Highway Safety: Factors Affecting Involvement in Vehicle Crashes (Letter
Report, 10/27/94, GAO/PEMD-95-3).

GAO found that driver characteristics far outweigh vehicle factors in
predicting crashes for passenger cars.  For example, the odds of a
20-year-old driver being involved in a single-vehicle, nonrollover crash
was about four times as great as that of a 50-year-old.  By comparison,
a 4,000-pound automobile 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
were women. 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 were as much as three times more likely
to be involved in single-vehicle rollover crashes as were heavy cars.
In other types of crashes, GAO found that car-size measures other than
weight, such as wheelbase or engine size, were better predictors of
crash involvement.  GAO found similar results when it applied its
methodology to crashes involving light trucks and vans.

--------------------------- Indexing Terms -----------------------------

 REPORTNUM:  PEMD-95-3
     TITLE:  Highway Safety: Factors Affecting Involvement in Vehicle 
             Crashes
      DATE:  10/27/94
   SUBJECT:  Motor vehicle safety
             Demographic data
             Transportation statistics
             Traffic accidents
             Motor vehicle standards
             Highway safety
             Statistical methods
             Motor vehicles
             Automobile industry
             Statistical data
IDENTIFIER:  North Carolina
             Michigan
             
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Cover
================================================================ COVER


Report to Congressional Requesters

October 1994

HIGHWAY SAFETY - FACTORS AFFECTING
INVOLVEMENT IN VEHICLE CRASHES

GAO/PEMD-95-3

Highway Safety


Abbreviations
=============================================================== ABBREV

  DOT - Department of Transportation
  GAO - General Accounting Office
  NHTSA - National Highway Traffic Safety Administration
  NPTS - National Personal Transportation Survey

Letter
=============================================================== LETTER


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
------------------------------------------------------------ Letter :1

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 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
------------------------------------------------------------ Letter :2

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 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
------------------------------------------------------------ Letter :3

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,
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 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. 


--------------------
\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. 


   PASSENGER CARS
------------------------------------------------------------ Letter :4


      DRIVER AGE
---------------------------------------------------------- Letter :4.1

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. 

   Figure 1:  Adjusted Odds Ratios
   Comparing Crash Involvement by
   Driver Age\a

   (See figure in printed
   edition.)

\a The 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
---------------------------------------------------------- Letter :4.2

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. 

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
---------------------------------------------------------- Letter :4.3

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
---------------------------------------------------------- Letter :4.4

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
---------------------------------------------------------- Letter :4.5

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 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). 

   Figure 2:  Adjusted Odds Ratios
   Comparing Crash Involvement by
   Car Weight\a

   (See figure in printed
   edition.)

\a The 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 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


--------------------
\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. 

\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). 


   LIGHT TRUCKS AND VANS
------------------------------------------------------------ Letter :5

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.)


   SUMMARY
------------------------------------------------------------ Letter :6

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. 

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


INDUCED EXPOSURE
=========================================================== Appendix I

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.  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


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. 

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. 

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


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 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. 


--------------------
\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). 

\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. 


THE NORTH CAROLINA DATA FILE
========================================================== Appendix II

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 single- or
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
------------------------------------------------------------


                          Table II.2
           
                      Types of Accidents

                                                    Cumulati
                                Frequenc                  ve
                                       y   Percent   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%
------------------------------------------------------------

LOGISTIC REGRESSION ANALYSIS FOR
PASSENGER CAR CRASH INVOLVEMENT
========================================================= Appendix III

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


                                   Two  Nonrollov
Accident type           All    vehicle         er   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-        5,655.178  4,137.856  5,524.596  2,546.841
 square
Model degrees of          9          9          9          9
 freedom
------------------------------------------------------------


