations (BACs) were examinedusingdata on fatal driver injuries from the Fatal AccidentReportingSystemin conjunctionwith driverexposuredata from the secondnationalroadsidebreath-testing survey.Basedon driverfatalitiesin single-vehicle crashes,it was estimatedthat each0.02 percentageincreasein the BAC of a driverwith non-zeroBAC nearlydoublesthe risk of being in a fatal crash.Crashrisk was foundto increasewith increasing BAC amongall of the six age and sex groupsstudied.At BACs in the 0.05-0.09 percentrange,the likelihoodof a crashwas at least ninetimesgreaterthanat zeroBAC for all agegroups.Younger drivers with BACsin the 0.05-0.09 rangehadhigherrelativerisksthan
N MOST U.S.jurisdictions, 0.10% blood alcohol con-
centration(BAC) is the typical thresholdset for the per se definitionof driving under the influence,and countermeasures aimedat alcohol-impaired drivinghavetraditionally targetedthesedriverswith high BACs (IIHS, 1987;
Williams, 1988).The percentage of fatally injureddrivers whose BAC
at the time
of the crash was at or above
0.10% declinedsteadilyfrom 48% in 1982to 39% in 1987 (IIHS, 1988). This declinerepresentsa remarkablereduction in the problemof alcohol-impaired drivingandattests to thecombined effectsof legalsanctions, mediacampaigns and reducedalcoholconsumption(Williams, 1988). The risk of crashinvolvementincreases steadilywith increasingdriver BAC and reacheshigh levelswell below 0.10% (Hurst, 1973; see also Moskowitz et al., 1985). About 11% of the fatally injured drivers (about 2,800) had BACs in the 0.01-0.09% range in 1986. In contrast to the decline in driver fatalities
at or above the 0.10%
threshold,the percentage of driverfatalitieswith positive BACs below it held steady between 1982 and 1987 (FARS, 1982-87). The proportionof BACs in this lower range is especiallyhigh among youngerdrivers and female drivers.Among 16-19 year old driversinvolvedin fatal crashesin 1986,about40% of thosewith a positive blood alcohol concentration had a BAC below 0.10%
(NHTSA, 1987). The comparablepercentagefor all fe-
Received:May 2, 1989.Revision:December9, 1989. *This work was supported by the InsuranceInstitutefor Highway Safety. 302
older drivers,and femaleshad higherrelative risksthan males.At very highBACs(at or above0.15 percent),the riskof crashing was 300 to 600 times the risk at zero or near-zero BACs. These relative
risk estimatesare considerably higherthan estimatedin otherstudies, but other studieshave based their estimates on all crashesrather
than single-vehicle crashesonly. In this study,relativeriskswere also lower when basedon driver fatalities in all crashes.However, whenplausibleassumptions were madeaboutthe BAC distributions of otherparticipantsin multiple-vehiclecrashes(whoseactualBAC is often unknown), the relative risks basedon the maximum BAC of
the crashparticipantswere nearly as high as thoseestimatedin single-vehiclecrashes.(J. Stud.Alcohol52: 302-310, 1991)
male driversin fatalcrashes,regardlessof age, was about 30%. In contrast,for maledriversin the 25-54 agegroup it was only about20%. Extensive research over the last three decades has demonstrated that the relative risk of involvement in motor
vehiclecrashesincreaseswith increasingdriver BAC regardlessof driverage, driver sex, crashtype or responsibility for the crash.The magnitudeof the relativerisk and the rate at whichit increases with increasing BAC depend on severalof thesefactors.Basedon driverfatalitydata from Canada,Mayhew and colleagues(1986) reported that at all BACs(includingzero) driversaged16-19 have higherrelative risks than older drivers and that the rate at whichthe risk increases with BAC is alsohigherfor the youngerage group(seealsoMayhew and Simpson,1983). There are no comparablydetailed investigations using U.S. driver fatality data. Borkenstein et al. (1974) investigated relativecrashrisk as a functionof BAC by driver age groupsfor policereportedcrashesin Grand Rapids, Mich., during 1962-
63. They reportedthat crashrisk increases steadilywith BAC in every age groupand the rate of increasevaried amongthe agegroupswith no systematic pattern.The relative crash risk as a function of BAC for males and fe-
males was also investigatedusing the samedata. Crash risk was reportedto increasewith driver BAC for both males and females,and femaleswere reportedto have higher crash risks than males in all but the 0.01-0.04% BAC range(in that rangethe risks were almostthe same for bothgroups).The interactionbetweenBAC anddriver sex was not investigated.
