United States General Accounting Office

GAO Report to Congressional Requesters

October 1994 HIGHWAY SAFETY

Factors Affecting

Involvement in Vehicle

Crashes

GAO/PEMD-95-3

GAO United States

General Accounting Office

Washington, D.C. 20548

Program Evaluation and

Methodology Division

B-256555 

October 27, 1994

The Honorable Ernest F. Hollings

Chairman, Committee on Commerce, Science, and Transportation

United States Senate

The Honorable Richard H. Bryan

Chairman, Subcommittee on Consumer

Committee on Commerce, Science, and Transportation

United States Senate

In our October 1991 report to you entitled Highway Safety: Have

Automobile Weight Reductions Increased Highway Fatalities?

(GAO/PEMD-92-1), we presented a number of findings regarding the

relationship between car weight and safety. Among other things, we found

the danger cited by some researchers and agency officials—that the

increase in lighter cars on the highways since the 1970’s would result in

dramatically higher highway death tolls—to be overstated and to have

excluded consideration of some important factors. One of these factors

was the lowered threat, from reductions in both weight and force of

impact, posed to other drivers on the road in multiple vehicle collisions.

At the time, we also reported that the safety effects of weight change or

any other automotive design factor could be confounded by many other

factors, chief among them driver attributes. For example, we discussed in

qualitative terms how a driver’s age could interact in different ways with

car size attributes. If it is true that younger drivers drive smaller cars and

also tend to drive more recklessly, then attributing the higher injury rates

in smaller cars simply to car size or weight might be misleading. However,

if it is true that elderly drivers drive larger cars and, if involved in a crash,

are more likely to be injured than younger drivers, then larger cars may

appear to be less safe than they really are.

Objectives, Scope,

and Methodology

You have requested that we investigate these relationships more

comprehensively and that we set the discussion of car size and safety into

the larger context of the relative contributions to highway safety of driver

attributes, vehicle characteristics, and their multiple interactions. Our

response to your request involved an investigation into two distinct, and

sometimes highly divergent, aspects of highway safety: crash involvement

and crashworthiness. The study of crash involvement focuses attention on

the factors likely to produce a crash. Crashworthiness, instead, examines

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B-256555 

the factors likely to produce serious injury, once a crash has occurred. The

present report deals with crash involvement—that is, with the driver or

vehicle characteristics that are related to the likelihood of a crash. The

attributes we examined included driver age, gender and driving history,

vehicle age and size (weight, wheelbase, and engine displacement). A

companion report will examine crashworthiness: the factors that affect the

likelihood of serious injury once a crash has taken place. A third report

will examine the relationship between automobile crashworthiness and

crash testing performed by the Department of Transportation.

In the present analysis, we have used a method known as “induced

exposure” to estimate the likelihood of crash involvement. This approach

assumes that not-at-fault drivers in two-vehicle accidents represent a

random selection of drivers and vehicles on the road. The ratio of at-fault

to not-at-fault drivers provides a measure of the relative involvement of

drivers and vehicles in accident causation. We used a data base containing

340,000 records, with details on accidents reported in North Carolina in

1990, to produce ratios of at-fault to not-at-fault North Carolina drivers.

Since these findings are based on data from only one state, they cannot be

generalized to the nation. However, we did compare the North Carolina

ratios to ratios we obtained from a Michigan data base and found the

figures to be close and the trends quite similar. This finding is consistent

with the logic of induced exposure—concerned with ratios of driver and

vehicle characteristics rather than their absolute numbers—and suggests

that the method may produce results that have more general applicability.

(See appendix I for a discussion of the induced exposure approach and

appendix II for descriptive statistics from North Carolina.)

Results in Brief We found that, when other factors are controlled for, driver characteristics

far outweigh vehicle factors in predicting crash involvement for passenger

cars. For example, the odds of a 20-year-old driver being involved in a

single-vehicle, nonrollover crash was over 4 times as great as that of a

50-year-old. By comparison, a 4,000-pound car was only 1.06 times as likely

to be involved in this type of crash as a 2,000-pound car. Similarly, drivers

with a history of previous traffic violations were more likely to be in a

crash, and men were more likely to be in single-vehicle crashes than

women. (Appendix III contains more detailed results of our passenger car

analyses.)

A car’s weight had little effect on the likelihood of a two-vehicle crash or a

single-vehicle crash that did not involve a rollover. However, light cars

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B-256555 

were as much as three times as likely to be involved in single-vehicle

rollover crashes as heavy cars. In other types of crashes, we found that

car-size measures other than weight (wheelbase or engine size) were

better predictors of crash involvement.

We found similar results when we applied our methodology to crashes

involving light trucks and vans. A driver’s age and violation history

significantly affected the likelihood of crash involvement for these types of

vehicles, as did vehicle age. In our analysis, however, driver gender did not

contribute significantly to the prediction of light truck and van crashes in

general (although it did in certain subcategories of these crashes). The

vehicle weight of the light trucks or vans was only a marginally significant

predictor. (Appendix IV contains more detailed findings.)

Our Analysis Any investigation of crash involvement must include more than counts of

units (vehicles or drivers). In order to calculate the relative odds of being

in a serious crash, it is necessary (but not sufficient) to compute, for

example, how many 1989 Ford Tauruses or how many 16-year-old males

are involved in serious crashes in a given time period. Without knowing

how many Tauruses or 16-year-old male drivers are on the road, we cannot

conclude whether these cars or these drivers are more or less likely than

other cars or drivers to be involved in crashes. We must, in other words,

know their exposure to crashes. For example, consider that it is generally

well known that, in absolute terms, elderly drivers are involved in fewer

serious crashes than younger drivers. But they also drive fewer miles, and

under less hazardous conditions, than younger drivers. In absolute terms,

therefore, elderly drivers pose a rather small highway safety problem.

When their relative exposure is considered, however, it turns out that, for

the miles they drive, elderly persons are disproportionately involved in

collisions, particularly two-vehicle collisions.

Crash exposure can be estimated in a number of ways. Vehicle exposure in

a given year is frequently measured by the number of vehicles registered.

Thus, in our previous report, we tracked the number of fatalities per

100,000 registered vehicles for different weight classes of cars. Driver

exposure can also be represented by a single count of the number of

licensed drivers in various categories (for instance, age groups or

geographic regions).

Such direct measures of exposure have serious limitations, however.

While we may know how many vehicles of a certain type are registered,

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B-256555 

we do not know how many miles (if any) and under what conditions they

are driven or by whom they are driven. If large cars are driven more miles,

and under more dangerous conditions, an estimate of crash involvement

based simply on the number of crashes per registered vehicle or even—if

such data were available—on crashes per mile driven would

underestimate their exposure and their safety.

For this reason, some researchers have turned to methods of estimating

exposure indirectly. For example, some calculate crash rates from a crash

data base as the ratio of at-fault to not-at-fault drivers of a certain type

(say, young females), arguing that the not-at-fault drivers serve as a

representative sample of drivers on the road—or “exposed”—under the

conditions represented by the data base. This method has the practical

advantage of allowing exposure estimates to be derived from the same

data base as the count of crashes and, arguably, the strategic advantage of

being more sensitive to the variations of driver and vehicle characteristics

than is possible with direct measures (see appendix I).

For this study, we employed such an indirect or “induced exposure”

method. We applied this method to the police-reported crash data base of

North Carolina for 1990 that was provided to us by researchers at the

University of North Carolina Highway Safety Research Center.1

 This data

base contains information on 183,616 crashes involving 484,258 individuals

and 325,277 vehicles.2

 We supplemented the crash data base by merging

with it information on the drivers’ history of previous traffic violations.

