a risk-based method for modeling traffic fatalities risk-based method for modeling traffic...
TRANSCRIPT
Risk Analysis, Vol. 27, No. 1, 2007 DOI: 10.1111/j.1539-6924.2006.00864.x
A Risk-Based Method for Modeling Traffic Fatalities
Kavi Bhalla,1∗ Majid Ezzati,2 Ajay Mahal,2 Joshua Salomon,2 and Michael Reich2
We describe a risk-based analytical framework for estimating traffic fatalities that combinesthe probability of a crash and the probability of fatality in the event of a crash. As an illus-trative application, we use the methodology to explore the role of vehicle mix and vehicleprevalence on long-run fatality trends for a range of transportation growth scenarios that maybe relevant to developing societies. We assume crash rates between different road users areproportional to their roadway use and estimate case fatality ratios (CFRs) for the differentvehicle-vehicle and vehicle-pedestrian combinations. We find that in the absence of road safetyinterventions, the historical trend of initially rising and then falling fatalities observed in indus-trialized nations occurred only if motorization was through car ownership. In all other casesstudied (scenarios dominated by scooter use, bus use, and mixed use), traffic fatalities rosemonotonically. Fatalities per vehicle had a falling trend similar to that observed in historicaldata from industrialized nations. Regional adaptations of the model validated with local datacan be used to evaluate the impacts of transportation planning and safety interventions, suchas helmets, seat belts, and enforcement of traffic laws, on traffic fatalities.
KEY WORDS: Developing countries; global health; motor vehicles; road traffic injuries; traffic safety;transportation growth
1. BACKGROUND
Road traffic injuries and fatalities account for 1.2million deaths worldwide (2.2% of global mortalityin the year 2002) and 2.6% of the total global burdenof disease, measured in terms of lost years of healthylife.(1) Recent projections have estimated that as in-come and vehicle ownership levels rise in the devel-oping world, the global number of road traffic deathswould increase by approximately two-thirds by theyear 2020.(2,3)
The link between traffic deaths and the size ofvehicle fleet was first explored by Smeed(4) in 1949using traffic fatality and registered vehicle statistics
1 Harvard Initiative for Global Health, Harvard University, Cam-bridge, MA, USA.
2 Harvard School of Public Health, Population and InternationalHealth, Boston, MA, USA.
∗ Address correspondence to Kavi Bhalla, Harvard Initiative forGlobal Health, 104 Mt. Auburn Street, Cambridge, MA 02138,USA; tel: 617-233-7700; kavi [email protected].
from 20 industrialized countries over the time period1930–1946. This analysis showed that fatalities pervehicle decreased monotonically with vehicle own-ership (i.e., vehicles per person) while fatalities percapita increased over this period. Since the late 1960s,however, fatalities per capita have fallen for mostindustrialized nations.(5) Soderlund and Zwi(6) usedmultiple regression analysis of cross-sectional dataon road traffic deaths in 1990 from 83 countries todescribe fatalities per vehicle and per capita as afunction of vehicle ownership levels, road density,income, health expenditure, and population density.The analysis showed that traffic fatalities increasedwith income at low incomes but fell at higher incomes.Fatalities per vehicle always fell. Using panel datafrom 1963–1999 for 88 countries, Kopits and Crop-per(3) developed an econometric model that relatedtraffic fatalities to income growth and vehicle owner-ship. The authors used this model to project world-wide traffic fatalities to the year 2020. Since the his-torical fatality trends in the industrialized world did
125 0272-4332/07/0100-0125$22.00/1 C© 2007 Society for Risk Analysis
126 Bhalla et al.
not reverse until their per capita income levels wereabove $8,000 (1985 international dollars), these mod-els predicted a large increase in traffic fatalities fordeveloping countries, which have significantly lowerincome levels at present.
Such econometric projections are valuable be-cause they provide visions of future public healthburden imposed by traffic injuries and fatalities. Pro-jections based on historical data, however, do notpredict the effects of unprecedented changes in thetransportation system. For instance, the regressionequations derived in Smeed(4) accurately predictedtraffic fatalities in the United Kingdom up to the mid1960s, when the traffic fatalities peaked. If these re-lationships were extrapolated to current times, how-ever, they would predict about four times the actualtraffic fatalities in the year 2000. The deviations froma rising trend in fatalities are often attributed to the in-troduction of road safety programs. Road traffic fatal-ities may also be influenced by other systemic changes.For example, rapid motorization in cities in many de-veloping countries has led to traffic congestion andlower vehicle speeds, which could cause a reductionin road fatalities, albeit with other health and welfareconsequences such as air pollution exposure or psy-chological stress. Similarly, many developing nationshave a vehicle mix (e.g., widespread reliance on scoot-ers) that has not been observed in the historical datafrom industrialized nations. Since many of these char-acteristics of the transportation sector are unique todeveloping countries, econometric models of trafficinjuries that rely on historical data from industrial-ized countries can result in highly uncertain or biasedpredictions.