ZADOR
The relative crashrisk was reportedto increasemore rapidly with increasingdriver BAC in single-vehicle crashes than in all multivehicle
crashes or in multivehicle
crasheswith at-faultdrivers;it also increasedmore rapidly in multivehicle crasheswith at-fault drivers than in multivehiclecrasheswith driversnot at fault (Borkenstein
et al., 1974). The authorsexplaintheir findingby noting that, whencrashinginto anothervehicle,high BAC drivers tend to collide with vehiclesoperatedbY "drivers from the averagedriving population,who for the most part havelow or zero percentBACs" (p. 107). The relative crashrisk for drivers fatally injured in single-vehicle crashesprovidesa goodmeasureof the true contribution
of alcohol to increased risk of involvement
the serious crash. For multivehicle
in
crashes the situation is
more complicated. When the relative crash risk is esti-
matedfrom BAC datafor only the driverswho are fatally injured in multivehiclecrashes,the estimatesare for the
combinedrisk of beingfatally injuredeitheras a responsible agent or as an innocentvictim. Becausedata are commonlyavailablefor fatally injureddrivers,this combinedrisk canbe estimatedwith little difficulty;however, the risk of beingfatally injuredin sucha crashdoesnot measure the true contribution of alcohol to crash risk. For
example, in a two-car fatal crash involving one driver with a high BAC who survivesand a soberdriver who dies, using the BAC of the fatally injured soberdriver would indicate such a crash to be unrelated to alcohol.
Only when both drivers in a two-car fatal crashare tested can the actual contribution
of alcohol be determined.
For
fatal multivehicle crashes, the contribution of alcohol to
crashrisk dependsnotonly on the BACsof fatally injured drivers but on the BACs of all the drivers involved. How-
ever, BAC data for survivingdriversare not obtainedin enoughcasesto developa reliablesamplefor analysis. The studies reviewed here have examined the effect of to one factor at a
driver BAC on crash risk in relation
time (for additionalreviews seeHurst, 1973, Jonah, 1986,
andWarrenandSimpson,1980).The presentwork focuses on thejoint effectsof driverageanddriver sexon relative fatalityrisk as a functionof BAC in single-vehicle crashes. Someestimatesfor multivehiclecrashesare also generated for purposesof comparison.This studyis basedon U.S. data on fatally injuredpassengervehicledriversfor 1985 and 1986 obtainedfrom the Fatal AccidentReporting System(FARS) anddriverexposuredataobtainedfrom the 1986nationalroadsidebreath-testing survey(Lundand Wolfe, 1991). Method
Driver exposuredata
The second national roadsidebreath-testingsurvey (Lund and Wolfe, 1991) was conductedin 1986 through-
303
out the contiguousUnited Statesusinga controlledprobability sample of 34 localities chosento representthe almost90% of the populationthat lived in countieswith more than 20,000 inhabitantsin 1970 (Lund and Wolfe,
1991). i Thesurveys wereconducted onFridayandSaturday nightsfrom 10 PM to 3 AM using separateroadside sites from 10 PM-12 midnightand from 1-3 AM along heavyand mediumvolumeroads(exceptfreeways).Participationin the surveywas voluntaryand 2,850 or 92% of the 3,100 stoppeddriversprovidedsatisfactorybreath samples.Only drivers of passengervehicles (cars and light trucks,includingvans,pickupsand four-wheel-drive vehicles) were interviewed. The driver counts from this
survey (weighted to take into accountthe estimatesof drinking by noncooperating drivers, the traffic countsat the roadsidesites and the relative populationsof each of the 24 stratain the sample)providedthe exposuredata for the presentstudy. The weightedcountsof drivers were classifiedby driver age (16-20, 21-24 and 25+), driver sex, time of observation(10 PM-12 midnightand 1-3 AM) and driver BAC (0.00-0.01%, 0.02-0.04%, 0.05-0.09%, 0.10-0.14% and 0.15%+).
