Technical Report

Bureau of Transportation Statistics

June 2015

Motor Vehicle Occupant Fatality Risk Based on Person-Time 

Exposed: Age, Sex, and Period of Week

by C. Craig Morris, Ph.D.

Abstract

During the 5 years from 2008 through 2012, motor vehicle crashes killed 34,091 people each year in the United 

States, on average, 23,783 (69.8) percent of whom were 

motor vehicle occupants. This study analyzes motor vehicle 

occupant fatality risk in terms of person-time exposed as 

a function of age, sex, period of week, and interactions of 

these factors. Results reveal strong circadian periodicities of 

occupant fatalities and fatality risk, with greater risk during 

late evening-early morning hours every day of the week and 

the greatest risk during Friday–Saturday and Saturday–Sunday evening-to-morning hours. But these circadian trends 

interact with age and sex whereby young male occupants 

exhibit the most fatalities and risk. The circadian variation in 

occupant fatality risk—across demographic age-sex populations, days of the week, and drunk- and nondrunk-driverrelated fatal crashes – suggests a drowsiness component 

acting alone, and sometimes synergistically with alcohol, 

to impair the judgment and performance of motor vehicle 

occupants.

Introduction

During the 5 years from 2008 through 2012 (the last year for 

which final data are available)1, motor vehicle crashes killed 

34,091 people each year in the United States, on average, 

23,783 (69.8) percent of whom were motor vehicle occupants (excluding motorcyclists) [1-3]. As a cause of death in 

the United States in 2009, traffic crashes ranked first among 

both 5–14 and 15–24 year olds, third among 1–4 year olds, 

and fifth among 25–44 year olds [4]. 

Motor vehicle occupant fatality risk is known to vary with 

a multitude of factors, e.g., occupant age, sex, personality, experience, day of week, time of day, location, weather, 

roadway type and design, vehicle type and size, safety 

1

 Each year, the National Highway Traffic Safety Administration (NHTSA) releases 

preliminary crash fatality data for the prior year and final crash fatality data for the 

year before the prior year [2, p. 3].

equipment and use (e.g., seat belts), crash type and energy, 

nature and number of vehicle occupants and their relationship with the driver, speed, alcohol and/or drug impairment, 

driver distraction, risk taking, aggressive driving, road rage, 

dementia, drowsiness or fatigue, and myriad other factors 

[5–43]. 

Safety risk analysts typically define risk as a probability or 

rate with severity constant, such as risk of a type of vehicle 

crash (e.g., roll-over) or fatality (e.g., occupant). Such risks 

are compared via relative risks, risk ratios, or risk differences, often using multivariate modeling to assess comparisons 

and interactions while statistically controlling confounding 

covariates [e.g., 44-45]. But such definitions of risk, and the 

statistical models based on them, are fraught with challenges often neglected. The main problems fall into two 

categories. 

First, analysts generally define risk as the rate of adverse 

event incidence per unit population, distance, or duration of 

exposure and implicitly assume that risk is uniform across 

times, places, and populations within exposure aggregates 

[46]. But if risk systematically varies across constituents of 

aggregates, then high- and low-risk constituents must appear less extreme, because aggregate risk is extrapolated 

to all constituents. Furthermore, since aggregate risk is a 

weighted average of constituent risks, where each weight is 

the proportion of exposure for a constituent, aggregate risk 

is biased against constituents with relatively less exposure.2

If a small proportion of exposure entails the greatest risk, as 

generally occurs,3 aggregate risk conceals that extreme risk. 

Yet high-risk constituents incur a large proportion of adverse 

2

 Given k arbitrarily defined constituents in an exposure aggregate, where fj = 

adverse event incidence for constituent j, tj = exposure for constituent j, and rj = fj/tj = 

risk for constituent j, the “average” aggregate risk is r = Σfj/Σtj = (f1/t1)(t1/Σtj) + (f2/t2)(t2/

Σtj) + ... + (fk/tk)(tk/Σtj) = r1(t1/Σtj) + r2(t2/Σtj) + ... + rk(tk/Σtj).

3

 For example, crash risk in aviation is greatest during takeoffs and landings under 

instrument meteorological conditions at night, but exposure to these conditions is a 

relatively small fraction of total flight time or distance.
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events,4 so identifying them is necessary to effectively 

mitigate aggregate risk. Since risk is associated with myriad 

factors, such as those noted above, the identification of 

high-risk constituents requires high-dimensional multivariate data disaggregation. 

Although detailed mishap data are often available (e.g., 

from incident reports or accident investigations), comparable exposure data are expensive and usually lacking [44, 

47–49]. So analysts either omit exposure measures [50] 

or proffer risk estimates based on coarsely aggregated exposure data such as population size or miles traveled by 

a heterogeneous population of people or vehicles under 

diverse conditions over a long period of time and broad 

geographic area [1-3]. But neither of the latter approaches 

facilitates identification of risk extremes and effective 

countermeasures. 

