Road accidents in Slovenia involving a pedestrian, cyclist or motorcyclist and a car

Accident Analysis and Prevention 33 (2001) 147–156

Road accidents in Slovenia involving a pedestrian, cyclist ormotorcyclist and a car

Marjan Simoncic *Institute for Economic Research, Kardelje6a pl. 17, 1000 Ljubljana, Slo6enia

Received 17 December 1999; received in revised form 2 March 2000; accepted 7 March 2000

Abstract

We analyse the group of road traffic accidents in Slovenia in which a car driver and a pedestrian, cyclist or motorcyclist areinvolved. At the beginning some basic data are presented from the available database on traffic accidents. The selected group isthen analysed by use of the logistic regression method. Based on the obtained results, some guidelines for transport policy action— aimed at decreasing the number of accidents with severe injury or fatality — are identified. © 2001 Elsevier Science Ltd. Allrights reserved.

Keywords: Transport policy; Road accidents; Logistic regression

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1. Introduction

Slovenia, former Yugoslav republic, became an inde-pendent state in 1991. It is a small country with twomillion inhabitants, whose area covers 20 000 km2. Bygross domestic product per capita Slovenia — as aneconomy in transition — ranks first among the Centraland Eastern European Countries (CEEC). In passengercars per 1000 inhabitants the corresponding figure forSlovenia in 1997 amounted to 385 (CEEC average was212 and the country ranked second on the list was theCzech Republic with 329 cars per 1000 inhabitants1). InSlovenia the car represents a strong status symbol,which makes it easier to understand why, even duringthe period of transition depression2, the number ofpassenger cars in use was growing by a rate of 30 000–60 000 newly registered cars per year. This and a rela-tively low price of fuel (compared with the

neighbouring countries) have contributed to a rapidlyincreasing volume of road traffic and rather poor roadsafety. Hereafter we will try to make it clear that roadtraffic safety is a serious problem in Slovenia and thatit goes only partly hand in hand with the motorisationdevelopment.

In the paper we discuss the following questions:1. what is road safety in Slovenia like in comparison

with other European countries;2. do data from the information system of the Ministry

of Interior (MI) allow us to estimate a quantitativemodel that would explain under what conditionsroad accidents result in fatal or serious injuries; and

3. is the estimated model of any help in devising policymeasures.

2. Comparison of road safety in Slovenia with otherEuropean countries

Road traffic fatalities are legitimately considered astoo high in practically all countries. It seems that theirper capita number is the smallest in underdevelopedcountries with a low motorisation level, grows in accor-dance with economic development up to a certain leveland then declines in highly developed countries. This isa simplified picture and exceptions do exist. According

* Tel.: +386-61-345787; fax: +386-61-342760.E-mail address: [email protected] (M. Simoncic).1 Source: The European Commission, Transport DG (see http://eu-

ropa.eu.int/en/comm/dg07/tif).2 GDP growth rates in 1991 and in 1992 were −9 and −6%,

respectively. Unemployment grew from 45 000 in 1990 to 129 000 in1993.

0001-4575/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved.PII: S0001-4575(00)00025-7

M. Simoncic / Accident Analysis and Pre6ention 33 (2001) 147–156148

Table 1Number of road traffic fatalities per 100 000 inhabitants in Slovenia in the period 1989–1998a

1993 1994 19981995 1996 1997Year 1989 1990 1991 1992

24.8 15.625.4 20.9 19.5 18.0Fatalities 27.7 25.9 23.1 24.6

a Source: Statistical Yearbook of the Republic of Slovenia.

to statistical data illustrating the year 19973, the follow-ing countries were in the worst situation regarding thenumber of road traffic fatalities per 100 000 inhabitants:1. Portugal, 23.3;2. South Korea, 22;3. Greece, 21.0;4. Slovenia, 17.9; and5. Poland, 17.5.By definition, fatality is a person who — within acertain time interval — dies because of a road accident,as its direct or indirect consequence. For the majorityof EU countries 30 days is used, with exceptions beingItaly (7 days), France (6 days), Portugal (1 day) andGreece (3 days). Therefore in EUROSTAT statisticscorrective factors are used for these countries, namely1.078 for Italy, 1.09 for France, 1.3 for Portugal and1.18 for Greece. Slovenian data are based on EU-ROSTAT-defined time interval (30 days).

