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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