Second, risk analysts generally define risk as the ratio of 

adverse events to exposure, where exposure is a normalizing measure of opportunity for adverse events to occur:

risk = adverse events / exposure. Eq. 1

This definition of risk (Eq. 1) is alternately viewed as a 

probability, rate, or both [47-49; 51, pp. 3–9], revealing 

fuzziness in the concept of risk. But the main problem is 

that alternative measures of exposure lead to discrepant risk definitions and absurdity. Exactly the same event 

entails different “risks” depending on which denominator is 

used. And a risk comparison of two events may give opposite results depending on which denominator is used. The 

root of this confusion is that most risk exposure measures 

confound key covariates with risk. 

For example, person time and person distance traveled 

are both regarded as appropriate exposure denominators for occupant fatality risk estimates and comparisons. 

But person distance is the product of speed and person 

time, so risk estimates and comparisons based on person 

distance are confounded with speed—a key covariate associated with mechanical energy and risk in all transportation domains. All else the same, risk comparisons based 

on person distance indicate lower risk for faster travel; 

e.g., at the extremes, pedestrian activity looks more risky, 

and space travel less, because “risk” measures based on 

person distance include speed in the exposure denominator. 

Morris (2015) analyzed eight common measures of 

transportation fatality risk exposure (person time, person distance, vehicle time, vehicle distance, population, 

registered vehicles, licensed drivers, and trips or operations), showed they are all functions of person time

exposed and (except person time) confounding covariates such as speed, and recommended person time as 

4

 For example, a large fraction of all motor vehicle occupant fatalities involve 

(especially young) males traveling during early morning hours on Saturday and 

Sunday, a relatively high-risk but small region of motor vehicle occupant exposure 

space (see Figure 5).

the exposure “denominator” for fatality risk estimates and 

comparisons within or across transportation modes (Table 

1) [52]. Multivariate risk models express risk as a function 

of covariates to assess risk comparisons or interactions of 

interest while statistically controlling confounding covariates [c.f., 44–45]. But an inappropriate exposure denominator invalidates inferences by confounding risk with key 

covariates, e.g., speed, occupancy, and average person 

time exposed per population member, registered vehicle, 

licensed driver, or trip (Eqs. 3–9 in Table 1). Use of an 

inappropriate exposure denominator defeats the normalizing purpose of an exposure denominator required for valid 

risk comparisons.

Definitions of risk based on inappropriate exposure denominators reduce to absurdity.5

 For example, consider 

definition of fatality risk with person distance (Table 1, 

Eq. 3) as opposed to person time (Table 1, Eq. 2) as the 

exposure denominator. For obvious reasons (e.g., both 

crash rates and crash severity increase exponentially with 

speed [53]), car occupants moving at 100 mph experience 

more fatality risk than occupants at 50 mph, all else the 

same for any period of time. But unless risk based on person time is at least twice as high at 100 mph as compared 

to 50 mph, risk based on person distance must be lower

at 100 mph than at 50 mph—an absurdity. If fatality risk 

based on person time at 100 mph is exactly twice that at 

50 mph, then risk based on person distance is exactly the 

same at 100 mph as at 50 mph—an absurdity. In general, 

unless speed is constant (thus cancels out), a risk comparison based on distance traveled confounds speed and 

risk differences. The greater the speed discrepancy, the 

greater the bias. Imagine risk based on person distance 

for space travelers gradually accelerating toward the 

speed of light: as their speed increases, all else the same, 

their fatality risk diminishes—an astronomical absurdity. 

Or, for a more practical example, imagine a risk comparison based on person distance traveled for pedestrian 

activity versus space travel. 

Finally, for an example available on a government website 

at the time of this writing, an actual risk comparison using 

total U.S. population as the exposure denominator (Table 

1, Eq. 6) reports motor vehicle-related fatality risk 13 times 

greater than motorcycle-related fatality risk [54]. But there 

is far more person time exposed to motor vehicle occupancy than motorcycling in the United States, and a risk 

comparison based on person time would yield the opposite 

results, consistent with universally accepted reality. Such 

confounding is less obvious (but just as serious) with other 

popular transportation safety risk exposure denominators, 

e.g., vehicle distance, which confounds both speed and 

occupancy with risk (Table 1, Eq. 5) and thus obscures 

whether changes in fatalities per vehicle distance traveled 

reflect changes in risk, speed, occupancy, or interactions of 

these factors with each other and/or other factors.

5 Reduction to absurdity is a time-honored logical argument method for proving the 

truth or falsity of propositions (e.g., see http://en.wikipedia.org/wiki/Reductio_ad_absurdum). 
3

Technical Report

Table 1: Functional Measures of Transportation Fatality Risk

fatalities

person time = risk

occupancy by time × risk

Eq. 2

fatalities

person distance

risk

speed

occupancy by distance

speed

= Eq. 3

fatalities

vehicle time = Eq. 4

fatalities

vehicle distance = Eq. 5 risk

fatalities

population = J × risk (J = person time/population) Eq. 6

fatalities

registered vehicles = K × risk (K = person time/registered vehicles) Eq. 7

fatalities

licensed drivers = L × risk (L = person time/licensed drivers) Eq. 8

fatalities

trips = M × risk (M = person time/trips) Eq. 9

SOURCE: Morris CC. Concept and measurement of transportation fatality risk. Bureau of Transportation Statistics. U.S. Department of Transportation. Washington, DC; 2015

Objectives

The present study assesses motor vehicle occupant fatality risk based on occupant hours of travel as a function of 

occupant age, sex, and period of week using U.S. data for 

2009. Pedestrians, pedal cyclists, motorcyclists, occupants 

of buses and large trucks, and occupants under 5 years of 

age were excluded due to lack of corresponding travel data 

for those populations. 