We performed separate logistic regression analyses of crash involvement

corresponding to three types of crashes (two-vehicle, single-vehicle

rollover, and single-vehicle nonrollover) and two types of

vehicles—(1) passenger cars and (2) light trucks and vans. Sixty-six

percent of the crashes in our analysis involved two vehicles, 29 percent

were single-vehicle nonrollovers, and 5 percent were rollovers. (Although

rollovers accounted for only a small proportion of crashes, this type of

crash is second only to frontal impacts in terms of deaths and injury

severity.) Sixty-eight percent of crashes involved passenger cars,

11 percent involved light trucks and vans, and 21 percent were between

1

At-fault drivers were defined as the drivers in two-vehicle collisions for whom the police report

indicated a violation. Collisions in which a violation was indicated for both drivers or for neither driver

(approximately 10 percent of all two-vehicle accidents) were excluded from the analysis.

2

Additional descriptive statistics on this data base are provided in appendix II. Because of missing data

points, particularly on vehicle weight, as well as our restriction of the analysis to one- and two-car or

light truck crashes, the effective data base for the individual analyses was substantially reduced. See

appendixes III and IV.

Page 4 GAO/PEMD-95-3 Highway Safety
B-256555 

cars and light trucks and vans. Appendix III presents the details of the

analyses of passenger cars, appendix IV the light truck and van results. We

present the main points here, first for passenger cars and, then, more

briefly, for light trucks and vans.

Passenger Cars

Driver Age We found no straight-line relationship between a driver’s age and crash

involvement. In general, drivers under 25 were at greatest crash risk,

followed by drivers over 65. The relationship was not the same for all

crash types. A 16-year-old driver was over seven times more likely to be in

a single-vehicle rollover crash, over five times more likely to be in a

single-vehicle nonrollover crash, and more than twice as likely to be in a

two-vehicle crash as was the safest driver overall—a 45-year-old.

Drivers least likely to be in a single-vehicle rollover crash were

62-year-olds. They were only one tenth as likely to be in such a crash as

16-year-olds. However, drivers in their mid-70s were about as likely as the

16-year-olds to become involved in a two-vehicle collision. As a driver’s

age approached 80 years, the likelihood of such involvement in a

two-vehicle collision increased sharply.

This was not true, however, of single-vehicle crashes. Elderly drivers were

more likely to be involved in single-vehicle nonrollovers than 40-year-olds

only after age 74 and in single-vehicle rollovers only after age 86. Figure 1

summarizes the effects of age by comparing each age’s odds of crash

involvement in each crash type with those of a 40-year-old’s.

Page 5 GAO/PEMD-95-3 Highway Safety
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Figure 1: Adjusted Odds Ratios Comparing Crash Involvement by Driver Agea

Odds

0

1

2

3

4

5

6

7

16 20 24 28 32 36 40 44 48 52 56 60 64 68 72

Driver Age

Two vehicle

Single, no rollover

Single, rollover

aThe odds ratios were calculated using the coefficients from the logistic regression equations

shown in appendix III, table III.2. The figures above compare the odds of crash involvement of

drivers of different ages to a 40-year-old driver, assuming all other factors included in the

equation are equal. The odds ratios tell how much more (or less) likely the outcome is in one

group versus the comparison group of 40-year-old drivers. An odds ratio of 1.0 means that there

is no difference between two groups in their odds of crash involvement. Values higher than 1.0

mean greater risk; values lower than 1.0 mean less risk.

Violation History Driving history was a strong predictor of crash involvement for two-car

and single-car crashes, ranking second only to driver age. A history of

alcohol-related convictions was a particularly powerful predictor. For

example, drivers with histories of nonalcohol traffic violations were only

1.15 times as likely to be involved in a single-car nonrollover crash as

drivers with a “clean” history. However, drivers with a history of drunk

driving were at least 3.7 times as likely as other drivers to be involved in

such a crash.

Page 6 GAO/PEMD-95-3 Highway Safety
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For two-car crashes, driving history was also a significant but less

powerful predictor. Drivers with prior alcohol violations were 2.1 times as

likely to be involved in a two-vehicle collision as drivers with no prior

violations and 1.6 times as likely as drivers with nonalcohol violations.

Driver Gender As noted earlier, driver gender affected the likelihood of involvement in

single-vehicle crashes only. Males were twice as likely as females to be

involved in either type of single-vehicle crash. Female drivers were

indistinguishable from male drivers in their likelihood of being involved in

a two-car collision.

Vehicle Age We introduced the age of vehicles into our model as a way of correcting

for the possibility that we might confuse the safety effect of a vehicle size

with that of its condition. As our earlier report found, passenger cars have

become, on the average, much lighter than they were in the 1970’s. Heavier

cars, therefore, are more likely to be older cars and, presumably, to be in

poorer condition. An analysis that did not control for this association

would be in danger of overestimating the crash involvement of heavy cars.

Half of the cars in our data base were model year 1984 or newer, and

80 percent were built after 1978. We found that, regardless of size, newer

cars were slightly less at risk for crash involvement. For example, if one

car were 5 years older than another, the older car would have a risk 1.12

times that of the newer. We cannot tell, however, whether this difference

stems from the deteriorated condition of the older car or the improved

design of the newer car.

It should also be noted that (as the Department of Transportation (DOT)

pointed out in its comments on a draft of this report) vehicle age may

capture the effect of more than simply vehicle characteristics. Older cars

may have more aggressive drivers and are more likely to be found in rural

settings.

Car Weight Car size can be expressed by different measures: wheelbase (the distance

between the front and rear axles), track width (the distance between the

left and right wheels), engine size, weight, and so on. Because all these

variables tend to be very highly correlated with one another, it is

frequently difficult to distinguish statistically their unique effects. It seems

reasonable to believe that each of these factors has a differential effect on

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the likelihood of being involved in different types of crashes.3 In one

research report, for example, the National Highway Traffic Safety

Administration (NHTSA) found that a combination of track width and center

of gravity was the best predictor of vehicle rollover.4

We developed three sets of models corresponding to the three measures of

car size readily available to us: wheelbase, weight, and engine

displacement. The full results of these analyses are in appendix V. Here we

are concerned with the relationship between car weight and crash

involvement.5

 Figure 2 summarizes this relationship by comparing the

odds for cars of different weights with the odds for a 2,678-pound car (the

median car weight in the sample) of being in a crash (for each of the three

crash types).

3

Our separate analyses of the contributions of weight, wheelbase, and engine size lend support to this

hypothesis. In predicting the likelihood of a single-vehicle nonrollover crash, engine size appeared to

be most important; for single-vehicle rollovers, wheelbase was most important; and weight contributed

more to the prediction of two-vehicle crashes than either of the other two. Overall, however, it is

important to note that, relative to that of driver-related measures, the contribution of the vehicle size

measures is substantially less (see appendix V).

4

P. Mengert et al., Statistical Estimation of Rollover Risk, DOT-HS-807-489 (Washington, D.C.: National

Highway Traffic Safety Administration, 1989).

5

All vehicle size measures (wheelbase, weight, and engine displacement) were provided as part of the

North Carolina data base and were derived from decoding vehicle identification numbers using R. L.

Polk & Co.’s VINA program.

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Figure 2: Adjusted Odds Ratios Comparing Crash Involvement by Car Weighta

Odds

0

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

Vehicle Weight (in hundreds of pounds)

Two vehicle

Single, no rollover

Single, rollover

aThe odds ratios were calculated using the coefficients from the logistic regression equations

shown in appendix IV, table IV.2. The figures above compare the odds of crash involvement of

vehicles of different weights to a vehicle at the median weight of 2,678 pounds, assuming all other

factors included in the equation are equal. The odds ratios tell how much more (or less) likely the

outcome is in one group versus the comparison group of cars at the median weight. An odds ratio

of 1.0 means that there is no difference between two groups in their odds of crash involvement.

Values higher than 1.0 mean greater risk; values lower than 1.0 mean less risk.

For each crash type, weight had a statistically significant effect, but the

effect was quite small for two-vehicle crashes and for single-vehicle

crashes where a rollover did not occur. The odds ratio curves for these

two crash types are almost mirror images of each other. The lightest and

the heaviest cars were slightly more likely to be involved in two-vehicle

crashes than were midweight cars and slightly less likely to be involved in

single-vehicle nonrollover crashes.

