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Crash risk by driver age, gender, and time of day using a new
exposure methodology☆
,
☆☆
Shirley Regev,
a,
⁎Jonathan J. Rolison,
b
Salissou Moutari
c
a
The School of Public Policy, University College London, The Rubin Building, 29/31 Tavistock Square, London WC1H 9QU, UK
b
Department of Psychology, University of Essex, Colchester, UK
c
Department of Mathematics and Physics, Queen's University Belfast, Belfast, UK
abstractarticle info
Article history:
Received 26 November 2017
Received in revised form 1 April 2018
Accepted 2 July 2018
Available online 07 July2018
Introduction: Concerns have been raised that the nonlinear relation between crashes and travel exposure invali-
dates the conventional use of crash rates to control for exposure. A new metric of exposure that bears a linear as-
sociation to crashes wasused as basis for calculating unbiased crash risks. This study compared the two methods
–conventional crash rates and new adjustedcrash risk –for assessingthe effect of driver age, gender, and time of
day on the riskof crash involvement and crashfatality. Method:We used police reportsof single-car and multi-car
crashes with fatal and nonfatal driver injuries that occurred during 2002–2012 in Great Britain. Results: Conven-
tional crash rates were highest in the youngest age group and declined steeply until age 60–69 years. The ad-
justed crash risk instead peaked at age 21–29 years and reduced gradually with age. The risk of nighttime
driving, especially among teenage drivers, was much smaller when basedon adjusted crash risks. Finally, the ad-
justed fatality risk incurred by elderly drivers remained constant across time of day, suggesting that their risk of
sustaining a fatal injury due to a crash is more attributable to excess fragility than to crash seriousness. Conclu-
sions: Our findings demonstrate a biasing effect of low travel exposure on conventional crash rates. This implies
that conventional methods do not yield meaningful comparisonsof crash risk between drivergroups and driving
conditions of varyingexposure to risk. The excesscrash rates typicallyassociated withteenage and elderly drivers
as well as nighttime driving are attributed in part to overestimation of risk at low travel exposure. Practical Appli-
cations: Greater attention should be directed toward crash involvement among drivers in their 20s and 30s as
well as younger drivers. Countermeasures should focus on the role of physical vulnerability in fatality risk of el-
derly drivers.
© 2018 The Authors. National Safety Council and Elsevier Ltd. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
Keywords:
Crash rates
Age
Sex
Time of day
Low-exposure bias
1. Introduction
Road traffic collisions are a major global health concern. They ac-
count for more than 1.2 million deaths worldwide each year and an
even larger number of serious injuries (World Health Organization,
2015). Obtaining a better understanding of the factors that contribute
to driver crash risk is critical for the development of effective road safety
policies and initiatives.
A wealth of road safety research has assessed driver characteristics,
such as age and gender, linked to elevated crash risk. These studies
have typically shown that the youngest and oldest drivers have much
higher fatal and non-fatal crash risks than drivers in the middle-age
ranges (Lam, 2002; Ma & Yan, 2014; McAndrews, Beyer, Guse, &
Layde, 2013; Williams, 2003; Williams & Shabanova, 2003; Zhou,
Zhao, Pour-Rouholamin, & Tobias, 2015). Several studies have also
found differences in fatal and nonfatal crash risks among subgroups of
older drivers. For example, there is evidence that drivers aged 70–74 ex-
hibit lower crash risk relative to drivers aged 75–79, with the highest
risk seen in drivers aged 80 and older (Cheung & McCartt, 2011;
Cicchino, 2015; Cicchino & McCartt, 2014).
Road safety research has also addressed associations between driver
gender and elevated crash risk.In general, female drivers are considered
safer than male drivers (Åkerstedt & Kecklund, 2001; Kim, Brunner, &
Yamashita, 2008; Ma & Yan, 2014; Massie, Green, & Campbell, 1997;
Zhou et al., 2015). However, some studies suggest that while women
tend to have fewer fatal crashes than men do, their risk of injury crashes
may be higher (Massie, Campbell, & Williams, 1995;
Santamariña-Rubio, Pérez, Olabarria, & Novoa, 2014).
In addition to crash involvement, driver's age and gender have also
been shown to affect the severity of crash outcomes (i.e. the risk of
fatal injury given a crash). Male and elderly drivers are more likely to
be fatally injured in a crash than female drivers and drivers in the
Journal of Safety Research 66 (2018) 131–140
☆Declarations of interest: None.
☆☆ Acknowledgments: The research was supported by a grant awarded by the UK
Engineering and Physical Sciences Research Council (EPSRC Reference; EP/M017877/1;
“A new metric for the assessment of driver crash risks”).
⁎Corresponding author.
E-mail address: s.dorchin-regev@ucl.ac.uk (S. Regev).
https://doi.org/10.1016/j.jsr.2018.07.002
0022-4375/© 2018 The Authors. National Safety Council and Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at ScienceDirect
Journal of Safety Research
journal homepage: www.elsevier.com/locate/jsr
younger age ranges (Huang & Lai, 2011; Kim, Ulfarsson, Kim, & Shankar,
2013; Li, Braver, & Chen, 2003; Valent et al., 2002; Vorko-Jović,Kern,&
Biloglav, 2006).
The risk ofcrash involvement also appears to vary with environmen-
tal factors, such as time of day. Crash risk is higher for nighttime com-
pared with other times of day, with the difference being more
pronounced for male drivers and at younger ages (Doherty, Andrey, &
MacGregor, 1998; Kim et al., 2013; Li, Baker, Langlois, & Kelen, 1998;
Massie et al., 1995). Time of day has also appeared to be associated
with crash severity, as drivers are more likely to sustain a fatal injury
due to nighttime crashes compared to daytime crashes, particularly
among the younger age groups (Huang & Lai, 2011; Valent et al.,
2002; Vorko-Jovićet al., 2006).