                                   Table III.2
                     
                               Parameter Estimates



Vari  Coeff        Prob  Coeff        Prob  Coeff        Prob  Coeff        Prob
able      .  S.E.     .      .  S.E.     .      .  S.E.     .      .  S.E.     .
----  -----  ----  ----  -----  ----  ----  -----  ----  ----  -----  ----  ----
Cons  5.150  .151  .000  4.226  .160  .000  4.216  .265  .000  5.256  .474  .000
 tant     3     8     0      5     3     0      1     2     0      4     8     0
Driv      -  .001  .000      -  .002  .000      -  .003  .000      -  .007  .000
 er   0.108     9     0  0.097     0     0  0.124     6     0  0.137     4     0
 age      0                  0                  5                  4
Age   0.001  .000  .000  0.001  .000  .000  0.001  .000  .000  0.001  .000  .000
 squ      2     0     0      1     0     0      1     0     0      1     1     0
 are
 d
Male  0.121  .012  .000      -  .013  .973  0.612  .023  .000  0.679  .042  .000
          9     5     0  0.000     2     5      6     2     0      0     5     0
                             4
Nona      -  .039  .000      -  .042  .000      -  .050  .000      -  .082  .000
 lco  0.758     1     0  0.492     5     0  1.309     9     0  1.396     3     0
 hol      2                  9                  4                  0
 vio
 lat
 ion
 \a
No        -  .038  .000      -  .042  .000      -  .050  .000      -  .081  .000
 vio  0.999     8     0  0.751     2     0  1.448     5     0  1.418     7     0
 lat      3                  5                  9                  0
 ion
Viol      -  .042  .000      -  .045  .000      -  .061  .000      -  .103  .000
 ati  0.663     3     0  0.298     5     0  1.648     2     0  1.772     5     0
 on       2                  3                  1                  0
 unk
 now
 n
Vehi      -  .001  .000      -  .001  .000      -  .002  .000      -  .004  .000
 cle  0.022     4     0  0.019     5     0  0.033     5     0  0.025     4     0
 yea      7                  3                  2                  7
 r
Vehi      -  .007  .058      -  .007  .005  0.044  .013  .000      -  .025  .000
 cle  0.013     2     6  0.021     5     1      8     0     6  0.097     6     1
 wei      5                  1                                     4
 ght
 \b
Vehi  0.000  .000  .130  0.000  .000  .010      -  .000  .002  0.000  .000  .078
 cle      2     1     4      3     1     5  0.000     2     7      8     5     0
 wei                                            7
 ght
 squ
 are
 d
--------------------------------------------------------------------------------
\a Contrast group for violations is "Has alcohol violation."

\b Vehicle weight is calibrated in hundredweights. 


--------------------
\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. 


LOGISTIC REGRESSION ANALYSIS FOR
LIGHT TRUCK AND VAN CRASH
INVOLVEMENT
========================================================== Appendix IV

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


Accident                         Two  Nonrollove
type                 All     vehicle           r    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-      868.5668     553.830     772.251     624.847
 square
Model                  9           9           9           9
 degrees of
 freedom
------------------------------------------------------------


                                    Table IV.2
                     
                               Parameter Estimates



Vari  Coeff        Prob  Coeff        Prob  Coeff        Prob  Coeff        Prob
able      .  S.E.     .      .  S.E.     .      .  S.E.     .      .  S.E.     .
----  -----  ----  ----  -----  ----  ----  -----  ----  ----  -----  ----  ----
Cons  5.777  .499  .000  3.996  .532  .000  6.698  .847  .000  7.498  1.16  .000
 tant     0     0     0      2     4     0      8     9     0      7    64     0
Driv      -  .005  .000      -  .005  .000      -  .008  .000      -  .012  .000
 er   0.115     0     0  0.102     3     0  0.124     4     0  0.149     8     0
 age      6                  7                  3                  0
Age   0.001  .000  .000  0.001  .000  .000  0.001  .000  .000  0.001  .000  .000
 squ      2     1     0      2     1     0      1     1     0      3     2     0
 are
 d
Male      -  .040  .966      -  .043  .043  0.229  .072  .001  0.313  .105  .002
      0.001     6     6  0.087     2     9      6     4     5      5     3     9
          7                  1
Nona      -  .074  .000      -  .082  .000      -  .099  .000      -  .131  .000
 lco  0.609     8     0  0.348     5     0  1.038     9     0  1.144     7     0
 hol      2                  7                  9                  8
 vio
 lat
 ion
 \a
No        -  .073  .000      -  .081  .000      -  .099  .000      -  .130  .000
 vio  0.820     9     0  0.560     7     0  1.249     1     0  1.254     8     0
 lat      9                  8                  3                  2
 ion
Viol      -  .086  .000      -  .094  .062      -  .126  .000      -  .170  .000
 ati  0.517     6     0  0.175     1     1  1.197     8     0  1.277     9     0
 on       3                  6                  3                  7
 unk
 now
 n
Vehi      -  .003  .000      -  .003  .000      -  .005  .000      -  .008  .000
 cle  0.023     4     0  0.019     6     0  0.037     6     0  0.036     0     0
 yea      3                  1                  0                  3
 r
Vehi      -  .022  .078      -  .023  .606      -  .038  .080      -  .055  .024
 cle  0.038     0     9  0.012     3     9  0.067     7     6  0.123     1     6
 wei      7                  0                  6                  8
 ght
 \b
Vehi  0.000  .000  .050  0.000  .000  .295  0.000  .000  .158  0.001  .000  .085
 cle      6     3     1      4     3     5      8     6     7      4     8     1
 wei
 ght
 squ
 are
 d
--------------------------------------------------------------------------------
\a Contrast group for violations is "Has alcohol violation."