The connection between car weight and rollover crashes, however, was

substantially stronger. The lighter the car, the greater were its odds of

rolling over. For example, the average 2,000-pound car was nearly three

Page 9 GAO/PEMD-95-3 Highway Safety
B-256555 

times as likely to be involved in a single-vehicle rollover crash as the

average 4,500-pound car.

This finding needs some qualification. Factors other than car weight are

probably more directly related to rollover propensity but, as we noted

earlier, the high intercorrelation of the various measures of car size make

the relationships difficult to disentangle statistically. When we used car

size measures other than weight in our analyses, we found a stronger

connection with rollover likelihood for wheelbase than for weight. (See

appendix V.) Research by NHTSA has demonstrated that rollover propensity

is related to several other vehicle factors, such as track width, weight

distribution, and braking stability.6

Light Trucks and Vans Our analysis of the crash involvement probability of light trucks and vans

yielded many of the same findings as our analysis of passenger cars. Full

details of the analysis are presented in appendix IV. Driver age and driving

history remained by far the best predictors of crash involvement. Drivers

involved in single-vehicle light truck crashes were one-and-a-quarter to

one-and-a-third times more likely to be male. However, whereas for

passenger cars driver gender appeared to be irrelevant to involvement in

two-vehicle collisions, women were slightly but significantly more likely to

be involved in a light truck two-vehicle collision than were men.

As with passenger cars, the vehicle factors were much less important than

the driver factors. However, older light trucks were significantly more

likely to be involved in all types of crashes. The relationship between light

truck weight and crash involvement was weaker than for passenger cars.

We found no relationship in two-vehicle crashes and only a marginally

significant relationship in single-vehicle crashes. The connection between

light truck weight and crash involvement was relatively strongest for

rollover crashes. As with passenger cars, the lightest of these vehicles

were more likely to roll over. However, all three alternative measures of

size again contributed relatively little to predictions of crash involvement,

and vehicle weight ranked either second or third among the size measures

in all light truck models. (See appendix V.)

6

We cited some of this research in earlier testimony before your committee when we reported that the

greater likelihood of lighter cars to roll over could be offset by a very small increase in track width.

See U.S. General Accounting Office, Automobile Weight and Safety, GAO/T-PEMD-91-2 (Washington,

D.C.: April 11, 1991).

Page 10 GAO/PEMD-95-3 Highway Safety
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Summary We developed models to predict the likelihood of crash involvement for

passenger cars and for light trucks and distinguished between three

different crash types: two-vehicle crashes, single-vehicle nonrollover

crashes, and single-vehicle crashes involving a rollover. We used driver

age, gender, and traffic violation history, as well as vehicle age and weight.

The six models we developed, while varying somewhat from one another,

provided a relatively consistent rank order of predictive importance for

these factors.

Among our findings, the following five may be the most significant. First,

information about the driver variables was much more important than

information about the vehicle variables in any of our estimates of the

relative likelihood of being in a traffic crash. Second, within the driver

variables we considered, a driver’s age was the strongest predictor,

followed (in most models) by the driver’s violation history and then by

gender. Third, of the two-vehicle variables we considered, vehicle age

contributed substantially more to our prediction of crash involvement than

did vehicle weight. Fourth, we modified our models slightly by substituting

other vehicle dimensions (wheelbase and engine size) for vehicle weight

and found that, of our six specific crash type models, five were predicted

better by these alternative measures than by weight.

Fifth and finally, we conclude that the induced exposure methodology we

demonstrated in our analysis offers reasonable expectation of yielding

results substantially more sensitive to the real world driving environment

than can be achieved through currently available direct exposure methods

without incurring prohibitive data collection costs.

Our work was performed in accordance with generally accepted

government auditing standards.

We have provided draft copies of this report to NHTSA officials and

discussed the study results with them. NHTSA also provided us with written

comments on the draft report. These comments and our response are

provided in appendix VI. We have incorporated their suggestions where

appropriate. We plan no further distribution of this report until 30 days

from the date of issue, unless you publicly announce its contents earlier.

We will then send copies to the Secretary of Transportation. We will also

make copies available to interested organizations, as appropriate, and to

others upon request.

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If you have any questions or would like additional information, please call

me at (202) 512-3092. Other major contributors to this report are listed in

appendix X.

Kwai-Cheung Chan

Director of Program Evaluation in

 Physical Systems Areas

Page 12 GAO/PEMD-95-3 Highway Safety
Page 13 GAO/PEMD-95-3 Highway Safety
Contents

Letter 1

Appendix I 

Induced Exposure

18

Appendix II 

The North Carolina

Data File

23

Appendix III 

Logistic Regression

Analysis for

Passenger Car Crash

Involvement

25

Appendix IV 

Logistic Regression

Analysis for Light

Truck and Van Crash

Involvement

27

Appendix V 

Alternative

Definitions of Vehicle

Size

29

Appendix VI 

Comments From the

Department of

Transportation

31

Page 14 GAO/PEMD-95-3 Highway Safety
Contents

Appendix VII 

Logistic Regression

Analysis Including

Roadway

Characteristics:

Passenger Cars

40

Appendix VIII 

Logistic Regression

Analysis Including

Roadway

Characteristics: Light

Trucks and Vans

42

Appendix IX 

Predicting Rollover

Versus No Rollover

Among Single-Vehicle

Accidents

44

Appendix X 

Major Contributors to

This Report

46

Tables Table I.1: Ratio of At-Fault to Not-at-Fault Drivers: Michigan 1987

and North Carolina 1990

19

Table I.2: Comparative Estimates of Exposure From the NPTS of

Vehicle Miles Traveled and Not-at-Fault Drivers From North

Carolina, 1990

21

Table II.1: Number of Records 23

Table II.2: Types of Accidents 24

Table III.1: Number of Cases and Model Chi-Squares 25

Table III.2: Parameter Estimates 26

Table IV.1: Number of Cases and Model Chi-Squares 27

Page 15 GAO/PEMD-95-3 Highway Safety
Contents

Table IV.2: Parameter Estimates 28

Table V.1: Change in –2 Log Likelihood From Base Model Using

Alternative Measures of Vehicle Size: Passenger Cars

29

Table V.2: Change in –2 Log Likelihood From Base Model Using

Alternative Measures of Vehicle Size: Light Trucks

30

Table VII.1: Number of Cases and Model Chi-Squares 40

Table VII.2: Parameter Estimates 41

Table VIII.1: Number of Cases and Model Chi-Squares 42

Table VIII.2: Parameter Estimates 43

Table IX.1: Number of Cases and Model Chi-Squares 44

Table IX.2: Parameter Estimates 45

Figures Figure 1: Adjusted Odds Ratios Comparing Crash Involvement by

Driver Age

6

Figure 2: Adjusted Odds Ratios Comparing Crash Involvement by

Car Weight

9

Abbreviations

DOT Department of Transportation

GAO General Accounting Office

NHTSA National Highway Traffic Safety Administration

NPTS National Personal Transportation Survey

Page 16 GAO/PEMD-95-3 Highway Safety
Page 17 GAO/PEMD-95-3 Highway Safety
Appendix I 

Induced Exposure

The use of indirect methods to estimate the risk of being involved in a

highway crash, variously referred to as “induced” or “quasi-induced”

exposure, dates back at least to the 1960’s. The method is based on

calculating the ratio of at-fault drivers or vehicles to not-at-fault drivers or

vehicles in two-vehicle accidents contained in police accident reports. Its

underlying assumption is that the not-at-fault drivers and vehicles

constitute a representative sample of the drivers, vehicles, and driving

conditions and their interactions for the geographical area being

examined.