It is well recognized that in order to allow for meaningful compari-
sons of crash risk among driver groups or driving environments, it is
necessary to take into account their differences in intensity of travel ex-
posure (Elander, West, & French, 1993; Wolfe, 1982). If travel exposure
is not controlled for, one cannot determine whether a higher number of
crashes for a particular group (or environment) is due to a greater ten-
dency for crash involvement or to greater exposure to travel situations
that may result in a crash (Chapman, 1973; Muhlrad & Dupont, 2010).
Traditionally, researchers have accounted for differences in expo-
sure by dividing the crash counts of a particular driver group (e.g., age,
gender) by either their annual travel (Li et al., 2003; Massie et al.,
1995, 1997), their group size in number of licensed drivers (Chen et
al., 2010; McAndrews et al., 2013), or a combination of travel and
group size (Doherty et al., 1998; Li et al., 1998). However, the use of
crash rate to account for differences in driving exposure is appropriate
as long as crash counts increase proportionally with increased driving
exposure. That is, when the association between crash frequency and
driving exposure, known as the ‘safety performance function,’is linear
(Elander et al., 1993; Qin, Ivan, & Ravishanker, 2004). Crash rate can
be defined as the slope of the line from the origins to a particular
point on the safety performance function. If the safety performance
function is non-linear, then crash rate will vary at different exposure
levels. Consequently, crash rates would not allow for meaningful risk
comparisons among driver groups or driving conditions with varying
levels of exposure (Elander et al., 1993; Janke, 1991; Qin et al., 2004).
Importantly, numerous road safety researchers (Elander et al., 1993;
Elvik, 2014; Janke, 1991; Langford, Methorst, & Hakamies-Blomqvist,
2006; Maycock, Lockwood, & Lester, 1991; Qin et al., 2004;seeaf
Wåhlberg, 2009 for review) reported thatthe relationship between an-
nual crash counts and driving exposure is in fact nonlinear. Specifically,
the relationship is often described as following a broadly logarithmic
curve, with an initial rapid increase in crash counts at low exposure
levels followed by gradually slowing down and finally flattening out at
high exposure levels. As a result, as the distance driven increases, the
crash rate per distance driven declines. Thus, it is a common finding in
the literature that low-mileage drivers have greater crash rate than
high-mileage drivers (Alvarez & Fierro, 2008; Antin et al., 2017;
Hakamies-Blomqvist, Raitanen, & O'Neill, 2002; Langford et al., 2006).
There are several possible explanations for the nonlinearity of the
safety performance function. First, high-mileage drivers clock a greater
proportion of their miles on freeways, whereas low-mileage drivers
tend to restrict their travel to relatively hazardous urban roads
(Hakamies-Blomqvist et al., 2002; Janke, 1991; Keall & Frith, 2004,
2006). Second, high-mileage drivers accumulate greater driving experi-
ence than low-mileage drivers and therefore may possess betterdriving
skills (Elander et al., 1993; Elvik, 2014). Finally, older drivers with visual
or physical impairments tend to reduce their driving exposure (Alvarez
& Fierro, 2008; Stutts, 1998); thus, a low-mileage group might include a
larger number of impaired drivers who are more inclined to be involved
in crashes (Keall & Frith, 2004; Langford et al., 2006, 2013).
Regardless of the underlying reasons, the exposure–crash relation-
ship is nonlinear, and hence crash rates become smaller with increased
driving exposure. Because of this, concerns have been raised in the road
safety literature that the use of crash rates may lead to biased risk com-
parisons when driver groups or driving conditions vary greatly in their
travel exposure (Elander et al., 1993; Elvik, 2014; Hauer, 1995; Janke,
1991; Qin et al., 2004). Accordingly, differences in crash rate between
groups or driving conditions may reflect variation in exposure rather
than variation in crash tendency. Consequently, the rate-based method
may lead to overestimation of crash risk for low-exposed drivers, and
underestimation for high-exposed drivers (for similar reasoning against
the use of rates to control for exposure to risk applied to biological and
epidemiological data see Allison, Paultre, Goran, Poehlman, &
Heymsfield, 1995; Curran-Everett, 2013; Packard & Boardman, 1999).
Acommonfinding in the literature is that young and elderly drivers
have lower driving exposure than other age groups in terms of distance
traveled and number of license holders (e.g., Fontaine, 2003; Keall &
Frith, 2006; Langford et al., 2006). It follows that in the case of age
group comparisons, the use of crash rates may lead to underestimation
of crash risk for low-exposed age groups, such as young and elderly
drivers, and overestimation of crash risk for high-exposed age groups,
such as drivers in the middle-age range. In line with this, the proportion
of low-annual travel drivers as a function of age has a U-shaped curve
similar to that typically observed for crash rate by age: Elevated values
for younger and older drivers relative to the middle-aged drivers
(Fontaine, 2003; Janke, 1991; Keall & Frith, 2006). This observation
has led to the theoretical notion, referred to as ‘low-mileage bias,’
whereby the elevated crash risk among elderly drivers might be the re-
sult of their low distance traveled (Hakamies-Blomqvist et al., 2002). In
accordance with this reasoning, comparing subgroups of drivers of dif-
ferent ages matched for distance driven has led to the oldest drivers
being the safest or just as safe as drivers in other age ranges (Alvarez
& Fierro, 2008; Fontaine, 2003; Hakamies-Blomqvist et al., 2002;
Langford et al., 2006).
Biased estimation of crash rates might also occur for gender compar-
isons in crash risk. Studies have reported that women of all ages are less
likely than men to have a driver's license, and those who do tend to
drive lower annual mileage (Fontaine, 2003; Li et al., 1998; Massie et
al., 1995; Santamariña-Rubio et al., 2014). It is conceivable then that
the rate-based crash risk of female drivers might be underestimated,
while their male counterparts might have an overestimated crash risk.