The primary measure of fatality risk is occupant fatalities per million occupant hours of travel (exposure). The 

amount of time people are exposed to a hazard (e.g., 

occupancy of a moving motor vehicle by a 20 year old 

male between midnight and 3:00 am Sunday morning) is 

a natural measure to normalize the incidence of adverse 

events (e.g., occupant fatalities) related to that hazard and 

facilitate comparisons of that risk to others across a broad 

spectrum of hazard domains. Estimates of minor, serious, 

and fatal motor vehicle occupant injury risk by age and sex 

based on both population size and occupant hours are also 

presented for comparison. 

Methods

The 2009 National Household Travel Survey (NHTS) 

provides detailed data on motor vehicle occupant travel in 

the United States [55–56]. In this nationally representative 

survey of U.S. households, respondents provided information about themselves and trips they made during a designated travel day shortly before they were contacted in the 

survey. Respondents provided their age, sex, day of trip, 

trip start and end times, and other information. Survey data 

were weighted to provide estimates for all trips made by 

all noninstitutionalized persons over 5 years of age in the 

United States during 2009. 

The data sources in the present study are: 

(a) Estimated U.S. motor vehicle occupant hours of travel 

data by age, sex, and period of week (day of week and time 

of day) from the 2009 National Household Travel Survey 

(NHTS), a nationally representative survey of U.S. households [55–56]; 

(b) Estimated U.S. population by age and sex for 2009 from 

the U.S. Census Bureau via the Web-based Injury Statistics 
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4

Query and Reporting System (WISQARS) maintained by the 

Centers for Disease Control [57];

(c) Motor vehicle occupant fatalities (excluding occupants 

of motorcycles, buses, and large trucks) for 2009 from the 

Fatality Analysis Reporting System (FARS) maintained by 

the National Highway Traffic Safety Administration, a database of information about the scenarios, vehicles, drivers, 

and passengers involved in all fatal motor vehicle crashes on 

public highways and roads in the United States [58]; and

(d) Estimated unintentional, traffic-related (on public highway), motor vehicle occupant injuries from the National 

Electronic Injury Surveillance System All-Injury Program 

(NEISS-AIP), a probability sample of U.S. emergency room 

hospitals maintained by the U.S. Consumer Product Safety 

Commission in cooperation with the U.S. Centers for Disease Control [59].

In the present study, risk of motor vehicle occupant injury or 

death is defined as occupant injuries or fatalities per million 

occupant hours of travel and, where feasible for comparison, 

per 100,000 population members. Because travel estimates 

are not available for occupants less than 5 years old, these 

young occupants are excluded from all analyses.

Injuries are defined as minor if the victim was treated and 

released, held for observation, or left the emergency room 

before treatment; serious if the victim was hospitalized or 

treated and transferred to another facility; and fatal if the 

victim died within 30 days of the trauma as a result of the 

trauma. These operational definitions of injuries and fatalities 

are objective and codify substantial differences in the degree 

of trauma sustained, but are not universal. There are no 

universal definitions of injury trauma. Alternative and multivariate definitions of injury and trauma impact, e.g., in terms 

of body part or organ system, diagnosis, disposition, impact 

on (quality) life expectancy, and so on, are beyond the scope 

of this paper. 

The statistical significance of differences and quantitative 

trends in estimated risk is assessed via analysis of deviance 

based on hierarchical quasi-likelihood generalized linear 

models relating the natural log of risk (the incident measure 

divided by the exposure measure) to covariates of interest, 

e.g., sex (dummy or effects coded), age (linear, quadratic, 

and cubic components of age coded via power polynomials), and the age by sex interaction (set of pairwise products 

of the age and sex codes). The generalized linear model 

scale parameter was estimated by the full model deviance 

divided by degrees of freedom. See Morris (2009) for more 

details and references on the statistical methodology [45]. 

Higher order interaction terms were assumed to reflect only 

nonsystematic (random) variation and omitted from regression models to increase degrees of freedom and statistical 

power. For tests of the statistical significance of generalized 

linear model coefficients (βj) in each hierarchical analysis of 

deviance, the null hypothesis was βj = 0, and the type I error 

criterion was .05 based on the F distribution. 

Results

Risk of Minor, Serious, or Fatal Occupant Injury by Age 

and Sex

Figures 1–3 give the estimated risk of minor (Figure 1), 

serious (Figure 2), or fatal (Figure 3) motor vehicle occupant 

injury by age group and sex with either population size (top 

panel) or occupant hours of travel (bottom panel) measuring 

exposure. With minor exceptions, and a difference in scale, 

the forms of the estimated risk distributions were similar for 

these two exposure measures at each risk severity level, i.e., 

minor, serious, or fatal injury. 