On the assumption that not-at-fault drivers represent the general

population of drivers, the ratio of at-fault to not-at-fault drivers yields an

estimate of the over- or underinvolvement of different levels of that

dimension in highway crashes. R. W. Lyles et al. offer an example of

estimating how much male drivers are overrepresented in interstate

highway accidents.1

 In 1988, 11,335 pairs of drivers were involved in

two-vehicle accidents in which fault was assigned on Michigan interstate

highways. Of the at-fault drivers, 8,366 (73.8 percent) were male, whereas

only 7,528 (66.4 percent) of not-at-fault drivers were male. Males were 1.1

times (73.8/66.4) overinvolved in interstate accidents relative to their

presence on these highways. Females, however, represented 26.2 percent

of at-fault drivers and 33.6 percent of not-at-fault drivers. Their

“involvement ratio,” therefore, was 0.78 (26.2/33.6). Lyles et al. conclude,

therefore, that when the calculation is adjusted for exposure, males

caused interstate highway accidents at a rate 1.4 (1.1/0.78) times that of

females.2

This indirect approach has a number of advantages. Foremost among them

is the ability to define accident exposure in terms of any driver, roadway,

or vehicle characteristic reported in the accident data base being used. For

example, given a sufficiently large data base, a researcher could estimate

the crash involvement risk of female drivers under 25 years of age on rural

roads in the dark and could determine whether female drivers are more

likely than males to become involved in accidents under such conditions.

1

R. W. Lyles et al., “Quasi-induced Exposure Revisited,” Accident Analysis and Prevention, 23:4 (1991),

275-85.

2

Another indirect measure of exposure has been used by Leonard Evans in examining the effects of car

size. Instead of using the not-at-fault driver, Evans bases his exposure measure for single-vehicle

crashes on the fatally injured pedestrian and estimates exposure for single-vehicle crashes from the

ratio of driver fatalities to pedestrian fatalities. His reasoning is that pedestrian fatalities associated

with a given type of vehicle or driver involved in a single vehicle accident will increase in relation to

the number of vehicles or drivers of that type on the road. See Leonard Evans, Traffic Safety and the

Driver (New York: Van Nostrand Reinhold, 1991).

Page 18 GAO/PEMD-95-3 Highway Safety
Appendix I 

Induced Exposure

Any attempt to measure exposure directly, at this level of detail, would be

prohibitively expensive.

Two major uncertainties are associated with induced exposure measures,

however. The first is common to any state or regional data base and

involves whether the data being used to form estimates adequately

represent other geographical areas and, hence, the universe to which they

are being extrapolated. In the case of induced exposure, the concern is not

that the absolute count within subcategories of drivers of vehicles may

vary from state to state—that is, that there might be, for example, more

light trucks or more elderly drivers in one state than another. (This is most

likely the case.) Rather, we are concerned with the ratios of at-fault to

not-at-fault drivers, however the absolute counts may vary geographically.

It is assumed that these ratios would be less prone to substantial variation

from one area to another. In other words, it is much less probable that

light trucks or elderly drivers have different driving-related attributes from

one state to another than that their numbers vary geographically.

Nevertheless, to test the seriousness of this concern, we compared by age

and gender the accident involvement ratios we obtained from the 1990

North Carolina data base we used for our study with ratios we calculated

from a data base of police-reported accidents in Michigan in 1987. In both

cases, we looked strictly at two-vehicle accidents in which only one driver

was considered at fault. The results are presented in table I.1.

Table I.1: Ratio of At-Fault to

Not-at-Fault Drivers: Michigan 1987

and North Carolina 1990

Michigan North Carolina

Age Male Female Male Female

Under 25 1.43 1.21 1.38 1.19

25-34 0.90 0.76 0.90 0.78

35-44 0.69 0.65 0.75 0.68

45-54 0.69 0.68 0.72 0.68

55-64 0.75 0.87 0.87 0.93

65-74 1.04 1.33 1.32 1.41

Over 75 2.25 2.73 2.92 2.91

While there is not absolute agreement between the involvement ratios

derived from the two data bases (the greatest discrepancy being between

the results for the oldest, male drivers), the figures are quite close and the

trends are remarkably similar.

Page 19 GAO/PEMD-95-3 Highway Safety
Appendix I 

Induced Exposure

The second uncertainty associated with the use of induced exposure is

potentially more serious and is less easily tested. Threats to the validity of

these estimates have been suggested, in particular the possibility of

systematic bias. It is possible that certain driver or vehicle types are more

likely to be identified by police as being at fault in a two-vehicle accident.

For example, in an ambiguous situation the police may be more inclined to

place blame on a young driver. On a different plane, it is possible that the

not-at-fault driver in a two-car accident is not totally without blame. This

driver’s ability to avoid accidents may be less than average; hence, he or

she may be more “accident-prone.” To the extent that accident-proneness

exists, the not-at-fault population less than perfectly represents of the

universe of drivers and vehicles.

The existence of such a bias cannot be tested directly, but indications of

whether its existence effectively distorts the estimates derived from

induced exposure methods can be tested both by comparisons internal to

the data base and by comparing the estimates with those derived from

direct exposure measurements. Lyles et al. used internal tests to determine

whether discernible bias entered their estimates. They reasoned that, if

not-at-fault drivers represent drivers on the road, we should find variations

in their characteristics that are related to different driving conditions. For

example, we know from direct observation that drivers on major freeways

are less likely to be female than drivers on more local roads. Induced

exposure findings should be consistent with observation and, in fact, Lyles

et al. found that 63 percent of not-at-fault drivers on U.S.-numbered routes

in Michigan were male, as opposed to 57 percent on local streets.

Furthermore, male at-fault drivers should strike approximately the same

proportion of male not-at -fault drivers as do female at-fault drivers. This

turned out to be the case. On U.S.-numbered routes, male at-fault drivers

struck male drivers 63 percent of the time and females 37 percent of the

time. Female at-fault drivers struck male drivers 62 percent of the time and

females 38 percent of the time.

Lyles et al. offer a series of similar crosschecks for the mutual

independence of the at-fault and not-at-fault populations across a variety

of conditions, including different roadway types, years, times of day, and

driver age categories. While there were wide variations in the distribution

of driver characteristics among different driving conditions, different

subsets within the same condition yielded nearly identical estimates of

exposure.

Page 20 GAO/PEMD-95-3 Highway Safety
Appendix I 

Induced Exposure

Comparisons with estimates formed from direct exposure methods are

less straightforward. We can, for example, obtain the distribution of

licensed drivers by gender from any state. However, we know that this

provides a biased estimate of drivers on the road. Using the Department of

Transportation’s (DOT’s) 1990 National Personal Transportation Survey

(NPTS), we found that over 15 percent of all women licensed drivers over

age 75 had not driven at all in the previous year (as contrasted with less

than 1 percent of licensed women drivers between 25 and 34).

NPTS itself is perhaps our most comprehensive direct exposure source, and

it is particularly valuable in discerning trends in travel habits in the United

States over time. Yet, besides being subject to the weaknesses of human

recollection, it is relatively insensitive to the quality of driving exposure.

While its estimates of miles driven by respondents may be quite reliable, it

cannot estimate the portion of miles driven under different conditions to

the level of detail that, arguably, an induced exposure method can.

Nevertheless, comparisons of induced exposure results with those derived

from more direct methods are informative. Accordingly, we compared our

estimates of age and gender distribution with those from NPTS. The

comparisons are presented in table I.2 in terms of the percentage of

vehicle miles driven (from NPTS) and the percentage of exposure to

accidents as derived from our data.

Table I.2: Comparative Estimates of

Exposure From the NPTS of Vehicle

Miles Traveled and Not-at-Fault Drivers

From North Carolina, 1990

Vehicle miles driven: NPTS Induced exposure estimates

Age Male Female Male Female

Under 25 8.01% 5.91% 14.01% 12.11%

25-34 18.30 10.14 13.81 13.25

35-44 16.69 9.46 10.40 10.01

45-54 10.46 4.78 6.36 5.51

55-64 6.87 2.92 4.58 3.48

65-74 3.29 1.61 2.90 2.05

Over 74 1.13 0.43 0.92 0.62

Overall 64.75% 35.25% 52.98% 47.03%

A comparison of the estimates of vehicle miles driven and of accident

exposure illuminates the differences between the two measures. Put

simply, not all miles are equal. It has been demonstrated that men tend to

drive substantially more freeway miles than women and that freeway miles

are the safest of all miles driven. These considerations are reflected in the

Page 21 GAO/PEMD-95-3 Highway Safety
Appendix I 

Induced Exposure

substantial difference between the overall gender distribution estimates

derived from the two measures.3

 While men may drive nearly twice as

many miles as women (65 percent versus 35 percent of all miles; see table

I.2), these are more often highway miles and, thus, are substantially safer,

with the result that their accident exposure is only moderately higher than

women’s using the induced exposure approach. Similarly, young drivers

drive fewer miles than middle-aged drivers, but their miles are

considerably more dangerous both because of their timing (nights and

weekends) and because of driver inexperience and risk-taking behavior.