\b Vehicle weight is calibrated in hundredweights. 


--------------------
\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. 


ALTERNATIVE DEFINITIONS OF VEHICLE
SIZE
=========================================================== Appendix V

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   Degrees
                                -2 log        of  Probabilit
                            likelihood   freedom           y
--------------------------  ----------  --------  ----------
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
------------------------------------------------------------


                          Table V.2
           
            Change in -2 Log Likelihood From Base
             Model Using Alternative Measures of
                  Vehicle Size: Light Trucks

                             Change in   Degrees
                                -2 log        of  Probabilit
                            likelihood   freedom           y
--------------------------  ----------  --------  ----------
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
------------------------------------------------------------


(See figure in printed edition.)Appendix VI

--------------------
\1 See, for example, A.  Agresti, Categorical Data Analysis (New
York:  Wiley, 1990), pp.  95-96. 


COMMENTS FROM THE DEPARTMENT OF
TRANSPORTATION
=========================================================== Appendix V



(See figure in printed edition.)

See comment 1. 



(See figure in printed edition.)

See comment 2. 



(See figure in printed edition.)

Deleted. 

Now p.  2. 

See p.  8. 

See p.  25. 

See comment 2. 



(See figure in printed edition.)

Now p.  4. 

Now p.  4. 

See comment 1. 

Now p.  7. 

Now p.  8. 



(See figure in printed edition.)

Deleted. 

Now p.  11. 

See comment 3. 

Now p.  18. 

Now p.  19. 

See comment 4. 

See comment 5. 


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, 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.  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). 


LOGISTIC REGRESSION ANALYSIS
INCLUDING ROADWAY CHARACTERISTICS: 
PASSENGER CARS
========================================================= Appendix VII

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

                   Rollover
                        and
                  nonrollov
                         er         No                   Two
Accident type      combined   rollover   Rollover    vehicle
----------------  ---------  ---------  ---------  ---------
N of cases, not-     52,915     52,915     52,915     52,915
 at-fault
N of cases, at       14,490     11,563      2,927     52,287
 fault
Total N of cases     67,405     64,478     55,842    105,202
Model chi-        20,519.69  15,418.32  9,470.896  4,270.173
 square                   6          6
Model degrees of         11         10         11         11
 freedom
------------------------------------------------------------