The use of crash rates can be equally regarded as inappropriate for
any driving conditions that differ substantially in travel exposure, such
as time of day. The proportion of night driving is considerably small
across all ages, as most of the driving is done during daytime (Keall &
Frith, 2004, 2006; Powell et al., 2007). For example, in one study, re-
searchers found that only 13% of drivers' total driving distance was
made at night (Keall & Frith, 2004). The small exposure to risk during
nighttime hours may therefore be associated with biased estimates of
crash rates, whereby nighttime crash risk is exaggerated relative to
other times of day. Moreover, given that age and gender differences in
travel exposure vary with time of day (e.g., Keall & Frith, 2004), disag-
gregating crash risk by time of day would be of relevance for risk com-
parisons among driver groups.
This paper aims to examine the extent to which the traditional crash
rate approach is biased for risk comparisons between age–gender
groups and across different times of day. To this end, we compared
the results of conventional crash rates to those of adjusted risk estima-
tors computed using a new exposure metric that provides a linear rela-
tionship for the safety performance function, as outlined below. We
hypothesized that when using conventional crash rate estimators,
young and elderly drivers would demonstrate a much higher risk of
crash involvement for fatal and nonfatal crashes compared to drivers
in the middle-age ranges; in contrast, when using adjusted risk estima-
tors, age differences in crash involvement risk would be substantially
reduced. Similarly, we hypothesized that the risk of crash involvement
for nighttime driving compared to driving during the day and evening
hours would be reduced when using the new adjusted risk estimators
compared to the traditional crash rates.
132 S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
As a further consideration, we also assessed the risk of crash fatality
(i.e., driver fatal injury given a crash had occurred) as estimated by the
traditional and adjusted methods. Fatality risk was defined as the ratio
of fatal crash involvement risk to both fatal and nonfatal crash involve-
ment risks. Our rationale was that if small driver numbers among the
young and elderly and infrequent travel atnight bias traditional assess-
ments of crash risk, then any measures of fatal injury risk based on this
approach would also be biased.
Single- and multi-vehicle crashes appear to differ substantially in
their characteristics and contributing factors (Bingham & Ehsani,
2012; Williams & Shabanova, 2003). Furthermore, it has been argued
that estimating crash risk of multi-vehicle collisions requires
adjusting for the travel exposure of all drivers involved (Elvik,
2014; Qin et al., 2004; Rolison, Moutari, Hewson, & Hellier, 2014).
Therefore, comparisons between conventional and adjusted crash
risk methods were made separately for single- and two-vehicle
crashes.
2. Materials and methods
2.1. Travel exposure data
Estimates of driving exposure in terms of trip numbers and license
holders were obtained from the United Kingdom (UK) National Travel
Survey for the periods of 2002–2012 (Department for Transport [DfT],
2012a). Trip numbers per driver were estimated annually for each
driver age range (17–20, 21–29, 30–39, 40–49, 50–59, 60–69, ≥70
years), gender, and time of day (daytime 06:00–18:00; evening
18:00–21:00; nighttime 21:00–06:00). Driver numbers in the popula-
tion were estimated annually for each age range and gender as the
product of the proportion of drivers in the UK National Travel Survey
sample (14,959 drivers on average, annually) and the estimated num-
ber of UK residents.
2.2. Road accident data
The road accident data were population-wide single- and two-car
collisions reported in Great Britain (England, Scotland, and Wales)
during the years 2002 through 2012. The road accident data were
recorded by police officials on location and were made available by
the University of Essex Data Archive after being processed by the
Department for Transport (DfT, 2012b). Driver deaths occurring
within 30 days following a road accident were classified as road
accident fatalities. Non-fatal collisions included non-fatal driver
injury cases.
2.3. Calculation for single-vehicle crashes
Traditional crash risk, γ
i
, was estimated by dividingthe crash counts,
x
i
, of each driver group, i, by the product of their estimated trips per
driver, y
i
, and their driver numbers in the population, z
i
, where:
γi¼xi
yizi
:ð1Þ
The γ
i
values were scaled annually by dividing each by the
largest across all driver groups (i.e., age, gender, time of day),
whereby γ
i
was equal to 1 for the driver group with the highest
crash risk.
Here, we employed the new exposure metric to provide a linear
safety performance function and remedy the biasing effects of crash
rates. Thisapproach involvesan alternative assessment of riskexposure.
Accordingly, the adjusted exposure, ξ
i
, of each driver group, i, is esti-
mated on theassumption that exposure should be high if the population
of a driver group is large and their trips are many, low if their population
is large andtheir trips are few,and higher if their population is small and
their trips are many than if their population is small and their trips are
few. It follows that:
ξi¼exp 2 zi
ðÞ−yi1−zi
ðÞ
1−yi
ðÞþexp 2 zi
ðÞ
;ð2Þ
where total trips per driver, yi, and the population, zi, are scaled values
that are calculated by dividing each value by the largest across driver
groups (i.e., age, gender, time of day).
The adjusted crash risk, γ
i
′, of each driver group, i, is estimated on
the assumption that the crash risk of a driver group should be high if
their crashes are many and their adjusted exposure is small, low if
their crashes are few and their exposure is high, and higher if their
crashes are few and their exposure is low than if their crashes are
many and their exposure is high. Thus:
γ0
i¼αAi1−ξi−xi
ðÞexp −2xi
ðÞ
1þexp −2xi
ðÞ
;ð3Þ
with:
α¼exp 1ðÞ
1−exp 1ðÞ
;ð3aÞ
and:
Ai¼1þxiexp −xi
ðÞ−ξiexp ξi−1ðÞ;ð3bÞ
where crash numbers, xi, are scaled values that are calculated by divid-
ing each value by the largest across all driver groups (i.e., age, gender,
time of day). As for traditional crash risks, the adjusted crash risks, γ
i
′,
were scaled annually by dividing each by the largest across all driver
groups. Relative risks and 95% confidence intervals were calculated
using beta regression analyses.