Driver fatality data
Driver fatalities occurringin the samepassengervehicle types included in the breath-testingsurvey were extractedfrom the FARS 1985and 1986data tapes.FARS is a computerizeddatabasecontainingvirtually all motor vehicle fatalities in the United Statesas reportedby state governmentsto the National Highway Traffic Safety Administration (NHTSA). To reduce the likelihood of a biased inferencedue to underreportingof driver BACs, the data were taken only from the 29 statesthat reportedthe BACs of at least 80% of fatally injureddriversto FARS driving 1985 and 1986 (Table 1). Also, to match driver fatalitiesto the roadsidebreath-testingsurveyexposureestimates,crashtimes anddayswererestrictedto thoseused for the survey,and crashesthat occurredon interstates, otherurbanfreewaysand expressways were excluded. Driver fatalities were classifiedby sex, age and time of the crashin the sameway as in the survey.The classification of driver BACs was as follows: 0.00-0.01%, TABLE1. StatesreportingBACsof at least80% of fatallyinjureddrivers to FARS
in 1985 and 1986
California
Kentucky
Colorado
Maine
New Mexico North Carolina
Connecticut
Maryland
Oregon
Delaware
Massachusetts
South Dakota
District of Columbia
Minnesota Montana
Utah Vermont
Hawaii Idaho Illinois Indiana
Nebraska Nevada New Hampshire New Jersey
Virginia Washington WestVirginia Wisconsin
304
JOURNAL
0.02-0.04%,
0.05- 0.09%, 0.10-0.14%,
OF STUDIES
0.15%+
ON ALCOHOL
and un-
known percent. This differs from the survey-basedexposure classificationin that the BACs of some of the fatally injured drivers were unknownand no secondaryinformation was availableto provide acceptableestimates.The drivers
with
unknown
BACs
were
eliminated
from
the
presentstudy.However,in stateswith very high levels of BAC reportingthere is little chancefor a systematicdifferencebetweenfatally injured driverswith knownBACs and fatally injured drivers with unknown BACs, so that eliminating the latter group is not likely to bias the results on the relative
risks of driver crash involvement
in rela-
tion to BAC.
Crasheswere classified into two types: crashesinvolving only the fatally injured driver and all other crashes. Most analyseswere restrictedto driver fatalitiesoccurring in the first categoryof crashes.
/ JULY
1991
5% level. All models fitted were hierarchical
in the sense
explainedin Bishop et al. (1975) so that when a factor was included in an interaction
term the main effects in-
cluded in that factor and certain other lower order interaction terms were also included in the model.
The model-based crash-rate estimates were used to cal-
culate relative risk. In one set of relative risk computations, drivers with BACs in the 0.00-0.01% range were chosen for the baseline. With this baseline choice, relative
risk measuresthe within-groupeffect of alcohol on the crash risk as a function of BAC. Within-grouprelative risk was estimatedfor the whole groupand for driversubgroupsdefinedin termsof age and sex. For another set of relative risk computations,male driversage 25 and over were chosenas the baseline.This groupwas chosenbecauseit is the largestamongthe six groupsin the study.With this baseline,relative risk measures the effect of age and sex differenceson the crash
Statisticalanalyses
rate when BAC is controlled for.