Let us state here that in the US, as a prototypecountry with highly developed road traffic, the numberof fatalities per 100 000 inhabitants in 1997 was 15.7.Among highly developed countries, displaying a highmotorisation level, let us mention Sweden (with 6.1fatalities per 100 000 inhabitants), UK (6.3), Nether-lands (7.5), Finland (8.5), Switzerland (8.3), Denmark(9.3) and Japan (8.9); all of them with the averagenumber of road fatalities per 100 000 inhabitants lessthan 10. In Table 1 we present this indicator as itdeveloped in time from 1989 to 1998.

Table 1 makes it clear that the year 1997 proved tobe even favourable, whereas the number of fatalities per100 000 inhabitants in 1994 was 25. That would placeSlovenia somewhere at the top of the list concerned.

It is interesting to note the relation between thenumber of fatalities and the volume of road traffic.Fuel consumption is a proxy variable upon which thevolume of road traffic can be approximated. In Fig. 1we present the dynamics of the quotient between thenumber of fatalities and the volume of fuel sold inSlovenia. One can note a lasting decrease in this quo-tient after 1983. Slovenia’s approaching to the EU hassignificantly raised the price of fuel during the last 2years. As it is still lower than its price in EU countries4,it will have to be raised further. Taking into accountthe regular behaviour in Fig. 1 and supposing that the

number of cars will not grow excessively5 this shouldfurther bring down the number of fatalities.

3. Road accidents data

In early 1990s the Ministry of Interior (MI) devel-oped an information system on road traffic accidentsthat has been under continuous maintenance. Existenceof a police report is a necessary and sufficient conditionfor accident data to be included in the database. A roadtraffic accident is usually defined as an event occurringin road traffic, in which at least one moving vehicle isinvolved, and which has resulted in injury to person ordamage to property. The actual number of road acci-dents is higher than the number of accidents reportedon by the police. From now on we base our analysis onMI data set, meaning that the existence of accidentreports by police is relevant for us. For each accidentthat was treated by traffic policemen there are severaldata elements, some related to the accident (place, date,time, severity, weather conditions, road conditions,traffic situation etc.) and others to participants (age,sex, driving experience, type of vehicle, use of protect-ing devices, severity of injury etc.).

In our paper we do not deal with all road trafficaccidents included in MI database; we focus primarilyon accidents involving two participants (from now ondenoted by ACCID2), namely:1. pedestrian or cyclist or motorcyclist (denoted by

PCM)6;

Fig. 1. Road fatalities per ton of sold gasoline in Slovenia.

5 If the real price of fuel grows, consumption of fuel per cardeclines. For how much, it depends on price elasticity.

6 This type of traffic participants is sometimes also called vulnera-ble road users or unprotected participants.

3 Source: Road fatalities, The European Commission, TransportDG (see http://europa.eu.int/en/comm/dg07/tif).

4 The price of Euro super is approximately 0.6 EUR per litre.

M. Simoncic / Accident Analysis and Pre6ention 33 (2001) 147–156 149

Table 2Number of road accidents involving a pedestrian, cyclist or motorcy-clist and a car — with the corresponding number of fatalitiesa

Year Number of Number of fatalities in ACCID2ACCID2

1994 11429091995 531341

24351996 761997 702802

511998 2247

a Source: MI.

