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ROAD RISK EVALUATION
Sylvain Lassarre
IFSTTAR
WHO, The world health report 2002. Reducing risks, promoting healthy life
Chapter 2 Defining and assessing risk.
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What is risk for road accident?
• Accident or crash = unwanted and unexpected collision (with different scenarios) , which results in a release of mecanical energy causing injuries with different severities) to road users
• Two dimensions : frequency/severity
of accident scenarios
• Used by automobile insurance companies (damages)
frequency
severity
Farmer’s curve
frequency/consequences
0,001
0,01
0,1
1
10
100
1000
10000
1 10 100 1000
consequences(>=k fatalities)
a
c
c
i
d
e
n
t
/
y
e
a
r
Road rail
Evans A. (1994) Evaluating public transport and safety measures. Accident
analysis & prevention, 26, 4, 411-428.
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The occurrence of accident as a Poisson
process
• The location and moment of an accident aredetermined by chance at a certain rate
• the occurence of accidents is represented bya stochastic spatio-temporal point process
Space
Time
• The number of accidents on a particular network of lenght L during a period (0,T] is a random count
variable Na(T), which follows a Poisson distribution
• The mean number of accident E(Na(t))=lLt is acumulative rate ,equal to the product of theinstantaneous rate of accident by the duration t andthe length L
• the mean = the variance
k!
e)(k)(T)P(N
k
a
LTLT ll
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• probability distribution for a Poisson law of mean 3,4
4,3440010108,21),(,
365
1
8
tx i
dudvvul
number of accidents
Probability
0
0,05
0,1
0,15
0,2
0,25
0 1 2 3 4 5 6 7 8 9 10
Road section 10 km long, 4400 veh/day
Models of accident severity
• the number of victims in an accident or the
cost of an accident is a random variable Z
• The number of victims or the total cost in a
set of accidents is a random sum of random
variables
• which follows a compound Poisson
distribution
ntN
inig
a
ZZZZtN)(
121 ...)(
)())(())((
)())(())((
2ZEtNEtNVar
ZEtNEtNE
ag
ag
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(Individual) Risk = Probability of occurence
of an adverse outcome during a stated period
of time which leads to consequences such as
death or injuries
t ime
0 10 20 30 40 50 60 70 80 90 100
987654321
=Instantaneous failure (death) rate
time age
hazard function 10
-4
20 t t+dt
2
100
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Computing individual risk
tt
duuhduuhtYPtYPRisk00
)())(exp(1)(1)(
Cumulative failure (death) rate = t
duuh0
)(
1000
2)2021()()2120()21,20(
21
20
duuhYPdeathP
Male in France in 1980
Risk indicators in public health (I)
• Mortality rate=number of fatality/person*year
Estimated by
yearaduringosedtsinhabiofnumberyearainfatalitiesofnumber
exptan
age
mortality rate 10-5
20
4,5
30
Road accident France
in 2000=13,5 *10-5
in 2003=10 *10-5
Definition of death
Migration effect
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Actuarial estimation
Age fatalities in 2003 Population 1/1/2003 Population 1/1/2004 Average population mortality rate
Total 6000 60 000 000 61 000 000 60 500 000 9,92
0_5 400 5 000 000 5 500 000 5 250 000 7,62
6_10
Agregating individual risks
• Burden =number of deaths or injuries that results from exposure
• collective risk=Average burden= individual risk*total exposure
Exemple : pedestrian accident in one year in Dehli
7*10-5*13*106*1 = 910 fatalities
11))(0(
1))(1(
l
l
lifeDP
deathDP
i
i
1)()(11
nDEDEn
ii
n
ii l
n
iitt ttDN
11, 1,
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Risk indicators in public health (II)
• Number of years of life lost = life expectancy(average age at death)*burden
Age at death for pedestrian = 24 years
Life expectancy at 24 = 40 years
Number of years of life lost = 40*910=36400 years
• Number of years lived with disability
• Number of disability adjusted life years = YLL+LLD
1 DALY = Loss of 1 healthy year
Relative mortality rate according to age
and sex for walking
Relative risk
1
Men
Women
0-5 5-10 50-60
Age
There are two main vulnerable groups :
young boys (5-10) and old women (>65).