In contrast to aggregate econometric analysis ofobserved trends, structural models that simulate thedynamic response of the transportation system can beused to study the impact of a range of variables thataffect traffic fatality rates. In this article, we develop arisk-based model for the relationship between trans-port mode, vehicle mix, and traffic fatalities. This isaccomplished by combining the probability of a crashbetween different road users and the probability of afatality in the event of a crash. An advantage of thismodel is that alternative scenarios of vehicle owner-ship and use—which may be based on income, vehicleprices, and policy choices—can be systematically an-alyzed. We illustrate this by using the model to sim-ulate the safety consequences that result from fourscenarios of transportation growth. Three of the sce-narios emphasize specific transportation modes (highbus use, high car use, high scooter use), and the fourth
represents a mixed-use base case scenario. Beyondthe illustrative application in this article, validated re-gional adaptations of the model can be used to evalu-ate the impacts of transportation planning and safetyinterventions, such as helmets, seat belts, and enforce-ment of traffic laws, on traffic fatalities in a commonframework.
We start with a crude model that assumes thatcars are the only mode of motorized transport avail-able in a society. We find broad similarities in trendswith historical data even with the simple model repre-sentation. Next, we extend the model to include othervehicle types and consider pairwise fatality risks de-rived from a review of the vehicle safety literature.
2. CRUDE MODEL: CARSAND PEDESTRIANS
First consider a simple model in which walkingand cars are the only available modes of transporta-tion. We assume that the probability of fatality in theevent of a crash is r for a pedestrian and negligible fora car occupant. If there is a commuting populationof N, of which C are car users and the remaining arepedestrians, the probability of a pedestrian-car crashis proportional to both the number of pedestrians aswell as the number of cars, C(N − C), and the proba-bility of a car-car crash is proportional to C·C. Thus, ifwe set the fatality risk in car-car crashes to 0, the percapita fatality risk is proportional to C(N − C)r/N,which is a parabolic function of the number of cars.As the society motorizes from all-pedestrians to all-occupants (Fig. 1), the aggregate fatality risk initiallyrises as additional cars pose an increasing threat tothe largely pedestrian population. But, when morethan half the commuting population consists of carusers (C = 0.5, peak of parabola), increasing motor-ization leads to a fall in the aggregate fatality risk. Onthe other hand, the aggregate risk per car, (N − C)r,is a linearly decreasing function of the number of cars.
The results of this simple model show patternsthat are qualitatively similar to the panel data re-ported by Kopits and Cropper(3) (Figs. 2A and 2B).Fatalities per vehicle always fall with increasing mo-torization, while fatalities per capita initially increasewith vehicle ownership and then fall, showing theinverted-U relationship that has been observed inpast studies.(3,6) These results are the consequenceof a “substitution effect,” where high-risk and low-threat pedestrians are replaced by low-risk and high-threat vehicles. Thus, the people who shift from beingvulnerable road users (VRUs) to vehicle occupants
Risk-Based Method for Modeling Traffic Fatalities 127
Fig. 1. Motorization and changing trafficrisk in a world with only cars andpedestrians. r is the threat to eachpedestrian per car, while the risk to caroccupants is assumed to be negligible incomparison.
Fig. 2. A comparison of historic panel data (1963–1999, 88 countries reported by Kopits and Cropper, 2005) for fatalities per person, (A),and fatalities per vehicle, (B), with predictions of the simple model, (C) and (D).
128 Bhalla et al.
diminish their own risks but raise the threat tothe remaining VRUs. At low levels of motoriza-tion, there are a large number of VRUs on thestreets and the increased threat to the populationoutweighs the decreased risk to the individual. How-ever, at high motorization levels there are rela-tively few VRUs, and the decreased personal riskleads to a falling trend in fatalities per capita evenin the absence of traffic safety interventions. Sim-ilarly, the aggregate population-level risk per vehi-cle is proportional to the number of at-risk people.Since each additional car in this crude model im-plies one fewer pedestrian, the at-risk population fallsmonotonically, resulting in falling fatalities per vehicle.
3. MULTIVEHICLE MODEL FORMULATION
Next, we expand the analysis to include othermodes of transportation that are commonly observedin developing countries. The probability of a fatalcrash between two road users can be modeled as theproduct of the probability that a crash occurs betweenthe road users and the probability that the crash is fa-tal. Thus, if cthreat
victim is the probability that a road user(victim) is struck by a vehicle (threat), and r threat
victim is thecase fatality ratio (CFR) for the victim of the crash,then the probability that the victim is killed is givenby
fatalthreatvictim = cthreat
victim × r threatvictim . (1)
We use the superscript to denote the transporta-tion mode of the threat and subscript to denotethe transportation mode of the victim. Thus, for in-stance, r car
scooter is the probability that a scooter-rideris killed in the event of a car-scooter crash, whiler scooter
car is the probability that the car occupant is killed.Single-vehicle crashes are incorporated by includ-ing the physical environment as a threat. Thus, forinstance, renvironment
scooter is the probability that a single-vehicle scooter crash is fatal. In this formulation,we assume that a crash can involve at most two ve-hicle types (in the United States 15% of fatal carcrashes involve more than two vehicles).(7) Mathe-matical formulation of crashes involving multiple ve-hicles is analogous to the model presented here.
