National Center for Statistics & Analysis - Research & Development - 400 Seventh St. SW - Washington, DC 20590

Research Note

U.S. Department

of Transportation

National Highway

Traffic Safety

Administration

July 1997

Fatal Crash Involvements--What are the Odds?

Ezio C. Cerrelli

Introduction

The risk of being involved in a fatal crash varies

considerably depending on specific crash

characteristics, i.e., those of the driver, vehicle and

environment. [For more on male and female fatal crash

involvement by age group, see Crash Data and Rates

for Age-Sex Groups of Drivers, 1994, Research Note,

October 1995.] A generally accepted measure of the

risk of a fatal crash is the ratio between the number of

fatal crashes associated with a specific set of conditions

and the amount of travel performed under the same

conditions.

To calculate risk values the appropriate values for the

numerator and the denominator of the ratio must be

available. In the case of fatal crash risk, the difficulties

in obtaining highly detailed classifications of motor

vehicle travel places a severe limitation on any attempt

to estimate the risk of incurring a fatal crash under

specific conditions.

Presently, travel data are not available at an adequate

level of detail to permit estimating the contribution of

any specific factor on the occurrence of a fatal crash. 

For example, the fatal involvement rates for male and

female drivers, based on the total travel performed by

the two groups of drivers, have, as an underlying

assumption, that travel characteristics are the same for

both male and female drivers. In other words, one must

assume that the proportion of daytime travel is the same

for male and female drivers. This assumption,

therefore, must also be made for the proportion of high

vs. low speed travel, day of week, type of crash, etc. 

While some of these assumptions may be valid, others

are may be highly unlikely.

In the absence of detailed data on travel under specific

conditions, the purpose of this study was to determine 

how the risk of being involved in a fatal crash,

conditional on the occurrence of a police-reported

crash, changes as a function of key crash

characteristics. In this case, general assumptions are

not needed, as crash involvements can be, in general,

classified in as many ways as fatal involvements. 

While the results do not provide a measure of the risk

of a fatal involvement, they do show how the value of

this risk varies as a function of key crash

characteristics. Although the results are expressed as

Odds Ratios, they can be considered to be

approximately equal to risk ratios since the probability

of a crash being fatal is very small.

Data and Analysis

Data from the Fatality Analysis Reporting System

(FARS) and the General Estimate System (GES) files

for the years 1993, 1994, and 1995 were used in this

analysis. Only drivers of passenger cars and light

trucks and vans were included in the study. Crashes

involving pedestrians or pedalcyclists and crashes

involving more than two vehicles were excluded. 

GES observations originate from a sample survey and

therefore are associated with a sampling weight

variable. The final data set for this study contained

99,139 fatal involvements and 207,909 unweighted

GES crash involvements representing, when

weighted, an estimated 28,071,714 involvements. 

Seven variables were retained for each observation in

the final data set described above. These variables

were classified as:

C Driver Sex, i.e., Female or Male

C Driver Age, i.e., Younger (less than 65) or

Older (greater than or equal to 65)

C Speed Limit, i.e., Low (less than 40mph),

Moderate (40 thru 50mph), High (55mph),

Highest (above 55mph)

C Hour of Day, i.e., as Daytime (6am to 9pm)

or Nighttime (9pm to 6am)

C Day of Week,, i.e., Weekday or Weekend

(6pm Friday through 6am Monday)
National Center for Statistics & Analysis - Research & Development - 400 Seventh St. SW - Washington, DC 20590

C Vehicle Type, i.e., Passenger Car (PC) or

Light Trucks and Vans (LTVs)

C Type of Crash, i.e, Single Vehicle, Rear End,

Side, or Head-on

Other variables or variable characteristics initially

included in the analysis were omitted when found not to

have a significant effect on the risk value. For example,

for driver age, drivers under 25 years old were

separated from the younger driver group, however

estimated risk values were no greater for drivers in this

age group compared to drivers aged 25-64. As result,

drivers under 25 years of age were combined with

drivers aged 25-64 to form a one group.

Survey Data Analysis software (SUDAAN ) was used TM

with the FARS and GES data to estimate a statistical

model to describe the variation in the risk value for the

selected variables. SUDAAN , developed at the TM

Research Triangle Institute, is designed to perform

statistical analysis of survey data, e.g., GES data. 

SUDAAN is appropriate for statistical analyses of TM

databases containing both census and survey data, in

this case, FARS (census) and GES (survey).

The final statistical model using SUDAAN provides TM

an estimate of the change in the risk of a fatal

involvement, given a crash, for each of the seven

variables. The results for any variable can also be

assumed to be independent of the effect of the

remaining variables, as the interactions among the

seven variables were excluded from the final statistical

model as these were found not to have a significant

contribution. The model can be used to provide

estimates of the direct contribution of each individual

variable to the risk of fatal involvement and for any

combination of the remaining variables. Standard

errors for each risk estimate are also provided in the

following results.