8. cause (2 — excessive driving speed, 3 — pedestri-an’s improper action, 6 — overtaking against reg-ulations, 7 — car manoeuvres, 11 — unsuitablesafety distance, 8 — other);

9. PCM is originator (1 — yes, 2 — no);10. age of PCM (1 — up to 10 years, 2 — from 10 to

19 years, 3 — from 20 to 29 years, 4 — from 30to 39 years, 5 — from 40 to 49 years, 6 — from 50to 59 years, 7 — 60 years or above);

11. alcohol intoxication of PCM (1 — no, 2 — yes);12. PCM’s sex (1 — male, 2 — female);13. CD is originator (1 — yes, 2 — no);14. age of CD (1 — up to 25 years (inclusive), 2 —

others);15. driving experience of CD (1 — up to 1 year

(inclusive), 2 — from 2 to 5 years, 3 — from 6 to10 years, 4 — 11 years or above);

16. alcohol intoxication of CD (1 — no, 2 — yes);and

17. CD’s sex (1 — male, 2 — female)Most of these attributes have proven as relevant

during testing of the quantitative model to be presentedin the next section. During testing some other attributeswere also taken into account, such as weather andtraffic conditions, road surface, traffic manoeuvring etc.All attributes are treated as categorical variables — inspite of the fact that some of them (e.g. age, drivingexperience, value of alcotest) could be taken into ac-count as interval or at least as ordinal variables. InTable 3 we present frequency data for attributes relatedto the ACCID2 type of accidents in the period from1994 to 1998. In the following section we restrict ourattention only to this data.

Use of protection devices is linked to PCM11. Crashhelmets are optionally worn by cyclists and prescribedby law for motorcyclists. Motorcyclists and cyclistswere taken into account, whereas for pedestrians thisattribute was treated as a missing value. A total of 29%of participants used protection devices and 41% did not(30% is related to pedestrians). A comparison with thenumber of motorcyclists involved in accidents revealsthat there were too many who did not use a helmet12.

Among vulnerable road users 30.3% were pedestri-ans, 55.5% were cyclists (and mopedists) and 14.2%motorcyclists. We added mopedists to cyclists, basedmainly on the fact that:1. mopedists have to use a bicycle path13 if there is

one,

2. car driver (denoted by CD).This type of accidents is fairly important regarding itsshare in all road fatalities (see Table 2). A comparisonwith Table 1 points out the fact that approximately20% of fatalities may be attributed to ACCID2 type ofaccidents7.

MI data on the severity of injuries for individualparticipants8 is categorised as follows:1. N, no injury;2. T, trace of injury;3. L, slight (light) injury;4. S, severe injury; and5. F, fatality.For our purpose injuries of individual participants inACCID2 are combined into the following two groups:1. severe injury or fatality (denoted by FS); and2. others (denoted by NTL).

For each accident of ACCID2 type we take intoaccount only the following attributes from MIdatabase:

1. outcome (1 — FS, 2 — NTL);2. use of protection devices (1 — yes, 2 — no);3. type of ‘unprotected’ participant (1 — pedestrian,

2 — cyclist, 3 — motorcyclist);4. time (1 — at night, 2 — during daytime9);5. day (1 — Sunday, 2 — Monday, 3 — Tuesday, 4

— Wednesday, 5 — Thursday, 6 — Friday, 7 —Saturday);

6. settlement10 (1 — in a settlement, 2 — out ofsettlement);

7. type of road (1 — motorway, 2 — local road, 3— main road, 4 — settlement with a street system,5 — regional road, 6 — settlement without astreet system);

7 And close to 30% for FS type of injury.8 And also for accident: its severity is defined by the injury of the

most severely injured participant.9 Estimated from the date (month) and time (hour) of the accident.10 In our paper a settlement is a group of contingent buildings that

can appear in a rural or urban area.

11 It is of no real significance for ACCID2 type of accidents if CDuses seat belt or not.

12 On the use of protection devices in Slovenia see also (Simoncic,1997).

13 This was changed by the Law on the safety of road trafficadopted in May 1998. Now they are not allowed to use bicycle paths.