3.1. The Probability of a Crash Event, cthreatvictim
For each pair of transportation modes, the prob-ability of a crash between the threat and the victimdepends on a number of factors that include:
1. The population of road users that belong to thevictim’s travel mode, Uvictim, and the numberof “at-risk” miles traveled (i.e., distance overwhich the victim is exposed to the threat) byeach of these road users, dvictim;
2. The total number of threat vehicles, Mthreat,and the number of miles traveled by each ofthese vehicles, dthreat;
3. Vehicle attributes (e.g., antilock brakes, visi-bility, stability);
4. Driver attributes (e.g., sociodemographiccharacteristics, license status, alcohol use,driver training);
5. Roadway infrastructure (pedestrian walk-ways, lane separating medians); and
6. Broader systemic attributes (legal and insur-ance systems);
that is,
cthreatvictim = f (Uvictim, dvictim, Mthreat, dthreat,
vehicle attributes, driver attributes,roadway attributes, systemic attributes).
We consider a specific form for this relationship
cthreatvictim = Kthreat
victim × Uvictim × dvictim × Mthreat × dthreat.
(2)
As written, the probability of a specific threat-victimcrash is proportional to the product of the total“at-risk” miles traveled by road users in the victim’stravel mode (Uvictim × dvictim) and the total distancetraveled by the vehicles that pose the threat (Mthreat ×dthreat). The proportionality constant, Kthreat
victim,accounts for all the other variables listed in items3–6 above and captures the relationship betweenroad use and the probability of a crash. Thus, forcar-pedestrian crashes, Upedestrian × dpedestrian is thenumber of at-risk miles walked by all pedestrians,Mcar × dcar is the total number of miles traveled by allcars, and Kcar
pedestrian is a proportionality constant thatrelates the rate at which shared roadway use resultsin pedestrian-vehicle crashes. Since the variablesMthreat and dthreat do not have a physical interpre-tation for single-vehicle crashes, we assume thatcenvironment
victim = Kenvironmentvictim × Uvictim × dvictim, so
that the proportionality constant Kenvironmentvictim relates
vehicle use to the probability of a single-vehiclecrash.
Risk-Based Method for Modeling Traffic Fatalities 129
3.2. The Case Fatality Ratio, r threatvictim
The CFR, the probability of fatality in the eventof a crash, depends on precrash variables that de-scribe the characteristics of vehicles and victims, thecrash variables, and the postcrash victim care. Theseinclude:
� Vehicle characteristics (e.g., size, mass, andshape) and safety design technology (e.g. avail-ability and use of seat belts and airbags);
� Victim attributes including age, sex, height,and weight;
� Crash conditions including vehicle speed, di-rection of vehicle travel, crash avoidance ma-neuvers, weather conditions, and roadway in-frastructure; and
� Postcrash medical care including responsetime of emergency medical services, and qual-ity of on-site and trauma care;
that is,
r threatvictim = f (vehicle attributes, victim attributes,
crash conditions, post crash medical care).
3.3. Computing Traffic Fatalities
Combining Equations (1) and (2),
fatalthreatvictim = Kthreat
victim × Uvictim × dvictim × Mthreat
×dthreat × r threatvictim . (3)
Vehicle occupancy relates the number of vehicles tothe number of occupants. Thus, Uvictim = ovictim ×Mvictim, where ovictim is the vehicle occupancy of thevictim’s transport mode. If Dvictim = Uvictim × dvictim isthe total at-risk vehicle distance traveled by road usersof the victim’s transport mode, and Dthreat = Mthreat×dthreat is the total distance traveled by threat vehicles,we get:
fatalthreatvictim = Kthreat
victim × ovictim × Dthreat × Dvictim
× r threatvictim . (4)
Total fatalities among road users in a particular modeof transportation can be computed by adding the fa-tality contributions from all threats. Thus, for instance,∑
threat fatalthreatcar computes all car-occupant fatalities.
Similarly,∑
victim fatalcarvictim is the total fatalities caused
by cars among other road users. The aggregate traf-fic fatalities (all victims from all threats) are then∑
threat
∑victim fatalthreat
victim.
4. MODEL APPLICATION
As an illustrative application of the methodology,we use the model (Equation 4) to analyze the role ofvehicle mix and vehicle prevalence on long-run fa-tality trends. This requires the following simplifyingassumptions (see discussion for the implications ofthese assumptions):
� Kthreatvictim is independent of the vehicle types in-
volved in the crash. This assumes that thedriver, vehicle, and the broader systemic at-tributes that affect the probability of a crashare the same for all vehicle types.
� Dthreat and Dvictim correspond to total milestraveled. This assumes that all travel is“at-risk” travel. All vehicles share the sameroadway and are equally exposed to eachother. This is not true of travel on limited accessinterstate highways, where pedestrians and bi-cyclists may be prohibited, but it is an appro-priate representation of urban travel in manydeveloping countries.