As shown in both panels of Figure 1, the risk of minor injury 

was greater for female than male occupants for occupants 

under 80 years of age with either population size (p=.026) or 

Figure 1: Risk of Minor Occupant Injury Per 

 100,000 Population Members (top panel) 

 and Per Million Occupant Travel Hours 

 (bottom panel) by Age and Sex in 2009

SOURCES: Centers for Disease Control (WISQARS website); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

Minor Injuries per Million Occupant Hours

0

250

500

750

1,000

1,250

1,500

1,750

2,000

2,250

2,500

5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

Minor Injuries per 100,000 Population

Age (years)

5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

Age (years)

Females

Males

Females

Males
5

Technical Report

occupant hours of travel (p=.008) as the exposure measure. 

In addition, whether risk exposure was defined in terms of 

population size or occupant hours of travel, the risk of minor 

injury was greatest for younger motor vehicle occupants, 

rising steeply from 15 years of age through 25 to 29, then 

declining and leveling off until about 80 years of age. Regardless of the exposure measure (population size, occupant hours), there were significant linear (p=.0002, p<.0001), 

quadratic (p<.0001, p=.011), and cubic (p<.0001, p<.0001) 

trend components in the association of risk with age, and 

none of these trend components interacted with sex.

As shown in both panels of Figure 2, the risk of serious injury 

appeared slightly greater for male occupants, but in fact, 

whether population size (top panel) or occupant hours of 

travel (lower panel) was the exposure measure, there was 

no significant sex effect, and no interaction of the linear, 

quadratic, or cubic components of age with sex. And there 

was no significant linear age effect whether population size 

or occupant hours of travel was the exposure measure. 

There was a significant quadratic age effect, but only with 

the occupant hours exposure measure (p=.011). Finally, 

there was a significant cubic age effect with either population 

size (p=.0008) or occupant hours (p<.0001) as the exposure 

measure, which confirms the most salient pattern in both 

panels of Figure 2 whereby serious injury risk increases 

dramatically from 10 to 20–24 years of age, declines and 

levels out from about 30–60 years of age, and then begins 

rising again to levels as great or greater than those in the 

early 20s.

As shown in both panels of Figure 3, regardless of exposure 

measure (population size, occupant hours), the risk of fatal 

injury was significantly greater for male occupants (p<.0001, 

Figure 3: Risk of Fatal Occupant Injury Per 

 100,000 Population Members (top panel) 

 and Per Million Occupant Travel Hours 

 (bottom panel) by Age and Sex in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Centers 

for Disease Control (WISQARS); Federal Highway Administration, National 

Household Travel Survey; and Bureau of Transportation Statistics; 2012.

5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

Age (years)

5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

Age (years)

0

5

10

15

20

25

Fatalities per 100,000 Population

Females

Males

0

0.25

0.50

0.75

1.00

1.25

1.50

Fatalities per Million Occupant Hours

Females

Males

Figure 2: Risk of Serious Occupant Injury Per 

 100,000 Population Members (top panel) 

 and Per Million Occupant Travel Hours 

 (bottom panel) by Age and Sex in 2009

SOURCES: Centers for Disease Control (WISQARS); Federal Highway 

Administration, National Household Travel Survey; and Bureau of Transportation Statistics, 2012.

0

1

2

3

4

5

6

7

Serious Injuries per Million Occupant Hours

5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

Age (years)

5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85+

Age (years)

0

25

50

75

100

125

150

Serious Injuries per 100,000 Population

Females

Males

Females

Males
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p=.0006). There was no significant linear age effect whether 

population size or occupant hours of travel was the exposure 

measure. There was a significant quadratic age effect, but 

only with occupant hours as the exposure measure (p=.014). 

Finally, there was a significant cubic age effect with either 

population size (p<.0001) or occupant hours (p<.0001) as 

the exposure measure, which confirms the salient pattern in 

both panels of Figure 3 whereby fatal injury risk increases 

sharply from 10 to 20–24 years of age, declines and levels 

out from 30–60 years of age, then begins rising again to 

levels as great or greater than those in the early 20’s. There 

was no significant interaction of the linear, quadratic, or cubic 

components of age with sex, confirming similar quantitative 

age effects for both sexes.

Risk of Fatal Occupant Injury by Sex and Period of Week

Motor vehicle occupant fatality risk increases on weekends, 

beginning Thursday, and is greatest on Saturday and Sunday for both males and females (Figure 4). Such temporal 

patterns of risk obviously cannot be identified using population size to measure exposure, because population size is 

constant across the temporal covariates (day of week, time 

of day) strongly associated with risk. The following analyses 

define risk in terms of occupant hours of exposure, and for 

brevity of expression, adopt the abbreviation fpm to denote 

occupant fatalities per million occupant hours. While the risk 

patterns in Figure 4 are interesting, they also mislead, because motor vehicle occupant fatality risk varies systematically with period of week, i.e., both day of week and time of 

day, and the greatest risks that certain populations of males 

and females experience during certain periods of the week 

are far greater than those shown in Figure 4. 