These relationships are shown in table I.2: using the induced exposure

method, men age 45-54 represent 6 percent of the population at risk while

men under 25 have twice the exposure (14 percent), whereas using NPTS

the percentages are only slightly different.

In summary, the induced exposure method offers a means of estimating

the relative risks of different types of drivers, vehicles, and driving

conditions at a level of refinement that cannot be approximated in practice

by any direct measurement technique. It yields summary estimates of

exposure that differ from the global estimates of direct measures such as

vehicle miles traveled, but the differences appear to be reasonable in view

of the larger number of factors taken into consideration by the induced

exposure method. Its estimates of relative risk appear to be quite stable

across different geographic, driver, vehicle, and roadway conditions. In

classic measurement terms, while the method’s predictive validity has not

been empirically demonstrated, evidence exists to support its reliability

and construct validity. Its practical utility is beyond question.

3

NPTS estimates do not exclude miles driven in commercial vehicles other than passenger cars, a fact

that would also inflate the difference in estimates since presumably more men than women drive such

vehicles.

Page 22 GAO/PEMD-95-3 Highway Safety
Appendix II 

The North Carolina Data File

The data set for our analysis was created from data tapes, provided by

North Carolina’s Division of Motor Vehicles, containing information on

accidents in North Carolina for calendar year 1990. The information is

derived from accident report forms filled out by investigating officers at

accident scenes. The Highway Safety Research Center at the University of

North Carolina added technical information concerning vehicles (such as

vehicle weight, wheelbase, and engine size), which was obtained by

decoding the vehicle identification numbers recorded on the accident

forms. We also merged information, collected by the Division of Motor

Vehicles, on drivers’ violation histories.

The data file contained one record for each individual unit (vehicle,

pedestrian, bicyclist, and so on) involved in the accident. Table II.1

provides counts of the types of individual records that were contained in

the North Carolina file. Table II.2 provides the distribution of accident

types in the data base. For the purposes of the current study, an accident

was considered a single- or two-vehicle accident on the basis of the count

of the number of in-motion, motorized vehicles involved. We excluded the

accident category labeled “Other” in table II.2, which may contain singleor two-vehicle accidents if the type of vehicle involved was not reported or

was a heavy truck, bus, or farm vehicle. The “Other” category also

contains accidents with three or more in-motion vehicles.

Table II.1: Number of Records

Record type Number

Moving vehicles 309,409

Parked vehicles 15,868

Pedestrians or bicyclists 3,747

Type not stated 11,118

Total 340,142

Page 23 GAO/PEMD-95-3 Highway Safety
Appendix II 

The North Carolina Data File

Table II.2: Types of Accidents

Frequency Percent

Cumulative

percent

Single vehicle

Nonrollover

Passenger cars 33,680 18.3% 18.3%

Light trucks and vans 9,780 5.3 23.7

Rollover

Passenger cars 5,398 2.9 26.6

Light truck and vans 2,435 1.3 27.9

Two vehicle

Passenger cars 63,674 34.7 62.6

Trucks and vans 4,414 2.4 65.0

Cars, trucks, and vans 32,211 17.5 82.6

Other 32,024 17.4 100.0

Total 183,616 100.0%

Page 24 GAO/PEMD-95-3 Highway Safety
Appendix III 

Logistic Regression Analysis for Passenger

Car Crash Involvement

The outcome variable for the logistic regression equations was a

dichotomous indicator of fault, coded “1” for at-fault and “0” for

not-at-fault drivers. For all the equations presented here, both single- and

two-vehicle accidents, the comparison group is not-at-fault drivers in

two-vehicle accidents.1

 A driver was considered at fault if the investigating

police officer checked one or more violations in the checklist provided on

the North Carolina accident report form. (In two-vehicle accidents, cases

were excluded if no violation was reported for either driver or if both

drivers had violations.)

The independent variables included

• driver age, including a squared term to capture the curvilinear relationship

between age and accident involvement;

• driver gender, with males coded “1” and females coded “0”;

• driver violation history, with four mutually exclusive categories: no

previous traffic violations, one or more previous violations not involving

alcohol, at least one alcohol violation (may also include nonalcohol

violations), and violation history unknown (all out-of-state drivers and

some North Carolina drivers are in this category). In the models shown,

the three categories given are in contrast to the group having

alcohol-related violations;

• vehicle age, last two digits of the vehicle model year;

• vehicle curb weight, expressed in hundreds of pounds and including a

squared term to capture the curvilinear relationship between vehicle

weight and accident involvement.

Table III.1: Number of Cases and Model

Chi-Squares Single vehicle

Accident type All Two vehicle Nonrollover Rollover

At fault 64,904 50,824 11,222 2,858

Not at fault 51,499 51,499 51,499 51,499

Total 116,403 102,323 62,721 54,357

Model chi-square 5,655.178 4,137.856 5,524.596 2,546.841

Model degrees of

freedom 9 9 9 9

1

Using not-at-fault drivers in two-vehicle accidents as the exposure group for single-vehicle accidents

can be justified as long as there is a control for factors known to discriminate between the two

accident types. Our models incorporated the strongest of the predictors of single- versus two-vehicle

accidents in our data base: driver age and driver gender. See R. W. Lyles, “Quasi-induced Exposure: To

Use or Not to Use?” presented at the Transportation Research Board annual meeting, January 10, 1994,

p. 4.

Page 25 GAO/PEMD-95-3 Highway Safety
Appendix III 

Logistic Regression Analysis for Passenger

Car Crash Involvement

Table III.2: Parameter Estimates

All Two vehicle Nonrollover Rollover

Single vehicle

Variable Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob.

Constant 5.1503 .1518 .0000 4.2265 .1603 .0000 4.2161 .2652 .0000 5.2564 .4748 .0000

Driver age –0.1080 .0019 .0000 –0.0970 .0020 .0000 –0.1245 .0036 .0000 –0.1374 .0074 .0000

Age squared 0.0012 .0000 .0000 0.0011 .0000 .0000 0.0011 .0000 .0000 0.0011 .0001 .0000

Male 0.1219 .0125 .0000 –0.0004 .0132 .9735 0.6126 .0232 .0000 0.6790 .0425 .0000

Nonalcohol

violationa

–0.7582 .0391 .0000 –0.4929 .0425 .0000 –1.3094 .0509 .0000 –1.3960 .0823 .0000

No violation –0.9993 .0388 .0000 –0.7515 .0422 .0000 –1.4489 .0505 .0000 –1.4180 .0817 .0000

Violation unknown –0.6632 .0423 .0000 –0.2983 .0455 .0000 –1.6481 .0612 .0000 –1.7720 .1035 .0000

Vehicle year –0.0227 .0014 .0000 –0.0193 .0015 .0000 –0.0332 .0025 .0000 –0.0257 .0044 .0000

Vehicle weightb –0.0135 .0072 .0586 –0.0211 .0075 .0051 0.0448 .0130 .0006 –0.0974 .0256 .0001

Vehicle weight

squared

0.0002 .0001 .1304 0.0003 .0001 .0105 –0.0007 .0002 .0027 0.0008 .0005 .0780

aContrast group for violations is “Has alcohol violation.”

bVehicle weight is calibrated in hundredweights.

Page 26 GAO/PEMD-95-3 Highway Safety
Appendix IV 

Logistic Regression Analysis for Light Truck

and Van Crash Involvement

The outcome variable for the logistic regression equations was a

dichotomous indicator of fault, coded “1” for at-fault and “0” for

not-at-fault drivers. For all the equations presented here, both single- and

two-vehicle accidents, the comparison group is not-at-fault drivers in

two-vehicle accidents.1

 A driver was considered at fault if the investigating

police officer checked one or more violations in the checklist provided on

the North Carolina accident report form. (In two-vehicle accidents, cases

were excluded if no violation was reported for either driver or if both

drivers had violations.)