� Kthreatvictim and r threat
victim are held constant in orderto analyze the role of vehicle mix and vehicleprevalence on crash fatalities. In future studies,changes in crash risk and CFR due to changesin infrastructure (e.g., divided roads), vehicledesign and use (e.g., seatbelts and airbags), andother systemic changes (e.g. enforcement ofspeed limits and emergency services for crashvictims) can be modeled by using time depen-dent values for K and r.
4.1. Computing Pairwise CFRs, r threatvictim
The pairwise CFRs, r threatvictim, can be represented
as a matrix with the threats listed in columns andthe victims listed in rows. The CFR matrix waspopulated in a sequence of 13 steps described inTable I. Wherever possible, we assume that the pair-wise CFRs, r threat
victim, correspond to a head-on crash ata mean speed of 30 km/h. We rely primarily on U.S.-based studies and data available from the NationalHighway Traffic Safety Administration (NHTSA).(11)
Since motorized two wheelers are a small propor-tion of the U.S. motor vehicle fleet, we estimatethe CFRs for crashes involving scooters based oncrash statistics from New Delhi.(13) The CFR matrix,r threat
victim, developed as described in Table I, is shown inTable II. Clearly, these pairwise risks evolve withchanges in technology and infrastructure. However,they are held constant in this application in order to
130 Bhalla et al.Ta
ble
I.St
eps
inC
onst
ruct
ing
the
CF
RM
atri
x
Thr
eat
Ped
estr
ian
Scoo
ter
Car
Bus
Env
iron
men
t
Vic
tim
Ped
estr
ian
[1]
[11]
[3]
[4]
[2]
Scoo
ter
[13]
[12]
[7]
[7]
[10]
Car
[1]
[8]
[5]
[6]
[10]
Bus
[1]
[9]
[6]
[5]
[10]
Env
iron
men
tN
AN
AN
AN
AN
A
1P
edes
tria
nspo
seno
thre
atto
othe
rpe
dest
rian
san
dto
occu
pant
sof
cars
and
buse
s.2
Ped
estr
ians
are
atno
risk
from
the
envi
ronm
ent,
that
is,i
njur
ies
from
falls
are
notm
odel
ed.
3C
ar-P
edes
tria
n:B
ased
onA
nder
son,
(8)
the
prob
abili
tyof
ape
dest
rian
fata
lity
inth
eev
ento
faca
r-pe
dest
rian
cras
his
0.08
.4
Bus
-Ped
estr
ian:
The
CF
Rin
abu
s-pe
dest
rian
cras
his
high
erth
anth
atin
aca
r-pe
dest
rian
cras
hbe
caus
eof
the
diff
eren
cein
vehi
cle
shap
ean
dm
ass.
Lefl
eran
dG
able
r(9)
com
pare
dth
ein
jury
risk
tope
dest
rian
sfr
omlig
httr
ucks
and
vans
(LT
Vs)
inth
eU
nite
dSt
ates
.The
yfo
und
that
atsp
eeds
inth
era
nge
of21
–30
km/h
,the
prob
abili
tyof
seri
ous
head
inju
rydu
eto
anLT
Vis
9.1%
high
erth
anw
hen
impa
cted
bya
car.
How
ever
,the
prob
abili
tyof
ase
riou
sch
esti
njur
yw
as12
8%hi
gher
.Sin
cebo
thhe
adan
dch
esti
njur
ies
are
aco
mm
onca
use
ofpe
dest
rian
fata
litie
s,w
eas
sum
eth
atth
epe
dest
rian
fata
lity
risk
from
LTV
sis
the
aver
age
ofth
ese
two
esti
mat
es(i
.e.,
the
CF
Ris
68.5
%hi
gher
than
that
from
cars
and
isse
tat0
.135
).Si
nce
the
popu
lati
onof
LTV
sin
the
Uni
ted
Stat
esla
rgel
yco
nsis
tsof
spor
tuti
lity
vehi
cles
and
pass
enge
rva
ns,t
hem
ass
ofth
eve
hicl
esst
udie
dby
Lefl
eran
dG
able
ris
sign
ifica
ntly
low
erth
anth
atof
abu
s.T
hus,
whi
leth
eir
anal
ysis
capt
ures
the
incr
ease
dth
reat
pose
dby
flat-
fron
tveh
icle
s,th
est
udy
does
nota
ccou
ntfo
rth
eef
fect
ofin
crea
sed
vehi
cle
mas
s.H
owev
er,s
ince
LTV
san
dbu
ses
are
both
muc
hhe
avie
rth
ana
pede
stri
an,w
eas
sum
eve
hicl
em
ass
can
beig
nore
das
anad
diti
onal
risk
fact
orin
vehi
cle-
pede
stri
ancr
ashe
s.5
Car
-Car
and
Bus
-Bus
:Jok
sch(1
0)an
alyz
edth
eN
atio
nalA
ccid
entS
ampl
ing
Syst
em,w
hich
prov
ides
repr
esen
tati
veda
taon
vehi
cle
cras
hes
inth
eU
nite
dSt
ates
.The
yfo
und
that
the
CF
Rfo
rdr
iver
fata
litie
sw
aspr
opor
tion
alto
the
four
thpo
wer
ofth
eve
hicl
eve
loci
ty.U
sing
thei
rfo
rmul
a,w
ese
tthe
CF
Rfo
roc
cupa
nts
inca
r-ca
ran
dbu
s-bu
sco
llisi
ons
to0.