Results

The GES cases are divided into twelve strata

containing about 100 probability sampling units

(PSU’s). In order to proceed with the SUDAAN

analysis, all FARS cases were assigned to a separate

stratum and assigned individual PSU numbers.

The results of the SUDAAN analysis can be

represented by a set of odds ratios, each representing

the relative odds of being involved in a fatal crash, once

involved in a police-reported crash, as a function of the

characteristics of each of the seven variables. [Please

note that driver involvement in a fatal crash does not

imply that the driver dies in the crash.] The results of

the analysis are shown in the following table:

Estimated Odds of Driver Fatal Crash

 Involvement by Key Driver and Crash 

Characteristics

Factor Odds 95%

Confidence

Interval

Male/Female 1.33 1.29 - 1.38

Older/Younger 2.59 2.37 - 2.84

Moderate/Low 2.83 2.40 - 3.33

Speed Limit

High/Low Speed 7.17 5.56 - 9.24

Limit

Highest/Low Speed 8.91 6.04 - 13.19

Limit

Weekend/Weekday 1.19 1.08 - 1.16

Nighttime/Daytime 1.91 1.79 - 2.03

LTV/PC 1.29 1.20 - 1.40

Side/Rear Collision 4.70 4.35 - 5.08

Single Vehicle/Rear 8.09 6.93 - 9.45

Collision

Head On/Rear 74.60 64.52 - 86.20

Collision

In the above table, the relative odds represent the ratio

of the odds of a fatal involvement of the first subgroup

vs. the lowest risk group, i.e. male vs. female, higher

speed limit vs. lower, etc. For example, the risk of

fatal crash involvement for male drivers is 1.33

compared to female drivers, so that male drivers have

an estimated 33% greater risk of fatal crash

involvement, given a crash, than female drivers. The

last column of the table presents the confidence

interval for the estimated risk value and provides a

measure of the statistical variability of the estimate. 

Finally, the risk value or odds for each variable

provides a measure of its contribution to the outcome

of the crash, independently of the effect of the

remaining factors.

Findings

The major contribution of this study is the

quantification of key driver and crash factors, rather

than the identification of these factors. That is, it was
National Center for Statistics & Analysis - Research & Development - 400 Seventh St. SW - Washington, DC 20590

generally accepted that the variables used in the for ‘Single Vehicle’ collisions are 8.1 times that for

analysis (hour of day, type of crash) were important in ‘Rear’ collisions. By far the factor that has the most

terms of their impact on crash outcome. Several of the severe effect on the odds is the occurrence of a ‘Head

variables, e.g., type of crash and speed limit, were On’ collision. In this case the odds are 75 times as

found to have fairly high odds ratios while other great as for ‘Rear’ collisions.

variables, e.g., driver age and driver sex were found to

have much lower estimated odds ratios. As such, this Overall, the odds of fatal involvement varies

study may be the first attempt at this type of analysis considerably as a function of these selected factors. 

based on a large body of data, and therefore, The odds ratios presented in this paper can be

comparable findings from other studies may not be considered to be independent and can be used to

available. calculate the odds ratio for any specific combination

In brief, the study finds that among all drivers involved the odds for a Male driver, in a Light Truck, at Night,

in crashes the odds for male drivers to be involved in a on a High (55 mph) speed road, involved in a Single

fatal crash are 1.33 times that for female drivers.

Drivers in the older age group, 65 years old and above,

display odds that are over two and one-half (2.59)

times that for their younger counterparts.

Being involved in a crash during nighttime hours

increases the odds of the crash being fatal by almost

two times (1.91) compared to daytime crashes.

Relative to crashes on roadways with ‘Low Speed’

limits, the odds for crashes on ‘Moderate’ speed limits

are 2.83 times as great, while the odds on “High’

posted sped limit are 7.17 times as great. Crashes that

occur on ‘Highest’ posted speeds have odds which are

8.91 times as great as those at “Low Speed’ limits.

Being the driver of an LTV increases the odds of the

involvement being fatal by 29 percent relative to

drivers of passenger cars.

Drivers involved in a ‘Side’ collision have odds of

being involved in a fatal crash that are 4.7 times that for

drivers involved in ‘Rear’ collisions. The same odds

of these factors versus its counterpart. For example,

Vehicle crash are about 190 to 1 (1.33 x 1.29 x 1.91 x

7.17 x 8.09) relative to a Female driver, in a

Passenger Car, in Daytime, on a Low (under 40 mph)

speed road, involved in Rear collision. The odds

ratios for any other combination of these factors can

be calculated similarly.

These results may serve a variety of purposes, among

which the identification of those factors with high

odds ratios, for example, in the ability to estimate the

severity of a crash for EMS response and resource

deployment.

For additional copies of this research note, please call

(202) 366-4198 or fax your request to (202) 366-

7078. For questions regarding the data reported in

this research note, contact Ezio Cerrelli [202-366-

5358] of the National Center for Statistics and

Analysis. This research note and other general

information on highway traffic safety may be accessed

by Internet users at

http://www.nhtsa.dot.gov/people/ncsa.