The independent variables included

• driver age, including a squared term to capture the curvilinear relationship

between age and accident involvement;

• driver gender, with males coded “1” and females coded “0”;

• driver violation history, with four mutually exclusive categories: no

previous traffic violations, one or more previous violations not involving

alcohol, at least one alcohol violation (may also include nonalcohol

violations), and violation history unknown (all out-of-state drivers and

some North Carolina drivers are in this category). In the models shown,

the three categories given are in contrast to the group having

alcohol-related violations;

• vehicle age, last two digits of the vehicle model year;

• vehicle curb weight, expressed in hundreds of pounds and including a

squared term to capture the curvilinear relationship between vehicle

weight and accident involvement.

Table IV.1: Number of Cases and

Model Chi-Squares Single vehicle

Accident type All Two vehicle Nonrollover Rollover

At fault 11,782 8,457 2,314 1,011

Not at fault 8,609 8,609 8,609 8,609

Total 20,391 17,066 10,923 9,620

Model chi-square 868.5668 553.830 772.251 624.847

Model degrees of

freedom

9 9 9 9

1

Using not-at-fault drivers in two-vehicle accidents as the exposure group for single-vehicle accidents

can be justified as long as there is a control for factors known to discriminate between the two

accident types. Our models incorporated the strongest of the predictors of single- versus two-vehicle

accidents in our data base: driver age and driver gender. See R. W. Lyles, “Quasi-induced Exposure: To

Use or Not to Use?” presented at the Transporation Research Board annual meeting, January 10, 1994,

p. 4.

Page 27 GAO/PEMD-95-3 Highway Safety
Appendix IV 

Logistic Regression Analysis for Light Truck

and Van Crash Involvement

Table IV.2: Parameter Estimates

All Two vehicle Nonrollover Rollover

Single vehicle

Variable Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob.

Constant 5.7770 .4990 .0000 3.9962 .5324 .0000 6.6988 .8479 .0000 7.4987 1.1664 .0000

Driver age –0.1156 .0050 .0000 –0.1027 .0053 .0000 –0.1243 .0084 .0000 –0.1490 .0128 .0000

Age squared 0.0012 .0001 .0000 0.0012 .0001 .0000 0.0011 .0001 .0000 0.0013 .0002 .0000

Male –0.0017 .0406 .9666 –0.0871 .0432 .0439 0.2296 .0724 .0015 0.3135 .1053 .0029

Nonalcohol

violationa

–0.6092 .0748 .0000 –0.3487 .0825 .0000 –1.0389 .0999 .0000 –1.1448 .1317 .0000

No violation –0.8209 .0739 .0000 –0.5608 .0817 .0000 –1.2493 .0991 .0000 –1.2542 .1308 .0000

Violation unknown –0.5173 .0866 .0000 –0.1756 .0941 .0621 –1.1973 .1268 .0000 –1.2777 .1709 .0000

Vehicle year –0.0233 .0034 .0000 –0.0191 .0036 .0000 –0.0370 .0056 .0000 –0.0363 .0080 .0000

Vehicle weightb –0.0387 .0220 .0789 –0.0120 .0233 .6069 –0.0676 .0387 .0806 –0.1238 .0551 .0246

Vehicle weight

squared

0.0006 .0003 .0501 0.0004 .0003 .2955 0.0008 .0006 .1587 0.0014 .0008 .0851

aContrast group for violations is “Has alcohol violation.”

bVehicle weight is calibrated in hundredweights.

Page 28 GAO/PEMD-95-3 Highway Safety
Appendix V 

Alternative Definitions of Vehicle Size

Models containing three alternative definitions of vehicle size were fitted

to the data. These were vehicle weight (in hundreds of pounds), engine

size (displacement expressed in cubic inches), and wheelbase (the

distance between the axles in inches). To allow comparisons of their

relative importance in predicting crash involvement, the improvement in

goodness of fit for each model over the base model (including driver age,

violation history, gender, and vehicle age) is presented in tables V.1 and

V.2.1

As noted in the text, (1) with the exception of single-car rollovers,

contributions to the model, though statistically significant in most cases,

are small in comparison to most variables in the base model, and

(2) different definitions are stronger depending upon the crash type being

predicted.

Table V.1: Change in –2 Log Likelihood

From Base Model Using Alternative

Measures of Vehicle Size: Passenger

Cars

Change in –2

log likelihood

Degrees of

freedom Probability

All crash types

Weight 9.607 2 .0082

Engine size 6.095 2 .0475

Wheelbase 8.159 2 .0169

Two-vehicle crashes

Weight 9.953 2 .0069

Engine size 8.547 2 .0139

Wheelbase 0.009 2 .9922

Single-vehicle nonrollover crashes

Weight 19.445 2 .0001

Engine size 30.922 2 .0000

Wheelbase 3.676 2 .1592

Single-vehicle rollover crashes

Weight 218.057 2 .0000

Engine size 167.355 2 .0000

Wheelbase 276.602 2 .0000

1

See, for example, A. Agresti, Categorical Data Analysis (New York: Wiley, 1990), pp. 95-96.

Page 29 GAO/PEMD-95-3 Highway Safety
Appendix V 

Alternative Definitions of Vehicle Size

Table V.2: Change in –2 Log Likelihood

From Base Model Using Alternative

Measures of Vehicle Size: Light Trucks

Change in –2

log likelihood

Degrees of

freedom Probability

All crash types

Weight 6.812 2 .0332

Engine size 7.556 2 .0229

Wheelbase 10.782 2 .0046

Two-vehicle crashes

Weight 22.818 2 .0000

Engine size 22.144 2 .0000

Wheelbase 42.512 2 .0000

Single-vehicle nonrollover crashes

Weight 12.078 2 .0024

Engine size 7.987 2 .0184

Wheelbase 12.951 2 .0015

Single-vehicle rollover crashes

Weight 26.840 2 .0000

Engine size 35.571 2 .0000

Wheelbase 58.808 2 .0000

Page 30 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

Note: GAO comments

supplementing those in the

report text appear at the

end of this appendix.

Page 31 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

See comment 1.

Page 32 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

See comment 2.

Page 33 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

Deleted.

Now p. 2.

See p. 8.

See p. 25.

See comment 2.

Page 34 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

Now p. 4.

Now p. 4.

See comment 1.

Now p. 7.

Now p. 8.

Page 35 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

Deleted.

Now p. 11.

See comment 3.

Now p. 18.

Now p. 19.

See comment 4.

See comment 5.

Page 36 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

The following are GAO’s comments on DOT’s June 20, 1994, letter.

GAO Comments 1. We share with DOT the belief that every reasonable effort should be

made to reduce the incidence of rollover crashes, which, as we noted in

our report, are second only to frontal collisions in deadliness. We would

be as concerned as DOT if our conclusion, that car size is substantially less

predictive of rollover crashes than are driver characteristics, were

misinterpreted to diminish the importance of efforts to reduce the rollover

propensity of vehicles.

The analyses we performed differ significantly from NHTSA’s rollover

research, but our conclusions are not in conflict. Our concern was with

the relative contribution of car size to crash involvement. We examined

this relationship in a general model that combined crash types and then

separately, using the traditional analytic taxonomy of multiple vehicle,

single-vehicle nonrollover, and single-vehicle rollover crashes. NHTSA, in

contrast, attempted to identify the factors that differentiated single-vehicle

rollover from nonrollover crashes. The vehicle factors it examined

included a number of constructs derived from laboratory measurements,

such as tilt table ratio, side pull ratio, and critical sliding velocity. The

single area of overlap between the NHTSA analyses and ours was in the

inclusion of wheelbase in NHTSA’s models and in one of our models.