Fig. 1A plots the relationship between scaled conventional crash rate
and exposure levels (with exposure defined as the product of trip num-
bers and population size). For comparison, Fig. 1B plots the relationship
between the scaled adjusted crash risk and exposure levels based on the
proposed exposure metric. These plots show that traditional crash rates
are increased at the lowest exposure level with a rapid decrease and
flattening out at higher exposure. In contrast, the adjusted crash risk
remained constant with exposure, enabling comparison of driver
groups that vary greatly in population numbers and amount of travel.
2.4. Calculation for multi-vehicle crashes
Traditional crash risk for two-car collisions was calculated using Eq.
(1) in the same way as for single-car crashes. In order to calculate two-
car adjusted crash risk, we employed the extended adjusted crash risk
metric, which explicitly accounts for all drivers involved in multicar col-
lisions. It follows that, for two-car crashes, adjusted crash risk, γ
i
′,is
equal to the geometric mean of the adjusted crash risks across each of
the other driver age ranges involved in the same collision, such that:
γ0
i¼Y
N
j¼1
αAij
1−ξij−xij
exp −2xij
1þexp −2xij
0
@1
A
1=N
;ð4Þ
with
α¼exp 1ðÞ
1−exp 1
ðÞ
;Aij ¼1þxij exp −xij
−ξij exp ξij−1
;ξij
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ξiξj
q;
where Nindicates the number of other driver ageranges involved in the
same multiple car collision. As such, the adjusted two-car crash risk of
each driver age range is aggregated after having adjusted for the risk
133S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
exposure of all other drivers involved in each multicar collision. As in
the single-car analysis, relative risks and 95% confidence intervals
were calculated using beta regression analyses.
3. Results
3.1. Driving exposure estimates
In terms of population size, as expected, the youngest and oldest
drivers were fewest in number in the population (Table 1). Specifically,
drivers aged 17–20 years were 87% fewer in number and drivers aged
70 years and above were 46% fewer in number than drivers aged 40–
49 years who represented the largest driver age group in the popula-
tion. In terms of the amount of travel, Table 1 shows that, expectedly,
trips per driver were fewest in number among men and women in the
youngest age range of 17–20 years and in the oldest drivers aged
70+. The average number of trips per driver was highest in the 50–59
age group for men and the 40–49 age group for women. For both gen-
ders, fewer trips were made at night than during daytime or evening.
In fact, only 8% of trips taken by men and 5% of trips taken by women
occurred at night.
3.2. Frequency of single-vehicle crashes
The 30–39 year age group had the highest frequency of daytime
crashes, whereas the 21–29 year age group had the highest crash fre-
quency during evening and night hours (Table 2). Crash numbers
decreased gradually with age to a minimumat 70 or more years, the ex-
ception being fatal crashes where there was a slight increase in the
oldest age group. Men and women showed similar trends, but with
lowerfrequencyforwomen.
3.3. Single-vehicle crash involvement risk
Traditional rates of crash involvement by driver age and gender
were calculated based on the estimated number of licensed drivers
and trip numbers in each age–gender group. The youngest age group
had an excess relative risk of being involved in fatal and nonfatal sin-
gle-car crashes compared with the reference group aged 60–69 years
(Table 3). Specifically, drivers aged 17 to 20, in both genders, had a
nearly 19-fold the risk of fatal crash involvement compared to drivers
aged 60–69 years. Similarly, the risk of non-fatal crash involvement
for teen drivers was about 15 times as high as that of drivers aged 60
to 69. There was a steep decline in the relative risk of crash involvement
with drivers' age, for both fatal and non-fatal crashes. The crash risk of
female drivers aged 70 and over was 2.20 and 1.33 times as high as
those of female drivers aged 60 to 69, for fatal and non-fatal crashes, re-
spectively. Male drivers aged 70 and over had a fatal crash risk compa-
rable with 60 to 60 year olds, and even showed 10% reduction in the
relative risk for nonfatal crashes. Overall, with the exception of elderly
drivers, the traditional method for calculating rate-based crash risks
followed the familiar age pattern whereby young drivers have a much
higher risk of crash involvement than other age groups.
Conversely, based on the adjusted risk estimators, relative risk for
fatal and non-fatal crash involvement peaked at age 21–29 years for
Fig. 1. Effectsof increasing exposure levels based on conventional exposure estimates (A) and the new exposure metric (B) on traditional and adjustedcrash risk.
Table 1
Estimated average annual tripand driver numbers in the population by age, gender, and
time of day in Great Britain, 2002–2012.
Trip numbers Driver numbers
Day Evening Night
Males
17–20 411 113 86 440
21–29 482 114 67 1,877
30–39 534 106 52 3,015
40–49 578 118 56 3,282
50–59 610 105 54 2,877
60–69 594 74 38 2,388
70+ 513 45 22 2,156
Females
17–20 391 99 56 391
21–29 517 97 42 1,974
30–39 609 88 29 2,980
40–49 647 104 36 3,109
50–59 552 81 33 2,542
60–69 457 51 24 1,888
70+ 388 31 16 1,301
Note. Trip numbers are annual numbers per driver in the population;driver numbers are
driver numbers in the population per 1,000 drivers.
Table 2
Single-car fatal andnon-fatalcrash counts by driverage, gender, and time ofday in Great
Britain, 2002–2012.
Fatal crash counts Nonfatal crash counts
Day Evening Night Day Evening Night
Males
17–20 16 10 44 2,081 938 2,251
21–29 35 16 66 4,101 1,347 2,616
30–39 40 16 35 4,702 1,218 1,637
40–49 28 10 19 4,251 948 1,112
50–59 17 7 12 3,086 591 578
60–69 12 2 5 1,682 286 234
70+ 19 2 2 1,188 155 101
Females
17–20 3 1 6 949 342 568
21–29 6 2 7 2,069 539 610
30–39 6 2 4 2,228 426 324
40–49 6 1 2 1,831 333 215
50–59 3 1 1 1,079 182 108
60–69 2 0 0 553 79 40
70+ 6 0 0 474 50 22
134 S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
men and at age 30–39 years for women. As illustrated in Table 3,therel-
ative risk of fatal and nonfatal crash involvementwas gradually reduced
across driver age ranges. Relative to male drivers in the 60–69 age
group, young male drivers aged 17 to 20 had only 1.79 and 1.67 times
as much risk for fatal and nonfatal crash involvement, respectively.