009.
6B
us-C
aran
dC
ar-B
us:I
nth
eev
ento
facr
ash
betw
een
vehi
cles
ofdi
ffer
entm
asse
s,w
eas
sum
eth
atth
epr
obab
ility
offa
talit
yin
the
impa
cted
vehi
cle
ispr
opor
tion
alto
the
mas
sra
tio
ofth
etw
ove
hicl
esin
volv
ed.T
his
isre
ason
able
beca
use
the
kine
tic
ener
gyof
each
vehi
cle
islin
earl
yre
late
dw
ith
thei
rm
ass.
We
assu
me
that
the
mas
sof
aty
pica
lbus
isab
oute
ight
tim
esth
atof
aca
r.T
hus,
sinc
eth
eC
FR
ina
car-
car
cras
his
0.00
9,th
eC
FR
for
the
car
occu
pant
ina
car-
bus
colli
sion
isei
ghtt
imes
grea
ter,
0.07
2,an
dth
atfo
ra
bus
occu
pant
isei
ghtt
imes
smal
ler,
0.00
1(r
ound
edto
thre
esi
gnifi
cant
digi
ts).
The
valid
ity
ofth
isca
lcul
atio
nca
nbe
veri
fied
byco
mpa
ring
wit
hth
efa
talit
you
tcom
ein
car-
truc
kim
pact
sin
the
Uni
ted
Stat
es.A
ccor
ding
toth
eN
atio
nalH
ighw
ayTr
affic
Safe
tyA
dmin
istr
atio
n(N
HT
SA),
inca
r-tr
uck
cras
hes
the
car
occu
pant
was
63ti
mes
mor
elik
ely
tobe
kille
dth
anth
etr
uck
occu
pant
.(11)
Our
anal
ysis
sugg
ests
that
this
rati
ois
64.H
owev
er,i
tsho
uld
beno
ted
that
truc
ksin
the
Uni
ted
Stat
esm
aybe
muc
hhe
avie
rth
ana
typi
calb
usin
ade
velo
ping
coun
try.
7C
ar-S
coot
eran
dB
us-S
coot
er:W
eas
sum
eth
atth
eth
reat
pose
dby
vehi
cles
tosc
oote
r-ri
ders
isth
esa
me
asth
atto
pede
stri
ans
(i.e
.,0.
08fo
rca
r-sc
oote
ran
d0.
135
for
bus-
scoo
ter)
.It
shou
ldbe
note
dth
atth
isri
skis
ast
rong
func
tion
ofhe
lmet
use.
Thu
s,in
the
abse
nce
ofa
helm
etth
eC
FR
for
asc
oote
rri
der
may
bem
uch
high
erth
anth
atfo
ra
pede
stri
anbe
caus
eof
the
high
erre
lati
veim
pact
spee
d.H
owev
er,i
nth
epr
esen
ceof
ahe
lmet
,the
CF
Rm
aybe
sign
ifica
ntly
low
er.
8Sc
oote
r-C
ar:B
ased
onm
otor
cycl
e-ca
rcr
ashe
sin
the
Uni
ted
Stat
esre
port
edby
NH
TSA
,(11)
the
mot
orcy
clis
tis
44ti
mes
mor
elik
ely
tobe
kille
dth
anth
eca
roc
cupa
nt.S
ince
this
num
ber
iscl
osel
yre
late
dw
ith
helm
et-u
sera
tes,
itsh
ould
beno
ted
that
helm
etus
eis
rela
tive
lylo
win
the
Uni
ted
Stat
es—
mos
tsta
tes
inth
eU
nite
dst
ates
dono
thav
eun
iver
salm
otor
cycl
ehe
lmet
law
s,an
din
the
abse
nce
ofsu
chla
ws
helm
etus
eis
appr
oxim
atel
y50
%.(1
2)T
hus,
ifw
eas
sum
eth
atsc
oote
rsbe
have
sim
ilar
tom
otor
cycl
esin
cras
hes,
the
CF
Rfo
rca
roc
cupa
nts
incr
ashe
sw
ith
scoo
ters
is1/
44of
0.08
(=0.
002)
.9
Scoo
ter-
Bus
:We
assu
me
that
scoo
ters
dono
tpos
ean
yth
reat
tobu
soc
cupa
nts.
10Si
ngle
-veh
icle
cras
hes:
Bas
edon
data
for
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Risk-Based Method for Modeling Traffic Fatalities 131
Table II. Case Fatality Ratio Matrix, r threatvictim
Threat
Pedestrian Scooter Car Bus Environment
VictimPedestrian 0[1] 0.040[11] 0.080[3] 0.135[4] 0[2]
Scooter 0.010[13] 0.021[12] 0.080[7] 0.135[7] 0.053[10]
Car 0[1] 0.002[8] 0.009[5] 0.072[6] 0.030[10]
Bus 0[1] 0[9] 0.001[6] 0.009[5] 0.037[10]
Environment NA NA NA NA NA
NA: Not applicable.Superscript [] denotes Step [] from Table I.
isolate the role of vehicle mix and vehicle prevalenceon fatality rates.