The intuitive idea behind the statistical analyses of thesedata is that the frequencyof fatalities amongcertain typesof driversrelative to the frequencyof similar drivers on the road (i.e., in the roadsidesurveys)is indicativeof how likely suchdriversmight be of receivinga fatal crash injury per unit of driving exposure.In other words, the relative frequencyof fatalities as comparedto the frequency of being included in the surveysis a measurefor fatality risk for a groupof drivers.By itself the numerical value of fatality risk cannot be interpretedbecausethis value dependson how extensivethe surveyswere: a larger survey would result in larger driver countsand smaller "risk." However, such risks can be validly compared amongdifferentgroupsof drivers and driversin high-risk groupscan be said to have higher risks of receivinga fatal crashinjury per unit of exposurethan driversfrom lower risk groups. For this study, driver fatalities divided by the correspondingweighted driver countsin the roadsidesurvey
Distribution of MBAC for drivers in two-vehiclecrashes
were termed
Partialjustificationfor this assumptionwas providedby Klein (1986) who comparedthe BAC distributionsof fatally injuredand survivingdriversinvolvedin fatal multivehiclecrashes.In 1985, 12%amongthesurvivingand10% amongthe fatally injured drivers had BACs in the 0.010.09% range (see Klein, 1986, Tables 14 and 15). The corresponding percentages during the sameyear were 31 and 28 for the 0.10% and over BAC range. (For 1984 the percentagesfor surviving drivers are somewhathigher.) The percentages providedby Klein are for all multivehicle crasheson all roadsand at all times and are not directly comparableto the percentagesin the presentstudy.
"crash
rates."
The size of one crash rate rel-
ative to the size of another crash rate can be used to com-
pare the risks measuredby the two crash rates. The numericalvaluethat resultsfrom this comparisonis called relativerisk. By definition,relativerisk is the ratio of one crashrate divided by anothercrashrate. The crashrate in the denominator
is called the baseline crash rate.
Crash rates were analyzed in terms of no more than four singlefactors(driverBAC, sex, age andtime of crash in relation to midnight) and their interactionsby fitting loglinearmodelsto the driver fatality and exposurecounts (seeAppendixI for details).The modelswere fitted using the maximum likelihood option offered by the loglinear modelingfacility (CATMOD) of SAS (1985). The phrase"the modelfit is adequate"meansthat the chi-squaretest basedon the residualsfrom the maximum likelihoodestimateswas not statisticallysignificantat the
The role of alcohol in two-vehicle
crashes should be es-
timated from the BACs of both drivers in the crash; un-
fortunately,the BACs of surviving drivers are often not known. However,undercertainstatisticalassumptions the distribution of the maximum BAC (MBAC) for drivers in
two-vehiclecrashescan be estimated.Specifically,if the BAC distributionof driverswho were fatally injuredand the BAC distribution
of drivers who survived in fatal two-
vehiclecrashesare statisticallyindependentand identical, then the common distributionof these surviving and fatally injureddriversis the sameas the BAC distributionof all driverswho werefatally injuredin two-vehiclecrashes. In this case, the MBAC distributionfunctionis simplythe squareof the BAC distributionfunction, and the rate of crashesby MBAC group was computedfrom the MBAC distributionthe sameway as the rate of crasheswas com-
putedfromtheBACdistribution byBACgroup. 2
Results
The relative driver fatality risk estimatesfor different BACs are displayedin Figure 1 for single-vehiclecrashes.
ZADOR
Using driverswith zero or near-zeroBAC as the baseline (i.e., relative risk is 1 for these drivers), the relative risks are 1.4 for BACs between 0.02-0.04%, 11.1 for BACs between 0.05-0.09%, 48 for BACs between 0.10-0.14% and about 380 for drivers with BACs at or above 0.15%.
Note that for positiveBACs the increasein relative risk with increasingBAC is approximatelylinear when plotted on the logscaleagainstthe midpointsof the BAC groups. For positive BACs, this relationshipcan be describedby the loglinearmodelgiven in Equation 1: In (RATE) = -3.26
(0.17)3
+ 32.68 BAC
305
TABLE2. Analysisof variancetable for the loglinearmodel of crash ratesin single-vehicle crashes
Intercept Age
df
X2
p
I 2
5.9 61.8
< .05 .05
Age x BAC
8
12.7
>.05
Sex x BAC
4
10.2
Alcohol-Related Relative Risk of Fatal Driver Injuries in Relation to Driver Age and Sex* PAUL L. ZADOR,
PH.r•.