Table 3Frequency data for selected attributes applied to participants of ACCID2 accidents (in the period 1994–1998)a

FrequencyAttribute Relative frequency (IN%)Class and its description

Outcome of accident 31811 — fatality or severe injury 24.19992 75.92 — other

3795Use of protection devices 28.81 — yes53802 — no 40.8b

39981 — pedestrian 30.3Type of vulnerable road user7308 55.52 — cyclist1867 14.23 — motorcyclist

2977Time 22.61 — at night10 196 77.42 — during daytimec

1359Day 10.31 — Sunday19332 — Monday 14.71832 13.93 — Tuesday19474 — Wednesday 14.81884 14.35 — Thursday24206 — Friday 18.41798 13.67 — Saturday

10 018Settlement 76.01 — in a settlement3155 24.02 — out of settlement

46Type of road 0.31 — motorway1015 7.72 — local road21523 — main road 16.35962 45.34 — settlement with a street system21125 — regional road 16.01599 12.16 — settlement without a street system

406Cause of accident 3.12 — excessive driving speed2180 16.53 — pedestrian’s improper action10816 — overtaking against regulations 8.2

7 — car manoeuvres 862 6.516018 — other 12.17043 53.511 — improper safety distance

6302PCM is accident originator 47.81 — yes6871 52.22 — no

911Age of PCM 6.91 — from 1 to 9 years4930 37.42 — from 10 to 19 years19573 — from 20 to 29 years 14.9

4 — from 30 to 39 years 1225 9.312235 — from 40 to 49 years 9.3

981 7.46 — from 50 to 59 years1946 14.87 — 60 and more years

1 — noAlcohol intoxication of PCM 11 989 91.01184 9.02 — yes

PCM’s sex 1 — male 9819 74.53217 24.42 — female

7791Car driver is accident originator 59.11 — yes5382 40.92 — no

3717Age of car driver 28.21 — 25 years or less9456 71.82 — more than 25 years

1995Driving experience of car driver 15.11 — up to 1 year (incl.)2871 21.82 — from 2 to 5 years23333 — from 6 to 10 years 17.7

4 — 11 years and more 5974 45.4

12 270Alcohol intoxication of car driver 93.11 — no903 6.92 — yes

9871Car driver’s sex 74.91 — male2 — female 3140 23.8

a Source: MI.b There are missing values in data where percentage values do not add up to 100.c Estimated from the date (month) and time (hour) of the accident.


Table 4Frequency of fatalities in road accidents involving pedestrians, cyclists or motorcyclists and cars — by age groups (for 1994–1998)a

Age class CyclistsPedestrians Motorcyclists

% Number %Number Number %

Up to 19 years 24 9.6 23 20.2 10 34.53.2 12 10.520–29 98 31.06.4 4 3.516 630–39 20.7

3440–49 13.7 10 8.8 2 6.914.1 17 14.950–59 135 3.419.3 18 15.848 160–69 3.4

8470 and more 33.7 30 26.3 0 0

100 114All 100249 29 100

a Source: MI. Table 2 includes also passengers and car drivers and that’s the reason for difference (with this Table) in total number.

cation of different traffic participants is a serious prob-lem in Slovenia and, indeed, also in many otherEuropean countries.

We have already pointed out that younger partici-pants (between 10 and 29 years of age) are the mostfrequent participants in ACCID2 type of accidents. Agestructure of fatal victims for this type of accidentsreveals a different structure (see Table 4). We can notethat older participants (50 years and more) account forapproximately 60% of all fatalities in ACCID2 acci-dents, thus showing an unbalance with the correspond-ing share in participants. Among younger participants— victims of ACCID2 — motorcyclists are predomi-nant, while among older participants pedestrians andcyclists are outstanding.

There may be some other data of relevance in MIdatabase that have not been used in our analysis. Let usmention the exact location of the place of accident, typeof car (specific make and model) and numerical valueof alcotest. It seems to us that some of data thatinfluence the appearance of accidents are missing, andsome of the existing data are not precise enough. Weare aware of the situation in Finland (see Isotalo et al.,1996) where data on severe traffic accidents are col-lected by highly qualified teams of experts (physician,technician, etc.). This enables them to include someadditional factors that contribute to accidents takingplace and to their severity.