These relative risks of crash involvement for male teen drivers were
about the same as those shown by middle-aged drivers and lower
than those of drivers in their 20s and 30s. For females, teen drivers
had 10% lower risk of being involved in a fatal crash and only 1.19
times as high risk of nonfatal crash involvement than drivers aged 60
to 69. Finally, the relative risk of the oldest female age group was com-
parable to 60–69 year olds for fatalcrash involvementand even reduced
by 6% for nonfatal crashes.
When crash involvement for age-gender groups was examined by
time of day, it was found that nighttime crashes accounted for 80%
(95% CI, 80%–81%) of the traditional single-car fatal crash risk for 17-
to 20-year-old men and 85% (95% CI, 84%–86%) for women (Fig. 2A).
To a lesser extent, nighttime crashes also accounted for a large propor-
tion of teen drivers' non-fatal crash rates, with 66% (95% CI, 66%–66%)
for men and 62% (95% CI, 62%–63%) for women (Fig. 2B).Hence,thetra-
ditional method of estimating driver crash risk indicates a high risk of
driving at night among the youngest drivers relative to other times of
the day.
In contrast, the adjusted crash risk metric revealed that crashes at
night accounted for a much smaller proportion of the overall crash
risk in the 17–20 year age range. Nighttime crashes accounted for 61%
(95% CI, 60%–61%) of the adjusted fatal crash risk for men and 53%
(95% CI, 53%–54%) for women (Fig. 2C). Just 47% (95% CI, 47%–47%) of
the adjusted non-fatal crash risk of 17- to 20-year-old male drivers
was accounted for by nighttime crashes, compared to 42% (95% CI,
42%–42%) for female drivers (Fig. 2D).
3.4. Single-car risk of fatal injury given crash involvement
The risk of fatal injury given crash involvement was measured as
fatal crash risk divided by the sum of fatal and non-fatal crash risk. Fig.
3shows the traditional and adjusted risk of fatal injury for each age
range and gender during daytime, evening, and nighttime hours. Risk
of fatal injury could range in value from 0 to 1. A value of 0.50 indicates
that the fatal crash risk of a driver group relative to other groups is equal
to the non-fatal crash risk relative to other groups. A value of greater
than 0.50 indicates a higher relative risk of fatal injury given crash in-
volvement and a value of less than 0.50 indicates a lower relative risk
of fatal injury.
Age differences in the risk of sustaining a fatal injury differed de-
pending on the method used to compute crash involvement risks. Risk
of fatal injury based on traditional crash rates showed an increase
from the 60–69year group to the oldest age group in men during day-
time and evening hours (Fig. 3A) and in women (Fig. 3B) during day-
time, evening, and nighttime. In contrast, when based on adjusted
Table 3
Traditional and adjusted single-vehicle crash risks for fatal and nonfatal collisions by
driver age and gender in Great Britain, 2002–2012.
Fatal relative risk Nonfatal relative risk
Traditional Adjusted Traditional Adjusted
Males
17–20 18.6 [17.6–19.8] 1.79 [1.75–1.83] 15.3 [14.7–15.9] 1.67 [1.63–1.70]
21–29 8.50 [7.96–9.11] 2.54 [2.50–2.59] 5.46 [5.24–5.68] 2.17 [2.14–2.20]
30–39 3.88 [3.63–4.14] 2.44 [2.39–2.49] 2.95 [2.81–3.09] 2.08 [2.05–2.12]
40–49 2.01 [1.87–2.15] 1.79 [1.75–1.83] 1.91 [1.82–2.00] 1.75 [1.72–1.79]
50–59 1.59 [1.49–1.70] 1.39 [1.35–1.43] 1.34 [1.27–1.41] 1.34 [1.32–1.36]
60–69 1.00 1.00 1.00 1.00
70+ 0.90 [0.80–1.01] 1.12 [1.08–1.15] 0.90 [0.85–0.94] 0.92 [0.90–0.93]
Females
17–20 18.8 [16.9–20.8] 0.94 [0.91–0.96] 14.8 [14.2–15.5] 1.19 [1.16–1.21]
21–29 5.63 [4.99–6.37] 1.19 [1.16–1.22] 4.44 [4.26–4.63] 1.65 [1.62–1.67]
30–39 3.38 [2.95–3.82] 1.39 [1.36–1.42] 2.46 [2.36–2.58] 1.67 [1.65–1.69]
40–49 1.77 [1.54–2.02] 1.24 [1.21–1.28] 1.52 [1.46–1.58] 1.45 [1.43–1.47]
50–59 1.74 [1.51–1.99] 1.13 [1.11–1.16] 1.20 [1.15–1.26] 1.18 [1.17–1.20]
60–69 1.00 1.00 1.00 1.00
70+ 2.20 [1.90–2.51] 1.03 [1.00–1.06] 1.33 [1.27–1.39] 0.94 [0.93–0.96]
Note. Crash risks were scaled annually by dividing their valuesby the largest across age
and gender. Relativerisks were estimated usingbeta regressionanalyses. Figuresin paren-
thesis indicate the bootstrapped 95% confidence intervals. Drivers aged 60–69years were
used as the reference group.
Fig. 2. Traditionalsingle-vehiclefatal (A) and non-fatal (B) crash risk andadjusted single-vehicle fatal (C) and non-fatal(D) crash risk by driverage and gender stacked for daytime (06:00
h–18:00 h),evening (18:00 h–21:00h), and nighttime (21:00h–06:00 h) hours. Leftand right columns represent maleand female crash risks, respectively.Traditional and adjusted crash
risks were eachscaled annually by dividing their values by the largest across driver groups.