                                   Table VII.2
                     
                               Parameter Estimates



Vari  Coeff        Prob  Coeff        Prob  Coeff        Prob  Coeff        Prob
able      .  S.E.     .      .  S.E.     .      .  S.E.     .      .  S.E.     .
----  -----  ----  ----  -----  ----  ----  -----  ----  ----  -----  ----  ----
Cons  3.429  .273  .000  2.980  .242  .000  1.970  .559  .000  4.132  .155  .000
 tant     0     2     0      0     0     0      2     2     4      3     9     0
Driv      -  .003  .000      -  .003  .000      -  .008  .000      -  .001  .000
 er   0.114     7     0  0.114     9     0  0.113     4     0  0.097     9     0
 age      7                  2                  0                  6
Age   0.001  .000  .000  0.001  .000  .000  0.000  .000  .000  0.001  .000  .000
 squ      0    04     0      0    05     0      8     1     0      1    02     0
 are
 d
Male  0.569  .024  .000  0.562  .025  .000  0.659  .049  .000      -  .013  .948
          9     1     0      5     5     0      8     2     0  0.000     0     2
                                                                   8
Nona      -  .054  .000      -  .056  .000      -  .103  .000      -  .041  .000
 lco  1.227     9     0  1.230     7     0  1.228     1     0  0.493     6     0
 hol      0                  2                  7                  8
 vio
 lat
 ion
No        -  .054  .000      -  .056  .000      -  .102  .000      -  .041  .000
 vio  1.454     5     0  1.451     3     0  1.447     6     0  0.746     3     0
 lat      9                  5                  4                  9
 ion
Viol      -  .064  .000      -  .067  .000      -  .124  .000      -  .044  .000
 ati  1.581     7     0  1.596     5     0  1.578     1     0  0.296     6     0
 on       5                  2                  3                  7
 unk
 now
 n
Vehi      -  .002  .000      -  .002  .000      -  .005  .001      -  .001  .000
 cle  0.027     5     0  0.027     5     0  0.016     0     3  0.017     4     0
 yea      9                  7                  1                  5
 r
Vehi      -  .013  .442  0.006  .002  .001      -  .029  .000      -  .007  .000
 cle  0.010     4     2      8     1     0  0.122     1     0  0.024     4     9
 wei      3                                     8                  4
 ght
Vehi  0.000  .000  .534     \a    \a    \a  0.001  .000  .024  0.000  .000  .001
 cle      1     2     7                         1     5     9      4     1     7
 wei
 ght
 squ
 are
 d
Rura  1.525  .023  .000  1.338  .024  .000  2.702  .064  .000      -  .014  .009
 l        7     4     0      6     5     0      0     9     0  0.037     2     0
 loc                                                               2
 ati
 on
Curv  1.872  .025  .000  1.795  .027  .000  2.302  .046  .000  0.031  .022  .158
 ed       1     7     0      9     1     0      1     9     0      9     7     8
 roa
 dwa
 y
--------------------------------------------------------------------------------
\a Quadratic term removed since main effect only achieves
significance without squared term. 


LOGISTIC REGRESSION ANALYSIS
INCLUDING ROADWAY CHARACTERISTICS: 
LIGHT TRUCKS AND VANS
======================================================== Appendix VIII

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


                   Rollover
                        and
                  nonrollov
                         er         No                   Two
Accident type      combined   rollover   Rollover    vehicle
----------------  ---------  ---------  ---------  ---------
N of cases, not-      8,971      8,971      8,971      8,971
 at-fault
N of cases, at-       3,444      2,392      1,052      8,777
 fault
Total N of cases     12,415     11,363     10,023     17,748
Model chi-        4,141.020  2,679.975  2,548.760    557.139
 square
Model degrees of         10         10         10         10
 freedom
------------------------------------------------------------