To analyze risk as a function of period of the week, consider 

the eight 3-hour periods each day starting at midnight (0000–

0300, 0300–0600, 0600–0900, 0900–1200, 1200–1500, 

1500–1800, 1800–2100, and 2100–0000). Define period 

of week as the sequence of these periods from Monday 

through Sunday. Figure 5 gives occupant fatalities (top), 

hours of travel (middle), and fatalities per million occupant 

hours (bottom) by sex and period of week in 2009. Vertical lines mark midnight. Males’ peak risk of 6.49 fpm during 

the period 12:00–3:00 am on Saturday morning (Figure 5, 

bottom) is about 19 times their “average” Saturday risk of 

0.35 fpm (Figure 4). Figure 5 shows substantially higher 

risks than the average daily risks in Figure 4 for every other 

late-evening/early-morning period of the week, not just those 

on weekends. Nevertheless, Figure 5 also misleads because 

occupant fatality risk varies substantially not only with occupant sex and period of week, but also with occupant age 

as shown above in Figure 3. The following analyses disaggregate the fatality and hours of travel data by occupant age, 

sex, and period of week to more accurately estimate and 

compare motor vehicle occupant fatality risk. 

Risk of Fatal Occupant Injury by Age, Sex, and Period 

of Week 

Figures 6–12 give occupant fatality risk in 2009 by sex 

and period of week for age groups 15–19, 20–29, 30–39, 

40–49, 50–59, 60–69, and 70+ years. Risk is strongly circadian6

 for both sexes in all age groups. To facilitate age comparisons, Figures 6–12 use the same risk scale (0–25 fpm). 

To facilitate inferential statistical analysis of the circadian 

data in Figures 6–12, each day was defined to begin and 

end at noon instead of midnight, with day 1 beginning at 

noon Sunday and ending at noon Monday, day 2 beginning 

at noon Monday and ending at noon Tuesday, etc. Similarly, period of day was defined as the sequence of eight 

3-hour periods in such a day, beginning at noon, as defined above. Defining day this way simplifies modeling the 

circadian variation in risk across the week via orthogonal 

polynomial coding of the linear and quadratic components 

of day and period of day thereby reducing model complexity and increasing degrees of freedom and statistical power. 

To further reduce model complexity, the risk data in each of 

Figures 6–12 were analyzed via separate hierarchical quasi-likelihood generalized linear regression models relating 

the natural log of fatality risk to the covariates: sex (dummy 

coded), day (linear and quadratic components coded via 

orthogonal polynomials), period of day (linear and quadratic 

components coded via orthogonal polynomials), day by 

sex, period of day by sex, and period of day by day. 

Figure 6 gives occupant fatality risk by sex and period of 

week for 15–19 year olds. The peak risk of 20.0 fpm for 

males during the 3:00–6:00 am period Sunday morning 

6 Circadian here means “being, having, characterized by, or occurring in 

approximately 24-hour periods or cycles (as of biological activity or function)” and 

does not denote or imply involvement of the circadian rhythm or biological clock 

(downloaded on 11 June 2012 at http://www.merriam-webster.com/dictionary/

circadian).

Figure 4: Occupant Fatalities Per Million 

Occupant Hours by Sex and Day of Week From 

Monday Through Sunday in 2009

SOURCE: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Mon Tue Wed Thu Fri Sat Sun

Occupant Fatalities/ Million Occupant Hours

Day of Week

Females

Males
7

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Figure 5: Occupant Fatalities (top), Hours of Travel (middle), and 

 Fatalities Per Million Occupant Hours (bottom) by Sex and 

 Period of Week From Monday Through Sunday in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal Highway Administration, National Household Travel Survey; and Bureau of Transportation Statistics, 2012.

0

500

1,000

1,500

2,000

2,500

3,000

5+ Year Old Occupant Travel Hours(millions) in 2009

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

Mon Tue Wed Thu Fri Sat Sun

Mon Tue Wed Thu Fri Sat Sun

Males Females

0

100

200

300

400

500

600

700

800

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

5+ Year Old Occupant Fatalitiesin 2009

Weekday Period

Mon Tue Wed Thu Fri Sat Sun

Males

Females

Males

Females

0

1

2

3

4

5

6

7

8

9

10

5+ Year Old Fatalities per Million Occupant Hoursin 2009
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Figure 6: 15- to 19-Year-Old Motor Vehicle