InsuranceInstitutefor Highway Safety, 1005 North Glebe Road, Arlington, Virginia 22201
ABSTRACT.
The relative risks of fatal crash involvement at various
bloodalcoholconcentrations (BACs) were examinedusingdata on fatal driver injuries from the Fatal AccidentReportingSystemin conjunctionwith driverexposuredata from the secondnationalroadsidebreath-testing survey.Basedon driverfatalitiesin single-vehicle crashes,it was estimatedthat each0.02 percentageincreasein the BAC of a driverwith non-zeroBAC nearlydoublesthe risk of being in a fatal crash.Crashrisk was foundto increasewith increasing BAC amongall of the six age and sex groupsstudied.At BACs in the 0.05-0.09 percentrange,the likelihoodof a crashwas at least ninetimesgreaterthanat zeroBAC for all agegroups.Younger drivers with BACsin the 0.05-0.09 rangehadhigherrelativerisksthan
N MOST U.S.jurisdictions, 0.10% blood alcohol con-
centration(BAC) is the typical thresholdset for the per se definitionof driving under the influence,and countermeasures aimedat alcohol-impaired drivinghavetraditionally targetedthesedriverswith high BACs (IIHS, 1987;
Williams, 1988).The percentage of fatally injureddrivers whose BAC
at the time
of the crash was at or above
0.10% declinedsteadilyfrom 48% in 1982to 39% in 1987 (IIHS, 1988). This declinerepresentsa remarkablereduction in the problemof alcohol-impaired drivingandattests to thecombined effectsof legalsanctions, mediacampaigns and reducedalcoholconsumption(Williams, 1988). The risk of crashinvolvementincreases steadilywith increasingdriver BAC and reacheshigh levelswell below 0.10% (Hurst, 1973; see also Moskowitz et al., 1985). About 11% of the fatally injured drivers (about 2,800) had BACs in the 0.01-0.09% range in 1986. In contrast to the decline in driver fatalities
at or above the 0.10%
threshold,the percentage of driverfatalitieswith positive BACs below it held steady between 1982 and 1987 (FARS, 1982-87). The proportionof BACs in this lower range is especiallyhigh among youngerdrivers and female drivers.Among 16-19 year old driversinvolvedin fatal crashesin 1986,about40% of thosewith a positive blood alcohol concentration had a BAC below 0.10%
(NHTSA, 1987). The comparablepercentagefor all fe-
Received:May 2, 1989.Revision:December9, 1989. *This work was supported by the InsuranceInstitutefor Highway Safety. 302
older drivers,and femaleshad higherrelative risksthan males.At very highBACs(at or above0.15 percent),the riskof crashing was 300 to 600 times the risk at zero or near-zero BACs. These relative
risk estimatesare considerably higherthan estimatedin otherstudies, but other studieshave based their estimates on all crashesrather
than single-vehicle crashesonly. In this study,relativeriskswere also lower when basedon driver fatalities in all crashes.However, whenplausibleassumptions were madeaboutthe BAC distributions of otherparticipantsin multiple-vehiclecrashes(whoseactualBAC is often unknown), the relative risks basedon the maximum BAC of
the crashparticipantswere nearly as high as thoseestimatedin single-vehiclecrashes.(J. Stud.Alcohol52: 302-310, 1991)
male driversin fatalcrashes,regardlessof age, was about 30%. In contrast,for maledriversin the 25-54 agegroup it was only about20%. Extensive research over the last three decades has demonstrated that the relative risk of involvement in motor
vehiclecrashesincreaseswith increasingdriver BAC regardlessof driverage, driver sex, crashtype or responsibility for the crash.The magnitudeof the relativerisk and the rate at whichit increases with increasing BAC depend on severalof thesefactors.Basedon driverfatalitydata from Canada,Mayhew and colleagues(1986) reported that at all BACs(includingzero) driversaged16-19 have higherrelative risks than older drivers and that the rate at whichthe risk increases with BAC is alsohigherfor the youngerage group(seealsoMayhew and Simpson,1983). There are no comparablydetailed investigations using U.S. driver fatality data. Borkenstein et al. (1974) investigated relativecrashrisk as a functionof BAC by driver age groupsfor policereportedcrashesin Grand Rapids, Mich., during 1962-
63. They reportedthat crashrisk increases steadilywith BAC in every age groupand the rate of increasevaried amongthe agegroupswith no systematic pattern.The relative crash risk as a function of BAC for males and fe-
males was also investigatedusing the samedata. Crash risk was reportedto increasewith driver BAC for both males and females,and femaleswere reportedto have higher crash risks than males in all but the 0.01-0.04% BAC range(in that rangethe risks were almostthe same for bothgroups).The interactionbetweenBAC anddriver sex was not investigated.