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NUTS-0 NUTS-1
NUTS0 par E
4 - 4,6 (2)4,6 - 7,1 (6)7,1 - 9,9 (8)9,9 - 13,4 (14)
13,4 - 17,5 (16)17,5 - 23,9 (4)
Mortality rate
Ecological analysis : influence of
population density on mortality rate
• By region
Mortality rate
population
density
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Risk indicators in road transport• Two dimensions of the risk for an operator or an insurer:
Frequency/severity of an accident (collision) between motorized vehicles, vulnerable road users, obsctacles
Accident risk = number of accidents/kilometre*year
= number of accidents/vehicle*year
= number of accidents/vehicle*kilometre
= number of accidents/vehicle*hour
Accident severity = number of deaths/accident
= number of injured/accident
= cost/accident
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. Injury rate in Norway (injuries per
million person kilometres of travel)
(source : Elvik, 1999).
injury rate
0,87 0,78
1,56
1,85
0,73
0,11
0
0,5
1
1,5
2
pedes
trian
cycl
ist
mope
d rid
er
moto
rcyc
le ri
der
youn
g dr
iver
safe
st driv
er
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Injury risk at junction (injured road users
per million road user passing through the
junctions) in swedish cities.
injury rate
0,13 0,18
0,82
0,05
0
0,2
0,4
0,6
0,8
1
pedestrian cyclist Moped and
moto rider
car user
Accidental mortality (fatality) rates
for transport and other activities
• Exposure assessment = Time spent in the activity
= Distance travelled
G-B fatality rate per fatality rate per
100 million hours100 million kilometres
Passenger travel by :
bus 1,4 0,06
rail 6 0,1
car 12,4 0,4
water 16 0,8
air 20 0,04
foot 27 7
bicycle 64 4,6
motorcycle 342 11,4
Employement:
all work 0,9
At home :
all ages 2,6
people over 75 22
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Problems of comparison
• Be careful
• Limits of the transportation system
• Categories of users : workers (pilot, driver, …), passengers, trepassers, suicides, …
• Detailed exposure : landing (air), crossing (foot)
• Standardisation (age/gender, density,…)
• Internal/external risk
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Regression Models classification
Direct approach
• Number of fatalities
• Mortality rate
– Linear additive models
E(Nit) = a+SbXit
– Multiplicative models /Log-linearmodels
E(Nit) = a PopitPXbit
LogE(Nit) =Log(Popit)+Loga+SbLogXit
– Normal/Poisson/NB
Indirect approach
• Mortality rate=
Motorisation rate * fatality rate
Smeed law
• On G-B 1907-1947
• On a set of 68 countries 1960-1967
31
32
tantan
tan
tinhabi
vehiclemotorisedc
tinhabi
fatality
tinhabi
vehiclemotorisedc
vehiclemotorised
fatality
Problem
Evolution in time of the number of fatalities
time
M/P
F/M
F/P
M/P
F/P
3
2
3
1
tan tinhabiehiclemotorisedvcfatality
Smeed R. J. (1949) "Some statistical aspects of road safety research", Journal
of the Royal Statistical Society. Series A (General), 112 (1): 1–34.
Smeed R.J. (1968) Variations in the pattern of accident rates in different countries and
their causes, Traffic Engineering & Control, 10 (7), pp. 364–371
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Oppe/Koornstra/Lassarre models
• The fatality rate is decreasing over time
Competition between
safety/mobility/demography
-b + +
2,18, Obt
tt vehiclemotorisedepopulationcfatality
dtiondmotorisat
dt
ndpopulatio >0
<0
Oppe, S. (1989). Macroscopic models for traffic and traffic safety. Accident Analysis and Prevention
21, 225-232.