                                   Table VIII.2
                     
                               Parameter Estimates



Vari  Coeff        Prob  Coeff        Prob  Coeff        Prob  Coeff        Prob
able      .  S.E.     .      .  S.E.     .      .  S.E.     .      .  S.E.     .
----  -----  ----  ----  -----  ----  ----  -----  ----  ----  -----  ----  ----
Cons  4.553  .543  .000  4.325  .591  .000  2.167  .902  .016  3.448  .337  .000
 tant     1     7     0      9     2     0      1     1     3      6     5     0
Driv      -  .008  .000      -  .009  .000      -  .014  .000      -  .005  .000
 er   0.124     5     0  0.116     2     0  0.142     4     0  0.102     2     0
 age      7                  8                  7                  1
Age   0.001  .000  .000  0.001  .000  .000  0.001  .000  .000  0.001  .000  .000
 squ      1     1     0      0     1     0      2     2     0      2    06     0
 are
 d
Male  0.194  .071  .006  0.190  .078  .015  0.214  .119  .072      -  .042  .050
          3     8     8      3     8     8      8     5     2  0.082     3     5
                                                                   7
Nona      -  .104  .000      -  .110  .000      -  .164  .000      -  .080  .000
 lco  0.993     4     0  0.990     8     0  1.157     5     0  0.368     7     0
 hol      4                  1                  3                  6
 vio
 lat
 ion
No        -  .103  .000      -  .109  .000      -  .162  .000      -  .079  .000
 vio  1.268     4     0  1.278     9     0  1.348     6     0  0.566     9     0
 lat      5                  9                  3                  4
 ion
Viol      -  .128  .000      -  .138  .000      -  .203  .000      -  .092  .032
 ati  1.146     8     0  1.181     9     0  1.195     0     0  0.197     1     2
 on       4                  4                  7                  2
 unk
 now
 n
Vehi      -  .005  .000      -  .006  .000      -  .009  .106      -  .003  .000
 cle  0.031     6     0  0.033     1     0  0.015     3     1  0.017     5     0
 yea      6                  5                  1                  2
 r
Vehi      -  .004  .000      -  .004  .000      -  .007  .000  0.012  .002  .000
 cle  0.018     2     0  0.015     6     9  0.039     1     0      2     6     0
 wei      9                  3                  2
 ght
 \a
Rura  1.666  .052  .000  1.400  .056  .000  2.626  .117  .000      -  .032  .398
 l        0     5     0      1     5     0      2     9     0  0.027     8     7
 loc                                                               7
 ati
 on
Curv  1.711  .055  .000  1.611  .059  .000  2.029  .083  .000  0.003  .051  .948
 ed       6     1     0      5     8     0      6     1     0      3     9     9
 roa
 dwa
 y
--------------------------------------------------------------------------------
\a Quadratic term for weight removed since main effect only achieves
significance without squared term. 


PREDICTING ROLLOVER VERSUS NO
ROLLOVER AMONG SINGLE-VEHICLE
ACCIDENTS
========================================================== Appendix IX

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

                                            Light trucks and
Accident type             Passenger cars                vans
--------------------  ------------------  ------------------
N of cases, rollover               2,927               1,052
N of cases, no                    11,563               2,392
 rollover
Total N of cases                  14,490               3,444
Model chi-square               1,127.879             210.994
Model degrees of                      10                  10
 freedom
------------------------------------------------------------


                          Table IX.2
           
                     Parameter Estimates


                        Coeff        Prob  Coeff        Prob
Variable                    .  S.E.     .      .  S.E.     .
----------------------  -----  ----  ----  -----  ----  ----
Constant                0.335  .504  .506      -  .856  .598
                            1     0     1  0.451     0     0
                                               3
Driver age                  -  .001  .000      -  .013  .027
                        0.009     9     0  0.030     6     1
                            3                  0
Age squared                \a    \a    \a  0.000  .000  .246
                                               2     2     8
Male                    0.028  .046  .537  0.004  .117  .972
                            9     9     9      1     1     1
Vehicle year            0.001  .004  .695      -  .008  .529
                            8     6     4  0.005     8     3
                                               6
Nonalcohol violation        -  .081  .689      -  .135  .578
                        0.032     9     9  0.075     5     8
                            7                  2
No violation                -  .081  .776      -  .135  .656
                        0.023     0     3  0.060     1     6
                            0                  1
Violation unknown           -  .106  .868  0.039  .181  .827
                        0.017     3     8      7     9     3
                            6
Vehicle weight              -  .027  .000      -  .006  .049
                        0.159     2     0  0.013     7     0
                            7                  2
Vehicle weight squared  0.001  .000  .000     \a    \a    \a
                            8     5     1
Rural location          1.325  .065  .000  1.249  .121  .000
                            7     4     0      2     2     0
Curved roadway          0.441  .044  .000  0.357  .077  .000
                            5     4     0      2     7     0
------------------------------------------------------------
\a Quadratic term removed since main effect only achieves
significance without squared term. 


MAJOR CONTRIBUTORS TO THIS REPORT
=========================================================== Appendix X

PROGRAM EVALUATION AND METHODOLOGY
DIVISION

Robert E.  White, Assistant Director
Beverly A.  Ross, Project Manager
Martin T.  Gahart, Project Adviser