135S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
crash risks, risk of fatal injury increased from age 60–69 years to the
oldest age group only during daytime for both men (Fig. 3C) and
women (Fig. 3D). Female drivers, particularly those in the 31–39 and
41–49 age groups, had a very low risk of fatal injury during daytime.
The risk of fatal injury based on traditional estimates was greater for
nighttime crashes than for crashes in the evening and daytime hours, in
both male (Fig. 3A) and female drivers (Fig. 3B). When based on the ad-
justed estimates, therisk of fatal injury for nighttime crashes was higher
than that of daytime crashes, but similar to that of crashes occurring
during evening hours, in both men (Fig. 3C) and women (Fig. 3D).
3.5. Frequency of two-vehicle crashes
As illustrated in Table 4, on average, multicar non-fatal crashes were
greatest in number among 21 to 29-year-old men and women. The fatal
crash frequency of women was greatest among 21–29 year olds,
whereas the fatal crash frequency of men was greatest in the 30–39
year age range. Non-fatal crash numbers declined with age to a mini-
mum at 70+ years, whereas numbers of fatal crashes declined with
age until a rise from age 60–69 years to age 70+ years. Fatal and non-
fatal crashes were greater in number during the daytime for men and
women than during evening or nighttime hours.
3.6. Multi-vehicle crash involvement risk
Traditional risk estimates for multi-vehicle fatal and non-fatal crash
involvement were calculated by driver age and gender. Crashrates were
highest among drivers aged 17 to 20 and reduced steeply with age
(Table 5;Fig. 4A and B). The risk of crash involvement for teen male
Fig. 3. Traditional and adjusted single-car risk of fatal injury given crash involvement by gender and driver age during daytime (06:00 h–18:00 h), evening (18:00 h–21:00 h), and
nighttime (21:00 h–06:00h) hours. Risk of fatal injury given crash involvement was calculated annually by dividing the single-car fatal crash risk by the sum of the single-car fatal and
non-fatal crash risk.
Table 4
Two-vehicle fatal and non-fatal crash counts by driver age, gender, and time of day in
Great Britain, 2002–2012.
Fatal crash counts Nonfatal crash counts
Day Evening Night Day Evening Night
Males
17–20 34 13 21 4,263 1,462 1,239
21–29 66 24 30 8,449 2,342 1,787
30–39 80 21 24 9,178 2,022 1,371
40–49 74 20 18 7,651 1,501 933
50–59 54 10 12 5,173 913 517
60–69 34 5 6 3,011 452 219
70+ 64 6 5 2,671 307 118
Females
17–20 8 2 3 1,833 551 357
21–29 17 3 4 4,256 952 466
30–39 13 3 3 4,423 778 305
40–49 14 4 3 3,615 635 237
50–59 13 2 2 2,229 373 140
60–69 10 2 1 1,168 172 61
70+ 22 2 1 1,084 111 37
Table 5
Two-vehicle fatal and nonfatal crash risks based on traditional andadjusted crash risk, by
driver age and gender in Great Britain, 2002–2012.
Fatal relative risk Nonfatal relative risk
Traditional Adjusted Traditional Adjusted
Males
17–20 7.75 [7.35–8.19] 0.98 [0.96–1.00] 11.1 [10.7–11.4] 1.10 [1.09–1.11]
21–29 3.23 [3.02–3.46] 1.22 [1.20–1.25] 4.56 [4.39–4.76] 1.44 [1.43–1.45]
30–39 2.04 [1.92–2.17] 1.34 [1.32–1.37] 2.74 [2.61–2.87] 1.45 [1.44–1.45]
40–49 1.51 [1.42–1.60] 1.33 [1.31–1.35] 1.76 [1.69–1.84] 1.34 [1.33–1.36]
50–59 1.15 [1.07–1.23] 1.10 [1.08–1.13] 1.28 [1.22–1.35] 1.12 [1.12–1.13]
60–69 1.00 1.00 1.00 1.00
70+ 1.75 [1.63–1.87] 1.13 [1.10–1.16] 1.12 [1.07–1.18] 1.01 [1.00–1.02]
Females
17–20 3.68 [3.28–4.13] 0.86 [0.84–0.87] 8.73 [8.37–9.09] 0.95 [0.95–0.96]
21–29 1.31 [1.19–1.44] 0.97 [0.95–0.98] 3.05 [2.94–3.18] 1.16 [1.16–1.17]
30–39 0.92 [0.83–1.01] 1.12 [1.11–1.14] 1.87 [1.79–1.95] 1.28 [1.27–1.29]
40–49 0.77 [0.70–0.84] 1.10 [1.08–1.12] 1.27 [1.22–1.32] 1.20 [1.19–1.21]
50–59 0.68 [0.62–0.74] 1.02 [1.01–1.04] 1.11 [1.06–1.17] 1.08 [1.08–1.09]
60–69 1.00 1.00 1.00 1.00
70+ 2.29 [2.11–2.49] 1.01 [0.99–1.02] 1.46 [1.39–1.53] 0.97 [0.96–0.97]
Note. Crash risks were scaled annually by dividing their values by the largest across age
and gender.Relative riskswere estimated usingbeta regression analyses. Figuresin paren-
thesis indicate the bootstrapped 95% confidence intervals. Drivers aged 60–69 years were
used as the reference group.
136 S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
drivers was 7.75 and 11.1 times ashigh as the risk of drivers in the safest
age group (60–69), for fatal and nonfatal crashes, respectively. Relative
to 60–69 year olds, the crash risk of other age groups of male drivers
varied between 1.15 and 3.23 for fatal crashes; and between 1.12 and
4.56 for nonfatal crashes. The oldest male group was 1.75 and 1.12
times as likely to be involved in fatal and nonfatal crashes respectively,
as compared to the 60–69 age group.