Lassarre S., (2001) « Analysis of progress in road safety in ten european countries », Accident
Analysis & Prevention, 33, 743-751.
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
1953
1956
1959
1962
1965
1968
1971
1974
1977
1980
1983
1986
1989
1992
1995
1998
2001
2004
tués
-5,4%/an-18%
-22%
Total France
10
100
1000
1940 1950 1960 1970 1980 1990 2000 2010
y = 6E+47e-0,0537x
y = 6E+46e-0,0528x
0
20
40
60
80
100
120
140
160
180
200
1950 1960 1970 1980 1990 2000 2010
TauxGB
TauxF
Exponentiel (TauxF)
Exponentiel (TauxGB)
Evolution
Traffic fatalities
In France
Vehicle kilometres
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National Policy measures
1
10
100
1000
1950 1960 1970 1980 1990 2000 2010
Kil
led
/1 0
00 0
00 0
00 v
eh
*k
m
G-BFrance
France G-B
Delorme R., Lassarre S., (2009) Les régimes français et britannique de régulation du risque
routier : la vitesse d’abord. Synthèse INRETS n° 57.
Delorme R., Lassarre S., (2014) A new theory of complexity for safety research. The case of
the long-lasting gap in road safety outcomes between France and Great Britain. Safety
science, 70, 488-503.
Distribution of the number of billion kilometres driven among
motorised road users in France and Great Britain
France
0%
20%
40%
60%
80%
100%
1949
1955
1961
1967
1973
1979
1985
1991
1997
VP VUL PL bus Cyclo+moto
G-B
0%
20%
40%
60%
80%
100%
19491955
19611967
19731979
19851991
1997
VP VUL PL bus moto
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Economy and road safety
80 countries 1963-1999 source IRF
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Macro panel data
Three types of relationships (homogeneous)
– Long term between the levels (cointegration) (long runpar.)
– Short term between the first differences (short run par.)
– Combination of dynamics: Error correction model (ECM)
itiit
ititit
ititit
GDPbaFAT
GDPGDTGDP
FATFATFAT
%%
%loglog
%loglog
1
1
itiit GDPbtaFAT loglog
)log(log
)log(logloglog
11
11
itit
ititiiitit
GDPbtFATC
GDPGDPbaFATFAT
41
Long-term elasticities
• Procedure xtmg Stata (elasticity = unweighted average of country elasticities)
base base+interventions base Kuznets
LGDP coef 0.45 0.69 0.61 14.2
std. err. 0.25 0.23 0.16 8.8
z 1.81 2.79 3.82 1.62
t coef -0.008 -0 .019 0.11 -0.002
std. err. 0 .008 0.008 0.14 0.014
z -1 -2.44 0.74 -0.16
t2 coef -0 .0005
std. err. 0.00028
z -1.64
LGDP2
coef -0.68
std. err. 0.46
z -1.48
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 10000 20000 30000 40000 50000 60000
e
l
a
s
t
i
c
i
t
y
GDP per capita
C. Antoniou et al. (2016) Relating traffic fatalities to GDP in Europe on the long
term . AAP, 92, 89-96.
30 countries in Europe, 1975-2012
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Conclusion• Risk as frequency/severity and counts
– Number of accidents and victims: Poisson process and distribution
et al.
• Public health risk indicators
– Rates, survival models and probability (individual)
– Mortality rate (per person*year), Nb of years lost and al.