ZADOR
The relative crashrisk was reportedto increasemore rapidly with increasingdriver BAC in single-vehicle crashes than in all multivehicle
crashes or in multivehicle
crasheswith at-faultdrivers;it also increasedmore rapidly in multivehicle crasheswith at-fault drivers than in multivehiclecrasheswith driversnot at fault (Borkenstein
et al., 1974). The authorsexplaintheir findingby noting that, whencrashinginto anothervehicle,high BAC drivers tend to collide with vehiclesoperatedbY "drivers from the averagedriving population,who for the most part havelow or zero percentBACs" (p. 107). The relative crashrisk for drivers fatally injured in single-vehicle crashesprovidesa goodmeasureof the true contribution
of alcohol to increased risk of involvement
the serious crash. For multivehicle
in
crashes the situation is
more complicated. When the relative crash risk is esti-
matedfrom BAC datafor only the driverswho are fatally injured in multivehiclecrashes,the estimatesare for the
combinedrisk of beingfatally injuredeitheras a responsible agent or as an innocentvictim. Becausedata are commonlyavailablefor fatally injureddrivers,this combinedrisk canbe estimatedwith little difficulty;however, the risk of beingfatally injuredin sucha crashdoesnot measure the true contribution of alcohol to crash risk. For
example, in a two-car fatal crash involving one driver with a high BAC who survivesand a soberdriver who dies, using the BAC of the fatally injured soberdriver would indicate such a crash to be unrelated to alcohol.
Only when both drivers in a two-car fatal crashare tested can the actual contribution
of alcohol be determined.
For
fatal multivehicle crashes, the contribution of alcohol to
crashrisk dependsnotonly on the BACsof fatally injured drivers but on the BACs of all the drivers involved. How-
ever, BAC data for survivingdriversare not obtainedin enoughcasesto developa reliablesamplefor analysis. The studies reviewed here have examined the effect of to one factor at a
driver BAC on crash risk in relation
time (for additionalreviews seeHurst, 1973, Jonah, 1986,
andWarrenandSimpson,1980).The presentwork focuses on thejoint effectsof driverageanddriver sexon relative fatalityrisk as a functionof BAC in single-vehicle crashes. Someestimatesfor multivehiclecrashesare also generated for purposesof comparison.This studyis basedon U.S. data on fatally injuredpassengervehicledriversfor 1985 and 1986 obtainedfrom the Fatal AccidentReporting System(FARS) anddriverexposuredataobtainedfrom the 1986nationalroadsidebreath-testing survey(Lundand Wolfe, 1991). Method
Driver exposuredata
The second national roadsidebreath-testingsurvey (Lund and Wolfe, 1991) was conductedin 1986 through-
303
out the contiguousUnited Statesusinga controlledprobability sample of 34 localities chosento representthe almost90% of the populationthat lived in countieswith more than 20,000 inhabitantsin 1970 (Lund and Wolfe,
1991). i Thesurveys wereconducted onFridayandSaturday nightsfrom 10 PM to 3 AM using separateroadside sites from 10 PM-12 midnightand from 1-3 AM along heavyand mediumvolumeroads(exceptfreeways).Participationin the surveywas voluntaryand 2,850 or 92% of the 3,100 stoppeddriversprovidedsatisfactorybreath samples.Only drivers of passengervehicles (cars and light trucks,includingvans,pickupsand four-wheel-drive vehicles) were interviewed. The driver counts from this
survey (weighted to take into accountthe estimatesof drinking by noncooperating drivers, the traffic countsat the roadsidesites and the relative populationsof each of the 24 stratain the sample)providedthe exposuredata for the presentstudy. The weightedcountsof drivers were classifiedby driver age (16-20, 21-24 and 25+), driver sex, time of observation(10 PM-12 midnightand 1-3 AM) and driver BAC (0.00-0.01%, 0.02-0.04%, 0.05-0.09%, 0.10-0.14% and 0.15%+).