It is not surprising, therefore, that we arrived at different conclusions

regarding the importance of different vehicle characteristics relative to

driver characteristics. Nevertheless, our findings also support the

relatively greater importance of vehicle characteristics in rollover crashes

than in other crash types. We found that lighter vehicles were more likely

to be involved in single vehicle rollovers. We further found that wheelbase

was a better predictor of rollover crashes than weight.

2. DOT made two suggestions for additional analyses to supplement our

single-vehicle rollover model. First, agency researchers suggested that we

include in our model some roadway characteristics that were beyond the

scope of the research originally requested. They also suggested that we

treat all single-vehicle crashes as one crash type and then perform a

second-level analysis to identify the factors that distinguish between

rollover and nonrollover crashes.

We performed these analyses and concluded that, while they provided

important additional information about the dynamics of rollover crashes,

Page 37 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

they did not substantially alter our conclusions about the relative

importance of the driver and vehicle characteristics we examined.

To respond to the first suggestion, we added two roadway variables to all

our models: whether the roadway was curved or straight and whether the

crash occurred in a rural or urban setting. The results of these analyses are

provided in appendix VII (passenger cars) and appendix VIII (light trucks

and vans). As anticipated, these roadway characteristics generally

contributed significantly to the predictive power of the models.

Single-vehicle crashes (rollover and nonrollover) are more likely to occur

on rural and on curved roadways. Two-vehicle car crashes are less likely

to occur on rural roads. The addition of these predictors, however, did not

change the predominant importance of driver factors over vehicle weight

in predicting crash involvement.

We also constructed a model combining both types of single-vehicle

accidents. We included the results of this model in appendixes VII and VIII.

As DOT anticipated, the single-accident model yielded results consistent

with our earlier findings, that driver age and violation history play the

strongest roles in involvement in single vehicle crashes, with little

contribution from the various vehicle characteristics. The aggregate

model, however, also finds the contribution of weight to single-vehicle

accidents nonsignificant. This is the net effect of the opposing influence of

weight in rollover and nonrollover accidents. As our original analyses

demonstrated, heavier cars are more likely to be involved in nonrollover

crashes and less likely to be involved in rollovers.

We constructed a second set of models (one each for passenger cars and

for light trucks and vans) to distinguish between rollover and nonrollover

single-vehicle accidents. The results of these analyses are presented in

appendix IX. The model produced the results anticipated by DOT—namely,

that roadway characteristics and, to a lesser extent, vehicle weight are

better predictors of whether a single-vehicle accident involves a rollover

than the driver characteristics in our model, although the analysis did find

that younger drivers were significantly more likely to be in a rollover than

a nonrollover crash.

Like the analysis, the interpretation of the models must be in two stages.

The findings suggest that driver characteristics predominate over vehicle

characteristics in placing a vehicle in a likely single-vehicle crash situation.

Page 38 GAO/PEMD-95-3 Highway Safety
Appendix VI 

Comments From the Department of

Transportation

Whether the resultant crash (if one does occur) involves a rollover is more

determined by roadway and vehicle considerations.1

3. While DOT considers induced exposure an “excellent” method for

measuring involvement risk in two-vehicle crashes, it expressed some

cautions about its use for single-vehicle crashes. In particular, DOT

suggested that the mix of light truck types (pickups, vans, and sport-utility

vehicles) is different in urban and rural settings, and therefore three

different light truck analyses should be performed. We agree that such

analyses could provide valuable information, but we believe that they

would unnecessarily expand the scope of this report. We reviewed the

relative likelihood of fatal accidents in different types of light trucks and

vans in a previous report.2

 The additional analyses we performed, at DOT’s

suggestion, that control for the urban and rural difference also address

this concern. (See appendixes VII and VIII.)

4. DOT further suggested that we perform additional tests of the ability

to generalize from the induced exposure method by comparing results

from a larger number of state accident data bases. Our comparison of

accident involvement ratios in North Carolina and Michigan (the two

usable data bases readily available to us) was intended only to illustrate

the relative consistency and reasonableness of the results obtained from

applying this methodology. Many more such comparisons will need to be

made before the exact parameters of the method’s applicability can be

defined. Nevertheless, the results obtained by different researchers over

the years from this approach to defining exposure are a strong argument

for its general utility.

DOT also suggested we include some additional details concerning our

analyses and references to other related work performed by NHTSA and

other researchers. We have incorporated these suggestions where

appropriate.

5. This statement has been changed in the text. See page 2.

1

The NHTSA methodology makes the simplifying assumption that all the single-vehicle accidents in an

accident data base would have occurred whether or not the vehicle rolled over. This is clearly not the

case; for example, a vehicle that left the road may have recovered without incident if it had not rolled

over, or it may have collided with a tree before rolling over. From the available state accident data

bases, it is impossible to determine which situations would not have resulted in a crash if the vehicle

had not rolled over. Unfortunately, the induced exposure method cannot answer this question, since

its reference crash type is a two-vehicle crash.

2

U.S. General Accounting Office, Highway Safety: Fatalities in Light Trucks and Vans, GAO/PEMD-91-8

(Washington, D.C.: November 1990).

Page 39 GAO/PEMD-95-3 Highway Safety
Appendix VII 

Logistic Regression Analysis Including

Roadway Characteristics: Passenger Cars

The outcome variable for the logistic regression equations was a

dichotomous indicator of fault, coded “1” for at-fault and “0” for

not-at-fault drivers. For all the equations presented here, both single- and

two-vehicle accidents, the comparison group is not-at-fault drivers in

two-vehicle accidents. A driver was considered at fault if the investigating

police officer checked one or more violations in the checklist provided on

the North Carolina accident report form. (In two-vehicle accidents, cases

were excluded if no violation was reported for either driver or if both

drivers had violations.)

The independent variables included

• driver age, including a squared term to capture the curvilinear relationship

between age and accident involvement;

• driver gender, with males coded “1” and females coded “0”;

• driver violation history, with four mutually exclusive categories: no

previous traffic violations, one or more previous violations not involving

alcohol, at least one alcohol violation (may also include nonalcohol

violations), and violation history unknown (all out-of-state drivers and

some North Carolina drivers are in this category). In the models shown,

the three categories given are in contrast to the group having

alcohol-related violations;

• vehicle age, last two digits of the vehicle model year;

• vehicle curb weight, expressed in hundreds of pounds and including a

squared term to capture the curvilinear relationship between vehicle

weight and accident involvement;

• rural location, coded “1” for rural locations and “0” for mixed or urban

locations;

• curved roadway, coded “1” if curved, “0” otherwise.

Table VII.1: Number of Cases and

Model Chi-Squares

Accident type

Rollover and

nonrollover

combined No rollover Rollover Two vehicle

N of cases, not-at-fault 52,915 52,915 52,915 52,915

N of cases, at fault 14,490 11,563 2,927 52,287

Total N of cases 67,405 64,478 55,842 105,202

Model chi-square 20,519.696 15,418.326 9,470.896 4,270.173

Model degrees of

freedom 11 10 11 11

Page 40 GAO/PEMD-95-3 Highway Safety
Appendix VII 

Logistic Regression Analysis Including

Roadway Characteristics: Passenger Cars

Table VII.2: Parameter Estimates

Rollover and nonrollover

combined No rollover Rollover Two vehicle

Single vehicle

Variable Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob.