For female teen drivers, the risk of being involved in a fatal crash was
3.68 times as high as that among female drivers aged 60 to 69.The 21–
29 and oldest age groups had 1.31 and 2.29 times as high fatal crash risk
as drivers aged 60 to 69. Fatal crash risk was reduced by 8% to 32%
among female drivers in the middle age ranges (30s to 50s) in compar-
ison to the 60–69 reference group. The risk of nonfatal crash involve-
ment among female drivers was highest for the 17–20 year olds, who
had a relative risk equal to 8.73; it then declined sharply with age up
to the oldest age group, having 1.46 times the risk compared to the ref-
erence age group.
In contrast with the age trends in traditional crash risk, adjusted
multicar fatal and non-fatal crash risk was highest among the 30–39
year age range and showed a gradual decline with age (Table 5;Fig.
4C and D). Compared with drivers aged 60 to 69, teen female drivers
had 14% less risk of being involved in a fatal crash and 3% less risk of
being involved in a nonfatal crash. For male teen drivers, their risk of
fatal crash involvement was comparable to drivers aged 60 to 69, and
they were only 1.10 as likely to be involved in a nonfatal crash. Female
drivers aged 70 and over had similar or slightly reduced risk of being in-
volved in a crash as drivers in the 60–69 age group. For males, the oldest
group of drivers had only 1.13 times the riskof fatal crash involvement
and their nonfatal crash risk was similarto that of drivers aged 60to 69.
Comparisons of crash involvement risk by driver group across time
of day revealed that crashes at nighttime accounted for 54% (95% CI,
54%–55%) of the traditional multicar fatal crash rates among 17 to 20-
year-old men and 52% (95% CI, 50%–54%) among women (Fig. 4A) and
accounted for 38% (95% CI, 38%–38%) of the traditional non-fatal crash
risk for 17 to 20-year-old men and 38% (95% CI, 38%–39%) for women
(Fig. 4B). Crash risks based on the adjusted method revealed a similar
multicar crash risk during nighttime relative to other times of day.
Accordingly, nighttime crashes accounted for 50% (95% CI, 50%–50%)
of the adjusted fatal crash risk for 17 to 20-year-old men and 52%
(95% CI, 52%–52%) for women and 43% (95% CI, 43%–43%) of the non-
fatal crash risk for men and 47% (95% CI, 47%–47%) for women.
3.7. Multicar risk of fatal injury given crash involvement
Risk of fatal injury based on traditional crash risks was greater in
nighttime crashes than in crashes during daytime or evening hours
among male (Fig. 5A) and female drivers (Fig. 5B). In contrast, based
on the adjusted crash risks, the risk of fatal injury for nighttime crashes
was similar to that of crashes occurring during evening hours, in both
men (Fig. 5C) and women (Fig. 5D). Similarly, age differences in fatal in-
jury risk differed depending on whether they were computed by the
traditional or adjusted crash risks. Based on traditional crash rates, the
risk of fatal injury increased from age 60–69 years to age N70 years dur-
ing daytime, evening, and nighttime hours among men (Fig. 5A) and
women (Fig. 5B). In contrast, the risk of fatal injury as measured by ad-
justed crash risks increased from age 60–69 years to age N70 years only
during the daytime for men(Fig. 5C) and women (Fig. 5D). As in the sin-
gle-vehicle analysis, female drivers' fatal crash risk was extremely low
during the daytime, especially among those in their 30s and 40s.
4. Discussion
Crash rates are commonly used to assess the risk of different driver
groups varying in exposure to risk. However, this approach requires
that crash frequency and the exposure index be correlated linearly —
an invalid assumption when using conventional measurement of expo-
sure. Here we applied a crash risk method based on a new exposure
metric, for which the number of crashes is proportional to the amount
of driving exposure. We found that traditional crash rates reduced
steeply from age 17–20 years through age 60–69 years. Adjusted crash
risk instead peaked at age 20–29 years and decreased gradually until
age 60–69 years. Additionally, elderly drivers had reduced crash in-
volvement and fatality risks when using the adjusted crash risk com-
pared to conventional crash rates. Finally, nighttime driving among
Fig. 4. Traditional 2-car fatal (A) and non-fatal (B) crash riskand adjusted 2-car fatal (C) and non-fatal (D) crash risk by driver age and gender stacked for daytime (06:00 h–18:00h),
evening (18:00 h–21:00 h), and nighttime (21:00 h–06:00 h) hours. Left and right columns represent male and female crash risks, respectively. Traditional and adjusted crash risks
were each scaled annually by dividing their values by the largest across driver groups.
137S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
teen drivers accounted for a smaller proportion of their single-vehicle
crash risk than implied by crash rates.
The dramatic reduction in conventional crash rates from young to
middle-age ranges reflects the common findings in the literature (e.g.,
Ma & Yan, 2014; McAndrews et al., 2013; Williams & Shabanova,
2003). However, the adjusted crash risks revealed a remarkably differ-
ent age-trend in driver risk: Crash risk was highest among 21–29 year
olds and thereon reduced gradually with age. The current results are
in agreement with those obtained in studies using disaggregated
models and quasi-induced exposure methods for crash risk analyses.
These studies have shown that the youngest and oldest age groups are
not the riskiest drivers. Rather, drivers in their 20s and 30s were those
demonstrating the highest crash risk (Kam, 2003; Stamatiadis &
Deacon, 1997). While the robustness of our findings is supported by
previousreports, we do not argue here against the enforcementof driv-
ing restrictions targeting young drivers. Justification for road safety reg-
ulations would also depend on drivers' ability to recognize their own
limitations and self-regulate their driving accordingly. The present in-
vestigation merely highlights that other age groups also exhibit sub-
stantial driver crash risk and may also benefit from targeted road
safety initiatives.
Drivers, especially young males, are reported to have higher crash
involvement rates at nighttime compared to daytime (e.g., Keall &
Frith, 2006). Adjusting appropriately for the infrequency of nighttime
travel, we discovered that crashes at night accounted for far less of the
single-car crash risk of teen drivers compared to the traditional method.
In Great Britain, young drivers are not restricted in their travel at night.