• Age, sex, population density
• Transportation risk indicators
– Exposure as vehicule*kilometre or hour
– Fatality rate (exponential decrease by « socio-technical learning »)
• Regression models and risk evolution
– Mobility versus safety
– National Interventions effects on levels (and trends)
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Relative risk=the likelihood of an adverse outcome
in people exposed to a particular risk (factor),
compared with people who are not exposed
• Seat belt use (car driver in frontal collision)
• Trees along the road
• Motorcycle/car
4)/(
)/(
wearingkilledPwearingnotkilledP
RR
8,1)/(
)/(
treeswithoutkilledPtreeswithkilledP
RR
6,274,12
342)/(
)/(
carkilledPmotorcyclekilledP
RR
Attributable risk= the proportion of disease in a
population that results from a particular risk to health
• Identify a risk factor and its distribution among the
population (exposure assessment)
• Estimate RR with a reference level (dose/response
assessment)
• Calculate AR with P(E+), the prevalence (the
proportion of the population exposed to the risk)
)1)((1
)1)((
RREP
RREPAR
)()()()(
)()(
)(
)()(
ERiskEPERiskEP
ERiskERisk
ERisk
ERiskERiskAR
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• If 30 % of car driver don’t use the seat belt, the
proportion of fatalities due to the non wearing of
seat belt is 50 %
47,09,19,0
)14(3,01)14(3,0
AR
Models of accident occurrence
• q(x,t)=traffic volume (veh/day)
l = accident/veh*km
...
),()(),(
),(),(
)(),(
),(
txqttx
txqtx
ttx
tx
ll
ll
ll
ll
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Accident risk models for road
sections and junctions
• Infrastructure, traffic factors playing a
role in the accident can be introduced
via explanatory variables {Xi, i = 1, ...,
K} into Poisson regression models
kiki XX
ii eE
ll
...11
at junction (trrl)
l = l0 Q1a Q2
exp(a SPEED + b %MOTO + c WIDTH)
Accident risk models for vehicles
and drivers
• Vehicle and behavioral factors playing a
role in the accident can be introduced
via explanatory variables {Xi, i = 1, ...,
K} into Poisson regression models
kiki XX
ii eE
ll
...11
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Applications of accident risk models
• The models are used for:– quantification of risk factors such as
geometric characteristics of the road, speed, ...
– diagnosis and specially identification of blackspots or dangerous zones in a network
– evaluation of the effectiveness of a safety measure
– prediction of the evolution of road accident burden
• Extension of these models is possible by adding an extra random variation term to the rate of accident to obtain a mixed Poisson process
Quantification of risk
factors• Cohort studies
RISK FACTOR ACCIDENT VEHICLES* KILOMETRES
PRESENT (+) n+ + ABSENT (-) n- -
WE CAN COMPARE THE RATES OF ACCIDENTS BETWEEN THE TWO
SAMPLES BY MEANS OF A RATE RATIO :
RR = l+ / l-
ESTIMATED BY
l
l
n
nrr
ˆ
ˆ
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Obstacles (trees) along the road
trees accident vehicles *kilometres
(*108)
present (+) 925 28,8
absent (-) 689 29,7
rr = 925 / 28,8
689 / 29,7 = 1,38
The accident rate is 1,4 times higher for road sections with trees
along the road compared to road sections without trees along the
road.
BEWARE OF CONFOUNDING
Confidence intervals
nnu
err
ervalconfidence
nnrrLog
11
)%21(100int
11)(rav
a
a
As the variance of Log rr is equal to 1
925 +
1
689 = 0,0025,
the confidence interval is[1,25 ; 1,52].
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Case / control studies
RISK FACTOR
INVOLVED IN AN ACCIDENT
YES (CASE) NO (CONTROL)
PRESENT n++ n+-
ABSENT n-+ n--
TOTAL n.+ n.-
The odds ratio of the probability of involvement with (+) and without (-) the presence of the risk factor
(1
)
(1
) is estimated by the ratio of the cross-
products n
n
n
n
Alcohol and driving
Alcohol involved in an accident
yes (case) no (control)
>0,8 g/l 12,5% 3,4%
<0,8 g/l 87,5% 96,6%
total 4 048 3040
rr = 12,5 x 96,
87,5 x 3,4 = 4,0
Beware of bias due to problems of comparability
solution = matching
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Main points to remember
• Make a distinct use of risk indicators from public health sector and transportation sector
• Work on exposure assessment
• Undertake epidemiological studies suchas cohort, case/control or matchedcase/control studies
and
• Use Poisson models to estimate the accident risk