Driver fatality data
Driver fatalities occurringin the samepassengervehicle types included in the breath-testingsurvey were extractedfrom the FARS 1985and 1986data tapes.FARS is a computerizeddatabasecontainingvirtually all motor vehicle fatalities in the United Statesas reportedby state governmentsto the National Highway Traffic Safety Administration (NHTSA). To reduce the likelihood of a biased inferencedue to underreportingof driver BACs, the data were taken only from the 29 statesthat reportedthe BACs of at least 80% of fatally injureddriversto FARS driving 1985 and 1986 (Table 1). Also, to match driver fatalitiesto the roadsidebreath-testingsurveyexposureestimates,crashtimes anddayswererestrictedto thoseused for the survey,and crashesthat occurredon interstates, otherurbanfreewaysand expressways were excluded. Driver fatalities were classifiedby sex, age and time of the crashin the sameway as in the survey.The classification of driver BACs was as follows: 0.00-0.01%, TABLE1. StatesreportingBACsof at least80% of fatallyinjureddrivers to FARS
in 1985 and 1986
California
Kentucky
Colorado
Maine
New Mexico North Carolina
Connecticut
Maryland
Oregon
Delaware
Massachusetts
South Dakota
District of Columbia
Minnesota Montana
Utah Vermont
Hawaii Idaho Illinois Indiana
Nebraska Nevada New Hampshire New Jersey
Virginia Washington WestVirginia Wisconsin
304
JOURNAL
0.02-0.04%,
0.05- 0.09%, 0.10-0.14%,
OF STUDIES
0.15%+
ON ALCOHOL
and un-
known percent. This differs from the survey-basedexposure classificationin that the BACs of some of the fatally injured drivers were unknownand no secondaryinformation was availableto provide acceptableestimates.The drivers
with
unknown
BACs
were
eliminated
from
the
presentstudy.However,in stateswith very high levels of BAC reportingthere is little chancefor a systematicdifferencebetweenfatally injured driverswith knownBACs and fatally injured drivers with unknown BACs, so that eliminating the latter group is not likely to bias the results on the relative
risks of driver crash involvement
in rela-
tion to BAC.
Crasheswere classified into two types: crashesinvolving only the fatally injured driver and all other crashes. Most analyseswere restrictedto driver fatalitiesoccurring in the first categoryof crashes.
/ JULY
1991
5% level. All models fitted were hierarchical
in the sense
explainedin Bishop et al. (1975) so that when a factor was included in an interaction
term the main effects in-
cluded in that factor and certain other lower order interaction terms were also included in the model.
The model-based crash-rate estimates were used to cal-
culate relative risk. In one set of relative risk computations, drivers with BACs in the 0.00-0.01% range were chosen for the baseline. With this baseline choice, relative
risk measuresthe within-groupeffect of alcohol on the crash risk as a function of BAC. Within-grouprelative risk was estimatedfor the whole groupand for driversubgroupsdefinedin termsof age and sex. For another set of relative risk computations,male driversage 25 and over were chosenas the baseline.This groupwas chosenbecauseit is the largestamongthe six groupsin the study.With this baseline,relative risk measures the effect of age and sex differenceson the crash
Statisticalanalyses
rate when BAC is controlled for.