 Occupant Fatality Risk by Sex and 

 Period of Week in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

0

5

10

15

20

25

Occupant Fatalities per Million Occupant Hoursin 2009

Mon Tue Wed Thu Fri Sat Sun

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

15-19 year 

old males

15-19 year 

old females

Figure 7: 20- to 29-Year-Old Motor Vehicle 

 Occupant Fatality Risk by Sex and 

 Period of Week in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

Mon Tue Wed Thu Fri Sat Sun

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

20-29 year 

old males

0

5

10

15

20

25

Occupant Fatalities per Million Occupant Hoursin 2009

20-29 year 

old females

Figure 8: 30- to 39-Year-Old Motor Vehicle 

 Occupant Fatality Risk by Sex and 

 Period of Week in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

Mon Tue Wed Thu Fri Sat Sun

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

30-39 year 

old males 30-39 year 

old females

0

5

10

15

20

25

Occupant Fatalities per Million Occupant Hoursin 2009

Figure 9: 40- to 49-Year-Old Motor Vehicle 

 Occupant Fatality Risk by Sex and 

 Period of Week in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

Mon Tue Wed Thu Fri Sat Sun

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

0

5

10

15

20

25

Occupant Fatalities per Million Occupant Hoursin 2009

40-49 year 

old males 40-49 year 

old females

is about 36 times the average Sunday risk of 0.56 fpm for 

this age-sex cohort. Similarly, the peak risk of 10.1 fpm for 

females during the 3:00–6:00 am period Thursday morning 

is about 33 times the average Thursday risk of 0.30 fpm 

for this age-sex cohort. Fatality risk was greater for male 

versus female occupants (p=.006). There was a linear day 

effect (p=.034) with risk increasing over the week. There 

was also a linear period of day effect (p=.008) (risk was 

higher in the latter part of the day as defined above). As 

expected given the highly circadian risk pattern, there was 

a quadratic period of day effect (p<.0001). There were no 

significant interactions, indicating similar day and period of 

day trends across males and females and similar period of 

day trends across days.

Figure 7 gives occupant fatality risk by sex and period of 

week for 20–29 year olds. The peak risk of 16.6 fpm for 

males during the 12:00–3:00 am period Saturday morning 

is about 16 times the average Saturday risk of 1.1 fpm for 

this age-sex cohort. Similarly, the peak risk of 9.4 fpm for 

females during the 3:00–6:00 am period Sunday morning is 

about 27 times the average Sunday risk of 0.35 fpm for this 
9

Technical Report

age-sex cohort. Fatality risk was greater for male versus 

female occupants (p<.0001). There was a linear day effect 

(p=.0007) with risk increasing over the week. There was 

also a linear period of day effect (p=.001) (risk was higher 

in the latter part of the day as defined above). As expected, 

there was a quadratic period of day effect (p<.0001). There 

were no significant interactions with sex, indicating similar 

day and period of day trends across males and females. 

There was a significant linear period of day by linear day 

interaction (p=.006), suggesting that the risk distribution 

shifted to later in the day as the week progressed.

Figure 8 gives occupant fatality risk by sex and period of 

week for 30–39 year olds. The peak risk of 6.3 fpm for 

males during the 12:00–3:00 am period Saturday morning 

is about 22 times the average Saturday risk of 0.29 fpm for 

this age-sex cohort. Similarly, the peak risk of 5.3 fpm for 

females during the 12:00–3:00 am period Saturday morning 

is about 37 times the average Saturday risk of 0.15 fpm for 

this age-sex cohort. Fatality risk was greater for male versus female occupants (p<.0001). And, as expected, there 

was a quadratic period of day effect (p<.0001). There were 

no other significant effects or interactions.

Figure 9 gives occupant fatality risk by sex and period of 

week for 40–49 year olds. The peak risk of 4.7 fpm for 

males during the 3:00–6:00 am period Sunday morning is 

about 19 times the average Sunday risk of 0.24 fpm for this 

age-sex cohort. The peak risk of 8.3 fpm for females during the 12:00–3:00 am period Thursday morning is about 

96 times the average Thursday risk of 0.09 fpm for this 

age-sex cohort. Fatality risk was greater for male versus 

female occupants (p<.0001). There was a linear day effect 

(p=.035) with risk increasing over the week. As expected, 

there was a quadratic period of day effect (p<.0001). There 

were no other significant effects or interactions.

Figure 10 gives occupant fatality risk by sex and period 

of week for 50–59 year olds. The peak risk of 3.4 fpm for 

males during the 12:00–3:00 am period Saturday morning 

is about 14 times the average Saturday risk of 0.24 fpm for 

this age-sex cohort. The peak risk of 1.7 fpm for females 

during the 12:00–3:00 am period Sunday morning is about 

15 times the average Sunday risk of 0.11 fpm for this agesex cohort. Fatality risk was greater for male versus female 

occupants (p<.0001). As expected, there was a quadratic 

period of day effect (p<.0001). There were no other significant effects or interactions.

Figure 11 gives occupant fatality risk by sex and period 

of week for 60–69 year olds. The peak risk of 3.4 fpm for 

males during the 12:00–3:00 am period Friday morning is 

about 15 times the average Friday risk of .23 fpm for this 

age-sex cohort. The peak risk of 2.5 fpm for females during 

the 12:00–3:00 am period Saturday morning is about 21 

times the average Saturday risk of 0.11 fpm for this agesex cohort. Fatality risk was greater for male versus female 

occupants (p<.0001). As expected, there was a quadratic 

period of day effect (p<.0001). There was also a significant 

quadratic period of day by sex interaction (p=.021). There 

were no other significant effects or interactions.

Figure 12 gives occupant fatality risk by sex and period 

of week for 70+ year olds. As shown above in Figure 3, 

fatality risk increases in the 70+ age group as compared 

to younger occupants, but the smaller population size of 

this age group increases variability in both fatalities and 

estimated travel time, and thus in estimates of fatality risk. 