Constant 3.4290 .2732 .0000 2.9800 .2420 .0000 1.9702 .5592 .0004 4.1323 .1559 .0000

Driver age –0.1147 .0037 .0000 –0.1142 .0039 .0000 –0.1130 .0084 .0000 –0.0976 .0019 .0000

Age squared 0.0010 .00004 .0000 0.0010 .00005 .0000 0.0008 .0001 .0000 0.0011 .00002 .0000

Male 0.5699 .0241 .0000 0.5625 .0255 .0000 0.6598 .0492 .0000 –0.0008 .0130 .9482

Nonalcohol violation –1.2270 .0549 .0000 –1.2302 .0567 .0000 –1.2287 .1031 .0000 –0.4938 .0416 .0000

No violation –1.4549 .0545 .0000 –1.4515 .0563 .0000 –1.4474 .1026 .0000 –0.7469 .0413 .0000

Violation unknown –1.5815 .0647 .0000 –1.5962 .0675 .0000 –1.5783 .1241 .0000 –0.2967 .0446 .0000

Vehicle year –0.0279 .0025 .0000 –0.0277 .0025 .0000 –0.0161 .0050 .0013 –0.0175 .0014 .0000

Vehicle weight –0.0103 .0134 .4422 0.0068 .0021 .0010 –0.1228 .0291 .0000 –0.0244 .0074 .0009

Vehicle weight

squared

0.0001 .0002 .5347 a a a 0.0011 .0005 .0249 0.0004 .0001 .0017

Rural location 1.5257 .0234 .0000 1.3386 .0245 .0000 2.7020 .0649 .0000 –0.0372 .0142 .0090

Curved roadway 1.8721 .0257 .0000 1.7959 .0271 .0000 2.3021 .0469 .0000 0.0319 .0227 .1588

aQuadratic term removed since main effect only achieves significance without squared term.

Page 41 GAO/PEMD-95-3 Highway Safety
Appendix VIII 

Logistic Regression Analysis Including

Roadway Characteristics: Light Trucks and

Vans

The outcome variable for the logistic regression equations was a

dichotomous indicator of fault, coded “1” for at-fault and “0” for

not-at-fault drivers. For all the equations presented here, both single- and

two-vehicle accidents, the comparison group is not-at-fault drivers in

two-vehicle accidents. A driver was considered at fault if the investigating

police officer checked one or more violations in the checklist provided on

the North Carolina accident report form. (In two-vehicle accidents, cases

were excluded if no violation was reported for either driver or if both

drivers had violations.)

The independent variables included

• driver age, including a squared term to capture the curvilinear relationship

between age and accident involvement;

• driver gender, with males coded “1” and females coded “0”;

• driver violation history, with four mutually exclusive categories: no

previous traffic violations, one or more previous violations not involving

alcohol, at least one alcohol violation (may also include nonalcohol

violations), and violation history unknown (all out-of-state drivers and

some North Carolina drivers are in this category). In the models shown,

the three categories given are in contrast to the group having

alcohol-related violations;

• vehicle age, last two digits of the vehicle model year;

• vehicle curb weight, expressed in hundreds of pounds;

• rural location, coded “1” for rural locations and “0” for mixed or urban

locations;

• curved roadway, coded “1” if curved, “0” otherwise.

Table VIII.1: Number of Cases and

Model Chi-Squares Single vehicle

Accident type

Rollover and

nonrollover

combined No rollover Rollover Two vehicle

N of cases, not-at-fault 8,971 8,971 8,971 8,971

N of cases, at-fault 3,444 2,392 1,052 8,777

Total N of cases 12,415 11,363 10,023 17,748

Model chi-square 4,141.020 2,679.975 2,548.760 557.139

Model degrees of

freedom 10 10 10 10

Page 42 GAO/PEMD-95-3 Highway Safety
Appendix VIII 

Logistic Regression Analysis Including

Roadway Characteristics: Light Trucks and

Vans

Table VIII.2: Parameter Estimates

Rollover and nonrollover

combined No rollover Rollover Two vehicle

Single vehicle

Variable Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob. Coeff. S.E. Prob.

Constant 4.5531 .5437 .0000 4.3259 .5912 .0000 2.1671 .9021 .0163 3.4486 .3375 .0000

Driver age –0.1247 .0085 .0000 –0.1168 .0092 .0000 –0.1427 .0144 .0000 –0.1021 .0052 .0000

Age squared 0.0011 .0001 .0000 0.0010 .0001 .0000 0.0012 .0002 .0000 0.0012 .00006 .0000

Male 0.1943 .0718 .0068 0.1903 .0788 .0158 0.2148 .1195 .0722 –0.0827 .0423 .0505

Nonalcohol violation –0.9934 .1044 .0000 –0.9901 .1108 .0000 –1.1573 .1645 .0000 –0.3686 .0807 .0000

No violation –1.2685 .1034 .0000 –1.2789 .1099 .0000 –1.3483 .1626 .0000 –0.5664 .0799 .0000

Violation unknown –1.1464 .1288 .0000 –1.1814 .1389 .0000 –1.1957 .2030 .0000 –0.1972 .0921 .0322

Vehicle year –0.0316 .0056 .0000 –0.0335 .0061 .0000 –0.0151 .0093 .1061 –0.0172 .0035 .0000

Vehicle weighta –0.0189 .0042 .0000 –0.0153 .0046 .0009 –0.0392 .0071 .0000 0.0122 .0026 .0000

Rural location 1.6660 .0525 .0000 1.4001 .0565 .0000 2.6262 .1179 .0000 –0.0277 .0328 .3987

Curved roadway 1.7116 .0551 .0000 1.6115 .0598 .0000 2.0296 .0831 .0000 0.0033 .0519 .9489

aQuadratic term for weight removed since main effect only achieves significance without squared

term.

Page 43 GAO/PEMD-95-3 Highway Safety
Appendix IX 

Predicting Rollover Versus No Rollover

Among Single-Vehicle Accidents

The outcome variable for the logistic regression equations was a

dichotomous indicator of vehicle rollover, coded “1” for rollover and “0”

for nonrollovers.

The independent variables included

• driver age, including a squared term to capture the curvilinear relationship

between age and accident involvement;

• driver gender, with males coded “1” and females coded “0”;

• driver violation history, with four mutually exclusive categories: no

previous traffic violations, one or more previous violations not involving

alcohol, at least one alcohol violation (may also include nonalcohol

violations), and violation history unknown (all out-of-state drivers and

some North Carolina drivers are in this category). In the models shown,

the three categories given are in contrast to the group having

alcohol-related violations;

• vehicle age, last two digits of the vehicle model year;

• vehicle curb weight, expressed in hundreds of pounds and including a

squared term to capture the curvilinear relationship between vehicle

weight and accident involvement.

• rural location, coded “1” for rural locations and “0” for mixed or urban

locations;

• curved roadway, coded “1” if curved, “0” otherwise.

Table IX.1: Number of Cases and

Model Chi-Squares Accident type Passenger cars Light trucks and vans

N of cases, rollover 2,927 1,052

N of cases, no rollover 11,563 2,392

Total N of cases 14,490 3,444

Model chi-square 1,127.879 210.994

Model degrees of freedom 10 10

Page 44 GAO/PEMD-95-3 Highway Safety
Appendix IX 

Predicting Rollover Versus No Rollover

Among Single-Vehicle Accidents

Table IX.2: Parameter Estimates

Passenger cars Light trucks and vans

Variable Coeff. S.E. Prob. Coeff. S.E. Prob.

Constant 0.3351 .5040 .5061 –0.4513 .8560 .5980

Driver age –0.0093 .0019 .0000 –0.0300 .0136 .0271

Age squared a a a 0.0002 .0002 .2468

Male 0.0289 .0469 .5379 0.0041 .1171 .9721

Vehicle year 0.0018 .0046 .6954 –0.0056 .0088 .5293

Nonalcohol violation –0.0327 .0819 .6899 –0.0752 .1355 .5788

No violation –0.0230 .0810 .7763 –0.0601 .1351 .6566

Violation unknown –0.0176 .1063 .8688 0.0397 .1819 .8273

Vehicle weight –0.1597 .0272 .0000 –0.0132 .0067 .0490

Vehicle weight squared 0.0018 .0005 .0001 a a a

Rural location 1.3257 .0654 .0000 1.2492 .1212 .0000

Curved roadway 0.4415 .0444 .0000 0.3572 .0777 .0000

aQuadratic term removed since main effect only achieves significance without squared term.

Page 45 GAO/PEMD-95-3 Highway Safety
Appendix X 

Major Contributors to This Report

Program Evaluation

and Methodology

Division

Robert E. White, Assistant Director

Beverly A. Ross, Project Manager

Martin T. Gahart, Project Adviser

(973379) Page 46 GAO/PEMD-95-3 Highway Safety
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