4.2. Computing the Proportionality Constant Kthreatvictim
In order to compute absolute fatality counts us-ing Equation (4), we need a numerical value for theproportionality constant, Kthreat
victim, which we estimatebased on crash statistics from New Delhi. In 2001, carsand pedestrians had a trip modal share of 18% and19%, respectively, and the resulting car-pedestrian in-teractions caused 102 pedestrian fatalities. Thus, usingEquation (4) and a pedestrian CFR of 0.08, the two-vehicle proportionality constant,Kthreat
victim, is approxi-mately 37,000. Similarly, Kenvironment
victim is approximately1,000, based on occupant fatalities in single-vehiclecar crashes in New Delhi.
4.3. Transport Growth Scenarios
We construct four scenarios of transport growththat represent widely differing motorization path-ways. Four transport modes are considered: walking,scooters, cars, and buses, which are assumed to carry40 people each.
In a review of urban travel in different regionsof the world with diverse sociocultural charac-teristics, public transportation use was found torange from 17% of all motorized trips (Shanghai,China) to 88% (Mumbai, India).(15) The ratio oftwo-wheeler ownership to car ownership rangedfrom 1:10 (Belo Horizonte, Brazil) to 4:1 (Chennai,India). Using these results as a guide, we constructtransportation growth scenarios such that in eachscenario a fixed proportion of all motorized travelis by bus and the remaining motorized travel isassigned between cars and scooters using a fixedratio. Each scenario starts with an all-pedestriansociety and incrementally increases the propor-tion of trips that involve motorized travel (i.e.,travel by scooter, car, and bus) from 0% to 100%.Since bus trips typically involve walking to and from
the bus stop, we include half a walking trip for eachbus trip. The four scenarios (Fig. 3) are:
� Base Case: A total of 40% of all motorized dis-tance traveled in the city is by bus and the ratioof miles traveled by scooter and by car is 1:1.Thus, at the beginning of the scenario all tripsare pedestrian. The proportion of trips that in-volve motorized travel is then increased in in-crements (40% bus, 30% scooter, 30% car) to100%.
� High Bus Use: A total of 80% of all motorizedtravel in the city is by bus and the ratio of milestraveled by scooter to those traveled by car is1:1.
� High Car Use: A total of 40% of all motorizedtravel in the city is by bus and the ratio of milestraveled by scooter to those traveled by car is1:10.
� High Scooter Use: A total of 40% of all mo-torized travel in the city is by bus and the ratioof miles traveled by scooter to those traveledby car is 4:1.
It should be noted that although these scenarios useextreme road use characteristics of existing trans-portation systems, they are not intended to mimicspecific cities. Thus, for instance, a large proportionof motorized travel in Mumbai is by bus but it is notsimilar to the High Bus Use scenario because the ratioof car to scooter use may be different.
5. RESULTS
Total traffic fatalities resulting from the fourtransportation growth scenarios are shown in Fig. 4.The fatality trend for the High Car Use scenario has aninverted-U shape similar to the outcome of the crudemodel in Fig. 2, which is an all car use scenario. At lowlevels of motorization, the rise in the number of cars
132 Bhalla et al.
Fig. 3. Four hypothetical transportation growth scenarios: road use modal shares plotted against the proportion of trips that include amotorized component. It should be noted that since bus trips include pedestrian travel, pedestrians are still a part of the transportation systemeven when 100% of all trips include a motorized component. This “residual” number of pedestrians varies depending on the proportion ofbus use in each scenario.
Fig. 4. Change in total traffic fatalities (all road users) computedfor four scenarios of growth in motorized travel.
causes a rapid increase in the threat to those usingnonmotorized modes, causing total fatalities to rise.At higher motorization levels, the benefit from thereduced number of VRUs dominates the increasedthreat from the additional vehicles, and the totalfatalities fall. Despite the qualitative similarity withthe simple model, the fatalities in the High Car Usescenario no longer return to zero even after 100%of all trips include a motorized component. Theseresidual fatalities exist for two reasons: first, unlikethe crude model, vehicle occupants have nonzerofatality risks; and second, there are a significantnumber of pedestrians (bus riders) even when alltrips include a motorized component. The magnitudeof the residual fatalities, which exist in all scenarios,depends on the final vehicle mix and is highest forthe scenarios involving a large number of scootersbecause of the high CFR of scooter riders.
Risk-Based Method for Modeling Traffic Fatalities 133
Traffic fatalities rise and fall only in the High CarUse scenario. In all other cases, fatalities rise mono-tonically. In the High Bus Use scenario, fatalities con-tinue to rise because even though bus occupants havelow CFRs, bus trips include travel as a pedestrian,which is a high-risk travel mode. Similarly, in the HighScooter Use scenario, transportation growth leads tothe substitution of a high-risk travel mode (walking)by another high-risk mode (scooters).