To get an idea about the relevance of the selectedgroup we present data relating to participants in acci-dents from the entire MI database of SF type ofseverity. From Table 5 we can see that among allparticipants in accidents with S or F severity of injurycar drivers are predominant. Next to CDs are passen-gers, pedestrians, motorcyclists and cyclists. It is a pitythat from MI data one can not find out which vehicleeach passenger was in and where he or she sat (in frontor in the rear). This was the main reason why we didnot include this important group of participants in ouranalysis. We hope that this will be improved in future.

2. mopeds have their motor’s working volume lessthan or equal to 50 ccm and maximum speed 550km/h.

Because a vast majority of ACCID2 type of accidentsinvolving mopedists happened in a settlement wherebicycle paths are (more or less) provided, this seems tobe the best solution.

The least number of accidents took place on Sunday(10.3%) and the most on Friday (18.4%). During theother days the number of accidents of ACCID2 typewas around 14%.

Out of the total number of accidents (13 173) ofACCID2 type, 76% happened in a settlement. Most ofthem happened in a settlement with a street system,followed by accidents on regional road, main road andin settlements without a street system.

PCM was accident originator in approximately onehalf of the total number of ACCID2 accidents.

The most frequent participants in ACCID2 accidentsare between 10 and 19 years old (37.4%), followed byparticipants from 20 to 29 years old (14.9%). The shareof the youngest (up to 9 years old) is also significant(6.9%).

Among PCMs men are predominant, women beingparticipants in less than one quarter of accidents(24.4%).

Car drivers are originators of accidents in 59% of allcases. CDs of age 25 years and less that were involvedin ACCID2 type of accidents account for 28.2%. Theseparticipants are deemed to be unreliable drivers (seeZnidarsic and Rovan, 1999), since they are involved ina disproportionately high number of accidents. AmongCDs 15.1% had driving experience of 1 year or less.There were 21.8% of CDs with experience between 2and 5 years, 17.7% with experience between 5 and 10years and 45.4% with driving experience of more than10 years.

About 9% of PCMs were intoxicated. The share ofintoxicated CDs is smaller than the one observed inPCMs, while the sex distribution is very similar. Intoxi-


Table 5Number of different participants in traffic accidents with fatal and severe injuries (the entire MI database; covering the period 1994–1998)a

F (fatality)S (in %)S (severe injury)Type of accident participant F (in %)

4 0.0 1 0.1Bus driverWorking machine driver 4 0.0 3 0.2

926.2 4.7693MotorcyclistCyclist 2087 18.7 227 11.5

11 0.1 0.12Van driverCar driver 3651 32.7 755 38.3

15.01676 352Pedestrian 17.82846 23.825.4 470Passenger

84 0.8 41 2.1Tractor driver1.5121 1.1 29Truck driver

197210011 177Column total 100

a Source: MI.

4. An estimate of economic loss attributable to roadaccidents involving a pedestrian, cyclist or pedestrian anda car

Table 3 shows us that there were 3181 accidents ofFS type among 13 173 ACCID2 accidents in the period1994–1998. It is obvious that huge economic loss re-sults from such accidents, not to speak of victims’relatives and their distress. Economic loss caused bythese accidents is of more relevance here because it maybe referred to when arguing about funds that should beengaged for investments in infrastructure and policymeasures aimed at reducing the number of accidents. Inwhat follows we present some data relating to selectedEuropean countries, summarised from the study (EU-RET, 1994)14. The data in Table 6 refer to costs oftraffic accidents as used by EU member states in theireconomic appraisal of road projects.

Big differences between countries can only partly beattributed to different definitions of fatality and severeinjury. They are mainly generated by different levels ofcountry development and the fact that given values areused in different contexts (some in social cost-benefitanalysis, others in multi-criteria analysis where someadditional criteria, related to safety, may be included).However, they are all based on the following threegroups of costs:1. direct financial costs related to the accident;2. loss of output value because of a fatality or injury;

and3. value of ‘pain, grief and suffering’ of victim’s

relatives.