The intuitive idea behind the statistical analyses of thesedata is that the frequencyof fatalities amongcertain typesof driversrelative to the frequencyof similar drivers on the road (i.e., in the roadsidesurveys)is indicativeof how likely suchdriversmight be of receivinga fatal crash injury per unit of driving exposure.In other words, the relative frequencyof fatalities as comparedto the frequency of being included in the surveysis a measurefor fatality risk for a groupof drivers.By itself the numerical value of fatality risk cannot be interpretedbecausethis value dependson how extensivethe surveyswere: a larger survey would result in larger driver countsand smaller "risk." However, such risks can be validly compared amongdifferentgroupsof drivers and driversin high-risk groupscan be said to have higher risks of receivinga fatal crashinjury per unit of exposurethan driversfrom lower risk groups. For this study, driver fatalities divided by the correspondingweighted driver countsin the roadsidesurvey
Distribution of MBAC for drivers in two-vehiclecrashes
were termed
Partialjustificationfor this assumptionwas providedby Klein (1986) who comparedthe BAC distributionsof fatally injuredand survivingdriversinvolvedin fatal multivehiclecrashes.In 1985, 12%amongthesurvivingand10% amongthe fatally injured drivers had BACs in the 0.010.09% range (see Klein, 1986, Tables 14 and 15). The corresponding percentages during the sameyear were 31 and 28 for the 0.10% and over BAC range. (For 1984 the percentagesfor surviving drivers are somewhathigher.) The percentages providedby Klein are for all multivehicle crasheson all roadsand at all times and are not directly comparableto the percentagesin the presentstudy.
"crash
rates."
The size of one crash rate rel-
ative to the size of another crash rate can be used to com-
pare the risks measuredby the two crash rates. The numericalvaluethat resultsfrom this comparisonis called relativerisk. By definition,relativerisk is the ratio of one crashrate divided by anothercrashrate. The crashrate in the denominator
is called the baseline crash rate.
Crash rates were analyzed in terms of no more than four singlefactors(driverBAC, sex, age andtime of crash in relation to midnight) and their interactionsby fitting loglinearmodelsto the driver fatality and exposurecounts (seeAppendixI for details).The modelswere fitted using the maximum likelihood option offered by the loglinear modelingfacility (CATMOD) of SAS (1985). The phrase"the modelfit is adequate"meansthat the chi-squaretest basedon the residualsfrom the maximum likelihoodestimateswas not statisticallysignificantat the
The role of alcohol in two-vehicle
crashes should be es-
timated from the BACs of both drivers in the crash; un-
fortunately,the BACs of surviving drivers are often not known. However,undercertainstatisticalassumptions the distribution of the maximum BAC (MBAC) for drivers in
two-vehiclecrashescan be estimated.Specifically,if the BAC distributionof driverswho were fatally injuredand the BAC distribution
of drivers who survived in fatal two-
vehiclecrashesare statisticallyindependentand identical, then the common distributionof these surviving and fatally injureddriversis the sameas the BAC distributionof all driverswho werefatally injuredin two-vehiclecrashes. In this case, the MBAC distributionfunctionis simplythe squareof the BAC distributionfunction, and the rate of crashesby MBAC group was computedfrom the MBAC distributionthe sameway as the rate of crasheswas com-
putedfromtheBACdistribution byBACgroup. 2
Results
The relative driver fatality risk estimatesfor different BACs are displayedin Figure 1 for single-vehiclecrashes.
ZADOR
Using driverswith zero or near-zeroBAC as the baseline (i.e., relative risk is 1 for these drivers), the relative risks are 1.4 for BACs between 0.02-0.04%, 11.1 for BACs between 0.05-0.09%, 48 for BACs between 0.10-0.14% and about 380 for drivers with BACs at or above 0.15%.
Note that for positiveBACs the increasein relative risk with increasingBAC is approximatelylinear when plotted on the logscaleagainstthe midpointsof the BAC groups. For positive BACs, this relationshipcan be describedby the loglinearmodelgiven in Equation 1: In (RATE) = -3.26
(0.17)3
+ 32.68 BAC
305
TABLE2. Analysisof variancetable for the loglinearmodel of crash ratesin single-vehicle crashes
Intercept Age
df
X2
p
I 2
5.9 61.8
< .05 .05
Age x BAC
8
12.7
>.05
Sex x BAC
4
10.2