Policymakers in countries where curfews are imposed on the youngest
drivers (McCartt & Teoh, 2015) should be cognizant that the contribu-
tion of nighttime driving to single-vehicle crashes of teenagers may be
exaggerated by traditional methods of analyzing crash risk.
Previous investigations using conventionalcrash rates have reported
increased crash risk in older age (e.g., Cicchino & McCartt, 2014; Massie
et al., 1995). We found that when controlling correctly for their small
driver numbers and infrequent travel, crash involvement and fatality
risks of elderly drivers were reduced. These findings are consistent
with past research showing that older driver crash risk appears high
due to the biasing effects of their small driving exposure (Alvarez &
Fierro, 2008; Antin et al., 2017; Fontaine, 2003; Hakamies-Blomqvist
et al., 2002; Langford et al., 2006). Future research should include iden-
tification ofage subgroups among older drivers given possible variation
in their driving exposure and crash risks (Cicchino, 2015; Cicchino &
McCartt, 2014).
Interestingly, our analysis revealed that among elderly drivers, the
risk of sustaining a fatal injury from a crash remained constant across
time of day. This finding lends support to the role of fragility in worsen-
ing injury outcomes for elderly drivers who are involved in crashes,
since fragility (unlike crash seriousness) is not expected to be influ-
enced by time of day. Therefore, countermeasures benefiting elderly
drivers should focus on improving in-vehicle technology to reduce in-
jury severity.
In either method, young and middle-aged drivers were more likely
to sustain a fatal injury from a crash that occurred at night than during
daytime. This resonates with previous research (e.g. Doherty et al.,
1998). However, the adjusted method also revealed that fatal injury
risk from nighttime crashes was similar to the risk from crashes in the
evening. Thus, the current findings support the need to report age com-
parisons in crash involvement and injury severity by time of day and
highlight the importance of accounting properly for the variability in
travel exposure across time periods.
Findings from both methods regarding gender differences in crash
risk were generally consistent with prior research; male drivers are
more likely to be involved in fatal and non-fatal crashes compared to fe-
male drivers (e.g., Kimet al., 2008; Zhou et al., 2015). The adjusted
method has also demonstrated that the fatal crash risk of women, par-
ticularly those in their 30s to 40s, was extremely low during daytime.
These data fit prior travel behavior research showing that women, espe-
cially those with children, aremore likely than mento make trips during
daytime with the intention of servingpassengers (e.g., Koppel, Charlton,
Kopinathan, & Taranto, 2011; Rosenbloom, 2006). Although the pres-
ence of passengers is associated with in-vehicle distraction (Koppel et
al., 2011; Stutts et al., 2005), having young passengers might be more
protective than harmful by reducing risk-taking behaviors among
women drivers. Future studies are needed to explore this possibility.
Fig. 5. Traditional and adjusted risk of fatal injurygiven multi-vehicle crash involvement by driver age and gender during daytime (06:00 h–18:00 h), evening (18:00 h–21:00 h), and
nighttime (21:00h–06:00 h) hours. Risk of fatal injury given crash involvement was calculated annually by dividing multi-vehicle fatal crash risk by the sum of multi-vehicle fatal and
non-fatal crash risk.
138 S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
Our investigation has a number of potential limitations. First, moti-
vated by concerns about the use of mileage in age comparisons of
crash risk (Janke, 1991; Langford et al., 2013), we used annual trip num-
bers as our indicator of travel per person. In our study,traditional crash
rates per trip produced the familiar pattern of excessive crash risk
among the youngest drivers. Using different travel indicators might
have resulted in smaller amount of risk exposure for older drivers and
consequently larger crash rates in this age group.Nevertheless, previous
studies have shown that reduction in travel associated with older age
occurs both in terms of frequency of trips and distance traveled (Sivak
& Schoettle, 2011). Second, we used self-reports of trips made, which
may be associated with reporting biases that differ with driver age
(e.g., Bricka & Bhat, 2006). Future studies may benefit from incorporat-
ing objective measures of risk exposure. Finally, we acknowledge that
the new crash risk approach is based on an exposure metric that is
more complex to compute in comparison to simple crash rate. Never-
theless, the new adjusted crash risk estimators are superior to the con-
ventional crash rates in producing unbiased risk comparisons for driver
groups and driving conditions that vary in their exposure to risk.
5. Conclusion
The current study applied a new approach to model crash risks
based on exposure metric that bears a linear relation with crashes.
Our findings draw attention to the invalidity of crash ratesfor risk com-
parisons among groups and conditions that vary in driving exposure.
Specifically, we have demonstrated that conventional crash rates over-
estimate the actual risk of crash involvement and fatal injury for the
youngest and oldest drivers as well as for nighttime driving. This work
has important practical implications for improving road safety initia-
tives, as meaningful comparisons are essential for identifying truly at-
risk drivers and driving conditions. It is hoped that the approach pre-
sented here will facilitate development of new crash modeling method-
ologies that are able to account for the non-linear shape of the safety
performance function, and provide reliable crash risk estimates for
road safety research and policies.
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Shirley Regev, PhD, is a Lecturer in the Department of Psychology at Oxford Brookes Uni-
versity in the United Kingdom. Dr. Regev's research is focused on applied cognitive psy-
chology in the context of transportation safety, especially driver distraction and risky
driving behavior. Her recent research includes projects related to statistical and cognitive
bias in road safety analysis.
Jonathan Rolison, PhD, is a Lecturer in the Department of Psychology at University of
Essex in the United Kingdom.His research is primarily in the area of risk taking behaviors
across adulthood.
Salissou Moutari, PhD, is a Senior Lecturer in the School of Mathematics and Physics, at
Queen's University Belfast in the United Kingdom. Dr. Moutari is also affiliated with the
Centre for Statistical Science and Operational Research (CenSSOR) at Queen's University
Belfast.
140 S. Regev et al. / Journal of Safety Research 66 (2018) 131–140