Using data for Portugal15 — comparable to Sloveniaby gross domestic product per capita — one can obtainthe following estimate of costs related to fatalities andsevere injuries for ACCID2 type of accidents in 1997:

70×78 230+540×6543

=9 009 320 ECU (in prices 1990)

Table 6Costs of road accidents in selected EU countries (in 1990 ECU perperson)a

Year of estimateFatality Severe injuryCountry

– 1990Denmark 628 147269 129France 24 390 1985

Germany 406 672 43 611 1985Greeceb 48 879 6 429 1987

79 310Netherlandsc 15 948 1992199078 230 6 543Portugalb

1990100 529 25 519Spaind

26 357935 149 1988UKFinlande 1 414 200 897 081 1990

984 980 139 755Sweden 1990

a Source: EURET study.b For Greece and Portugal authors used estimates from studies and

not official values.c This value is used in a system for deciding about priorities

between road projects. It only covers costs of the lost production andother identified costs. Costs related to grief and pain of relatives arenot taken into account.

d Value related to a severe injury is in use for a slight injury.e Value for a severe injury is related to an injury that causes a

permanent incapability for work.

15 In 1997 the gross domestic product (at current prices and atcurrent exchange rates) per capita equalled US$9814 in Portugal andUS$9161 in Slovenia.

14 Similar data is also available in COST 313 Report (see Alfaro etal., 1994).


This figure16, relating only to accidents of ACCID2type, can serve as a basis when deciding about funds fordifferent policy measures aimed at decreasing the num-ber of fatalities and severe injuries.

5. A quantitative model dealing with accident severity

Our aim in this section is to estimate a model thatcaptures an eventual connection between the severity ofan accident of ACCID2 type and the values of differentattributes, in relation to the accident and to its partici-pants. We are interested in factors causing a fatal orserious injury outcome, as opposed to slight or noinjury outcome. There are different options availablefor the model, but we have selected the logistic regres-sion which seems particularly suitable when, as in ourcase, the majority of attributes are categorical variables.Hereafter we present a short description of the method(for a more serious presentation of this method seeAgresti, 1990).

We have a dependent variable Y — categorical vari-able that may figure in any of J classes (J]2)17. Let usalso denote by x a vector of attributes. Individualattributes are also considered as categorical variables.The corresponding statistical model may be put in thefollowing way18:

P(Y= j/x )=exp(gj(x))/�

1+ %J−1

m=1

exp(gm(x ))�j=1, 2, … , J−1 (1)

P(Y=J/x )=1/�

1+ %J−1

m=1

exp(gm(x ))� (2)

where the following notation is used:

gj(x )=bj0+ %p

k=1

bjkxk j=1, 2, … , J−1 (3)

We can write the given model in form of a generalisedlogit model:

logP(Y= j/x )P(Y=J/x )=gj(x )=bj0+ %

p

k=1

bjkxk

j=1, 2, …, J−1 (4)

In general we have a system of (J−1) equations thathave to be estimated from existing data. Unknownparameters b may be estimated by the maximum likeli-hood method, taking into account that variable Y isdistributed according to a multinomial distribution —in our case binomial. Components of vector x arecategorical variables and are transformed into dummyvariables with values 0 or 1.

When independent variables xk (k=1, 2, …, p) aredummy variables, the following formula is relevant:

P(Y= j/(x1, x2, …, xk=1, …, xp))P(Y=J/(x1, x2, …, xk=0, …, xp))

=exp(bjk)

k=1, 2, …, p j=1, 2, …, J−1 (5)

This ratio is called the odds ratio and allows an easyinterpretation of estimated parameters.

We are not aware of any theory explaining factorswhich influence the severity of road accidents. But it isobvious that the occurrence of a road traffic accidentand its severity in general depends on:1. participants (their experience, behaviour, use of pro-

tection devices, etc.);2. road (traffic density, road type, design, etc.);3. vehicle (type, age, maintenance, etc.);4. dynamic situation specific aspects — such as

cause(s) of the accident, weather conditions, time ofthe day — and stochastic influences.