Even though transportation growth through carownership (High Car Use) eventually causes fatalitiesto have a falling trend, fatalities are higher than thosein the High Scooter Use scenario over much of therange of motorization levels and substantially higherthan the High Bus Use scenario. The former findingis because although scooter riders do not have theprotection of a metal shell (and, thus, have relativelyhigh CFRs), they pose a much smaller threat than carsto other VRUs, who dominate the vehicle mix in allthe scenarios considered. The High Bus Use scenarioresults in lower fatalities than the other scenarios forthe entire range of motorization levels because busesresult in far fewer additional vehicles (occupancy of40) leading to a much smaller increase in threat toother road users.
Unlike total fatalities, fatalities per vehicle show amonotonically decreasing trend with increasing pro-portions of motorized travel (Fig. 5). The decreaseis most rapid for scenarios dominated by car or bususe because of the much higher protection offeredby these vehicles when compared with scooters; the
Fig. 5. Change in fatalities (all road users) per unit motorizedtravel computed for four scenarios of growth in motorized travel.
decrease is slowest for the scenarios that rely heavilyon scooter use.
In order to examine the threat posed by eachtransport mode in the Base Scenario, we use a series ofsimulations that start by setting all the pairwise CFRsto zero and then progressively return them to theirvalues in Table II. Note that the marginal contribu-tion of each CFR to total fatality is independent ofthe order in which the CFRs are introduced becausecrashes between different vehicle pairs are mutuallyexclusive. In Fig. 6, Curve (1) is generated by settingall CFRs to zero except r car
pedestrian, which was set at 0.08.This analysis is similar to the crude model describedearlier—only car-pedestrian risks are considered andcar occupants are at no risk. As before, the result is aparabola that peaks at 50% motorized travel. Curve(2) is generated by introducing the threat from cars toscooters, r car
scooter. This results in much larger residualfatalities because of the vulnerability of scooter ridersto impacts from cars. Curves (3) and (4), which addthe threat from cars to occupants of cars (r car
car) andbuses (r car
bus), lie only slightly above Curve (2). Thus,the primary threat posed by cars is to pedestrians andscooter riders.
Curve (5), which adds the threat from buses toall road users (i.e., introduces rbus
pedestrian, rbusscooter, rbus
car,and rbus
bus) produces only a slight increase in fatalities,suggesting that buses contribute little to traffic fatali-ties in the Base Case. Curves (6) and (7) introducethe additional threat from scooters to pedestrians,r scooter
pedestrian, and to other scooter riders, r scooterscooter. The ad-
ditional pedestrian fatalities are large initially, whenthe amount of motorized travel is small, but fall whenthe proportion of motorized travel become large. Sim-ilarly, the additional scooter fatalities are higher athigh levels of motorized travel. The additional threatfrom scooters to vehicle occupants (Curve (8)) resultsin a negligible increase in fatalities.
Curves (9) and (10) add the fatalities from single-vehicle crashes. Scooter fatalities make up a largeproportion of these fatalities (Curve (9)). As ex-pected, most of the additional fatalities from single-vehicle crashes occur when the proportion of motor-ized travel is high. Finally, Curve (11) adds the fewfatalities that occur among scooter riders due to im-pacts with pedestrians to yield the Base Case.
6. DISCUSSION
While it is common to ascribe the increase in traf-fic fatalities that occurred prior to the 1970s in the richcountries to growth in vehicle fleet, the subsequent fall
134 Bhalla et al.
Fig. 6. Change in total fatalities due toprogressively introducing CFRs (fromTable II) in the Base Case scenario.
in fatalities is usually attributed to the introduction ofsafety programs (see, for instance, World Report onRoad Traffic Injury Prevention(1)). Our analyses, us-ing both a simple model of cars and pedestrians and amore complete model that includes a broader vehiclemix, demonstrates that the rise and fall in fatalities percapita and the fall in fatalities per vehicle observed inhistorical data(3) can also occur due to the interplay ofthe increased safety afforded by using a vehicle andthe increased threat that each additional vehicle posesto VRUs. This inverted-U pattern in fatalities is notdriven by a similar rise and fall trend in the number ofaccidents. In fact, in the crude model the number ofaccidents, ∼(N − C) · C + C · C, grows linearly with in-creasing cars. Instead, in our model the fall in fatalitiesoccurs because the vehicle mix shifts from predomi-nantly VRUs with high CFRs to vehicle occupantswho have low CFRs. These results are consistent withthe findings of Bishai et al.(18) who analyzed fatality,injury, and accident rates in 41 countries and foundthat even though fatalities decrease in richer coun-tries with increasing income, the number of crashescontinues to rise. However, it should be noted thatthe model ignores nonfatal injuries, which representa significant fraction of the public health burden ofroad traffic crashes, and should be included in a moredetailed analysis.
Fatalities per capita fall even though we hold theCFR of each victim-threat pair constant in time and
thus do not include the effects of most safety inter-ventions. Safety interventions, of course, have a cru-cial role in the dynamics of traffic fatalities. Depend-ing on when an intervention is introduced, it acts toeither decrease the rate of rise or hasten the fall intraffic fatalities.