Figure 10: 50- to 59-Year-Old Motor Vehicle 

 Occupant Fatality Risk by Sex and 

 Period of Week in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

Mon Tue Wed Thu Fri Sat Sun

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

50-59 year 

old males

50-59 year 

old females

0

5

10

15

20

25

Occupant Fatalities per Million Occupant Hoursin 2009

Figure 11: 60- to 69-Year-Old Motor Vehicle 

 Occupant Fatality Risk by Sex and 

 Period of Week in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

Mon Tue Wed Thu Fri Sat Sun

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

0

5

10

15

20

25

Occupant Fatalities per Million Occupant Hoursin 2009

60-69 year 

old males

60-69 year 

old females
Technical Report

10

Nevertheless, a strong circadian periodicity of occupant 

fatality risk is apparent in Figure 12 for this age group as 

well. Fatality risk was greater for male versus female occupants (p=.0002). There was a linear period of day effect 

(p=.002). And, as expected, there was a quadratic period of 

day effect (p<.0001). There were no other significant effects 

or interactions.

Risk of Fatal Occupant Injury by Drunk-Driver Relatedness and Period of Week 

Figure 13 gives occupant fatalities (top panel) and fatalities per million occupant hours of travel (bottom panel) by 

drunk-driver-relatedness and period of week in 2009. This 

analysis partitions occupant fatalities based on whether 

or not the crash was determined to involve a drunk-driver 

(whether or not the fatally injured occupants or driver of 

their car was drunk). Dividing those fatalities, respectively, 

by occupant hours of travel yields the risks, respectively, 

of drunk- or nondrunk-driver-related occupant fatality. Note 

that these risks have nothing to do with the risks of occupant fatality while the driver of the occupant’s vehicle is either drunk or not, which risks cannot be estimated because 

whether the driver was drunk or not is not queried (and 

would be suspect even if it were) in the NHTS source of occupant travel data. Both drunk- and nondrunk-driver-related 

occupant fatalities exhibit strong circadian periodicities, but 

out of phase, with drunk-driver-related fatalities peaking just 

after midnight and nondrunk-driver-related fatalities peaking 

just after midday. Also, while drunk-driver-related fatalities 

steadily increase over the week, with sharp increases early 

Saturday and Sunday, nondrunk-driver-related fatalities 

remain about the same Monday through Friday and decline 

on Saturday and Sunday (top panel). Nevertheless, both 

drunk- and nondrunk-driver-related occupant fatality risk 

peaks in the early morning hours after midnight (bottom 

panel).

To facilitate statistical analysis of the circadian risk data in 

Figure 13, each day was again defined to begin and end 

at noon rather than midnight, and period of day was again 

defined as the sequence of eight 3-hour periods in such 

a day. The drunk-driver- and nondrunk-driver-related risk 

data in Figure 13 were analyzed, respectively, via separate 

hierarchical quasi-likelihood generalized linear regression 

models relating the natural log of fatality risk to the covariates: day (linear and quadratic components coded via 

orthogonal polynomials), period of day (linear and quadratic 

components coded via orthogonal polynomials), and period 

of day by day (set of pairwise products of the day and 

period of day codes). Drunk-driver-related occupant fatality 

risk increased through the week as revealed by a linear day 

effect (p=.015), was circadian as confirmed by a quadratic 

period of day effect (p<.0001), and shifted later in the day 

as the week progressed as revealed by a linear period of 

day by linear day interaction (p=.035). Nondrunk-driverrelated occupant fatality risk was circadian as confirmed 

by a quadratic period of day effect (p=.034), with no other 

significant effects. 

The risk data in Figure 13 must be interpreted cautiously, 

because drunk-driver-related occupant fatality risk is also 

strongly associated with age and sex (e.g., young male 

occupants exhibit the greatest risk by far). The purpose 

of Figure 13 is to show that occupant fatality risk remains 

strongly circadian with drunk-driver-related fatalities removed. Although many factors are correlated with period 

of day and week, such as darkness, traffic volume, travel 

purpose, and so on, the remarkable circadian periodicity of 

occupant fatality risk—across demographic age-sex populations, days of the week, and drunk- and nondrunk-driverrelated fatal crashes—suggests a drowsiness component 

acting alone, and sometimes synergistically with alcohol, to 

impair the judgment and performance of motor vehicle occupants. Much evidence in the literature, some of which is 

discussed below, supports a drowsiness explanation of the 

circadian occupant risk data reported herein.

Conclusions

While previous research has demonstrated age, sex, day of 

week, and time of day effects on motor vehicle crashes and 

crash risk based on trips, vehicle miles, or occasionally occupant miles traveled [e.g., 16, 19, 23–25, 30, 41, 46], the 

present study appears to be the first to define and quantify 

motor vehicle occupant fatality risk in terms of occupant 

hours of travel. Results demonstrated the robust circadian 

periodicity of motor vehicle occupant fatality risk across 

age-sex populations, days of the week, and drunk- and 

nondrunk-driver-related fatal crashes, with much higher risk 

during late-evening and early-morning hours every day of 

the week and the greatest risk during the Friday–Saturday 

and Saturday–Sunday late evening-early morning hours 

Figure 12: 70+ Year-Old-Motor Vehicle 

 Occupant Fatality Risk by Sex and 

 Period of Week in 2009

SOURCES: National Highway Traffic Safety Administration (FARS); Federal 

Highway Administration, National Household Travel Survey; and Bureau of 

Transportation Statistics, 2012.