Our results suggest that the vehicle mix in alter-native scenarios of transportation growth influencesboth the form of the time pattern and the absolutelevels of traffic fatalities. In the absence of safety inter-ventions, the inverted-U form of total traffic fatalitiesoccurs only in transportation scenarios dominated bycar use. In the presence of vulnerable modes of motor-ized transport (such as scooters, mopeds, and motor-cycles), traffic fatalities continue to increase with mo-torization. Interestingly, the scenario involving highscooter use results in traffic fatalities that are simi-lar in magnitude to those resulting from the scenarioinvolving high car use. This is the case because eventhough scooter riders are at much higher fatality riskthan car occupants, they pose a much smaller threatto other road users. Thus, the aggregate outcomes ofthe two scenarios are similar.
Historic data (Fig. 2B) show a monotonicallyfalling trend in fatalities per vehicle. In our analysisa similar trend is observed for all transport growthscenarios because of the steady decline in the pop-ulation of VRUs. However, it should be noted thatEquation (3) suggests that a decline in fatalities per
Risk-Based Method for Modeling Traffic Fatalities 135
vehicle could also occur if vehicle occupancy was tofall over time as often happens with income growth.
Traffic fatalities are lowest in the scenario dom-inated by bus use. This result should be interpretedwith caution because our experience with a localmodel of traffic fatalities suggests that buses can posethreats that have not been included in this analy-sis. Crash statistics from New Delhi indicate that ourmodel probably underestimates the number of busrider fatalities and bus-related pedestrian fatalities,many of which occur at bus stops.(13) Aggressive driv-ing by bus operators coupled with poorly designed busshelters that force passengers to wait on the streetcan lead to a much higher rate of bus-pedestriancrashes than estimated by our model. Clearly, theseeffects should be included in local applications ofthe model, especially when evaluating the impactsof targeted interventions. For example, in the high-capacity bus systems of Curitiba, Brazil, and Bo-gota, Colombia, suitable infrastructure and design(e.g., dedicated bus lanes and bus shelters) have re-duced the risks to passengers waiting for and board-ing buses, resulting in a much safer bus transportationsystem.(16)
Other shortcomings and assumptions of thismodel can be classified into two sets:
� Assumptions related to crash probability: Inthis initial application, we model crash risk asa linear function of vehicle use, which assumesthat all vehicles (as well as pedestrians) sharethe same roadway. While such mixing of motor-ized and nonmotorized modes is uncommon inindustrialized nations, shared road use is com-mon in the urban centers of many developingcountries. Appropriate adjustments to expo-sure can be made to model scenarios wheretraffic is less homogeneous. We also assumethat total miles traveled remains constant andthe only change is through shift in transportmodes. Experience from cities worldwide sug-gests that during economic growth, growth inmotorized trips outstrips road building, lead-ing to higher vehicle densities (congestion),and, thus, an increase in the number of crashes(see also below).
� Assumptions related to the CFR: Since theCFR matrix is largely derived from U.S.-basedstudies, it may underestimate the true fatalityrisks expected in the developing world. How-ever, the CFRs in Table II have a range oftwo orders of magnitude, and small changes
in these CFRs do not significantly alter the fa-tality trends. Furthermore, we hold the CFRsconstant in time in order to isolate the effectsof vehicle mix and prevalence on fatality out-comes. As with the probability of crash (dis-cussed above), traffic congestion can have aconsiderable effect on CFRs because it reducescrash speed. At speeds of about 30 km/h, thecrash speed has a larger effect on bicyclistsand pedestrians than on occupants.(8,10) In ouranalysis, a 5% decrease in crash speed causesthe traffic fatality trend of the Base Case tobe uniformly lowered by approximately 7%;an increase in speed of 5% causes fatalities toincrease by approximately 25%.
Detailed calibration of the model against real-world data is needed before it can be applied to pol-icy analysis. In the absence of such data, we have ap-plied the methodology to perform a qualitative ex-ploration of traffic fatality outcomes for hypotheticaltransportation growth scenarios. However, when de-tailed information about the traffic stream is knownfor a particular region (country, city, or traffic cor-ridor), suitable crash-risk models can be developed(see, for instance, Reference 17). These locally vali-dated models can be used for long-term regional plan-ning (e.g., identifying optimal vehicle mix, and evalu-ating the impact of dedicated bus lanes) as well asfor the evaluation of short-term targeted interven-tions (e.g., speed limits and motorcycle helmets) thatare implemented over time periods in which the ba-sic characteristics of the transportation system remainconstant.
ACKNOWLEDGMENTS
Kavi Bhalla is a recipient of a David E. Bell Fel-lowship awarded by the Harvard Center for Popu-lation and Development Studies. This research wassupported in part by Grant PO1-17625 from the Na-tional Institutes on Aging. The authors are gratefulto Elizabeth Kopits and Maureen Cropper for theircomments and for sharing their international fatalitydata set.
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