Mon Tue Wed Thu Fri Sat Sun

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

70+ year 

old females

70+ year 

old males

0

5

10

15

20

25

Occupant Fatalities per Million Occupant Hoursin 2009

58 ≈ 4 

fatalities 

/0.07M 

occupant 

hours 

(unstable)

32 ≈ 7 

fatalities 

/0.22M 

occupant 

hours 

(unstable)
11

Technical Report

Figure 13: Occupant Fatalities and Fatality Risk by Drunk-Driver 

 Relatedness and Period of Week in 2009 

SOURCES: National Highway Traffic Safety Administration (FARS); Federal Highway Administration, National Household 

Travel Survey; and Bureau of Transportation Statistics, 2012.

0

100

200

300

400

500

600

700

800

900

1,000

5+ Year Old Occupant Fatalitiesin 2009

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

00-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-2100-0306-0912-1518-21

Weekday Period

Mon Tue Wed Thu Fri Sat Sun

Mon Tue Wed Thu Fri Sat Sun

Not Drunk 

Driver Related

Drunk 

Driver Related

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5+ Year Old Occupant Fatalities per Million Occupant Hours in 2009

Not Drunk 

Driver Related

Drunk 

Driver Related
Technical Report

12

when more fatalities and higher fatality risk are associated with drunk-driver-related crashes. But these circadian 

trends also interact with age and sex, with young male 

occupants exhibiting the most fatalities and fatality risk and 

the difference in risk between male and female occupants 

diminishing with age.

The circadian periodicity of motor vehicle occupant fatality risk across age-sex populations, days of the week, and 

drunk- and nondrunk-driver-related fatal crashes suggests 

a drowsiness component acting alone, and sometimes synergistically with alcohol, to impair the judgment and performance of motor vehicle occupants. A drowsiness explanation is supported by considerable evidence in the literature, 

including a recent study estimating that 16.5 percent of fatal 

crashes in the United States from 2000 to 2008 involved a 

drowsy driver [60]. Both homeostatic and circadian rhythm 

(biological clock) processes influence the neurobiological 

need to sleep, and the longer the time awake, the greater 

the pressure to sleep and difficulty resisting it [61]. Falling 

asleep at the wheel, and departing the roadway at high 

speed with no sign of braking, is the most obvious drowsiness-related crash type, but not the only or even most 

prevalent one [50]. Drowsiness causes a variety of impairments of sensorimotor and cognitive processes essential to 

safe driving, e.g., slower reaction times to stimuli, reduced 

vigilance in attention-demanding tasks, and deficits in 

information processing such as memory performance and 

processing and integrating information [61–62].

Furthermore, evidence that sleep deprivation depletes 

self-regulatory resources necessary to sustain executive 

processes related to self-control, hostility, and impulse 

inhibition, thereby increasing deviance from societal norms 

[63], may explain some deviant roadway activities (excessive acceleration, speeding, drunk driving, etc.) during late 

night–early morning periods, when many motor vehicle 

occupants have been awake hours into their usual sleep 

periods and already carry a debilitating sleep debt [64, p. 

70] accumulated over prior days of insufficient sleep. 

The circadian periodicity of motor vehicle occupant fatality 

risk has implications for occupant injury and fatality risk reduction efforts. First, these results identify regions of motor 

vehicle occupant exposure space where occupant fatality 

risk is highly concentrated and where mitigation resources 

must be focused to effectively reduce this risk.

Second, it is misleading for public health communications 

to describe motor vehicle occupant risk as if it were uniform 

over time and other factors, e.g., “An average of 92 people 

died each day in motor vehicle crashes in 2012—one every 

16 minutes.” [1, p. 1] This widely prevalent miscommunication of risk information ignores the strong association of 

motor vehicle occupant fatalities and risk with age, sex, period of week, and other factors, and reinforces the fatalistic 

view that fatalities are random and there is little we can do 

to predict or prevent them. 

Third, the results suggest that providing accurate risk 

information to the public, e.g., in driver education and 

advertising, could reduce risk by encouraging people, especially young high-risk populations, to monitor and control 

exposure to high risk regimes of motor vehicle travel. Public 

health messaging and education is needed to accurately 

convey the distribution of motor vehicle occupant risk 

across age, sex, and period of week, and to communicate 

mitigation strategies, e.g., minimizing high risk travel, getting sufficient sleep, and being vigilant for and appropriately 

responsive to impulsive or otherwise deviant driver behaviors during such travel—whether in one’s own vehicle or 

another’s. 

Fourth, these results suggest the possibility of an inexpensive onboard risk monitoring device, using strong indicators of motor vehicle occupant risk (such as period of week 

and other reliable predictors) to indicate risk to drivers and 

passengers and facilitate their ability to monitor and control 

exposure to the highest risk regimes of motor vehicle travel. 

But such instrumentation must be carefully researched 

and developed before implementation to prevent undesirable side effects such as driver distraction or risk-seeking 

behaviors. 

Finally, these results implicate sleep deprivation and 

drowsiness as critical underlying components of motor 

vehicle occupant fatality risk that need to be more widely 

recognized and studied, better communicated to the public 

and policy makers, and systematically addressed via all 

feasible means.

End Note

The views in this paper are those of the author and do not 

necessarily represent the official views of the U.S. Department of Transportation or any other agency or staff.

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