In MI database there are attributes related to acci-dents and to participants that cover all four aspects. Inestimating the model we selected different attributesthat cover all of the mentioned aspects. There exist anumber of different possible choices because some at-tributes are highly correlated (weather and road condi-tions, age and driving experience, etc.). We removedsome attributes from the analysis because in the estima-tion process they were statistically insignificant andaggregated some others with too many categories. Thefinal result is based on common sense (i.e. statisticalfacts on road accidents that are in our knowledge) andacceptable according to statistical theory. In the estima-tion process the statistical package Logdiscr, Version2.0 (see Lim, 1999) was used19. Results were alsochecked by TSP 4.3 (see TSP, 1996). Final estimationresults are presented in Table 7.

Other data-relevant to the estimation process-include:1. number of observations, 13 173;2. number of categorical attributes, 11;3. number of response categories, 2;4. total number of attributes (including 0–1 variables),

30;5. reference category in the model — outcome class 2;6. −2× log likelihood=13 063.

16 This is a restrictive estimate for Slovenia. Based on age structureof PCM we have estimated a loss of value-added of the approxi-mately same amount, taking into account only fatalities.

17 In our case we have J=2.18 P(Y=J/x ) stands for conditional probability of the event that

the outcome of Y falls under class j, under condition that values ofattributes related to the particular accident are equal to (vector) x .Exp stands for exponential function.

19 Logdiscr is a freeware. The free use of this software is kindlyappreciated.


Table 7Estimation results

Unstandardised b Standard error P-valueaClass Odds ratioIndependent variable

Intercept 1.04366 0.17 0.000

−0.03363 0.61Use of protection devices 0.5831 — yes 0.9672 — no

1 — pedestrianType of PCM 0.18727 0.09 0.037 1.206−0.29536 0.072 — cyclist 0.000 0.744

3 — motorcyclist

0.28283 0.05Time of day 0.0001 — at night 1.3272 — during daytime

Day in week 1 — Sunday 0.10721 0.09 0.214 1.1132 — Monday −0.05513 0.08 0.498 0.946

−0.16195 0.083 — Tuesday 0.052 0.8504 — Wednesday −0.17799 0.08 0.030 0.837

−0.04933 0.08 0.545 0.9525 — Thursday−0.07622 0.086 — Friday 0.322 0.927

7 — Saturday

−0.45907 0.07Settlement 0.011 — in a settlement 0.6322 — out of settlement

Type of road 1 — motorway 0.19999 0.33 0.542 1.221−0.20427 0.11 0.0712 — local road 0.815−0.10676 0.093 — main road 0.219 0.899

4 — settlement with streets −0.41408 0.07 0.000 0.661−0.121455 — regional road 0.09 0.174 0.886

6 —settlement without streets

Cause of accident 11 — unsuitable safety distance −1.45299 0.22 0.000 0.2340.41499 0.06 0.0002 — excessive driving speed 1.5140.21228 0.083 — pedestrian’s improper action 0.012 1.236

6 — overtaking against regulations −0.26814 0.10 0.005 0.765−0.60646 0.08 0.0007 — car manoeuvres 0.545

8 — other

Age of PCM 1 — from 1 to 9 years −0.73109 0.09 0.000 0.481−0.98799 0.07 0.0002 — from 10 to 19 years 0.372−1.13483 0.083 — from 20 to 29 years 0.000 0.321

4 — from 30 to 39 years −0.92731 0.09 0.000 0.396−0.68427 0.08 0.000 0.5045 — from 40 to 49 years−0.36232 0.096 — from 50 to 59 years 0.000 0.696

7 — 60 and more years

−0.34399 0.07PCM’s intoxication 0.0001 — no 0.7092 — yes

Age of CD 1 — 25 years or less 0.22978 0.05 0.000 1.2582 — more than 25 years

−0.60683 0.08CD’s intoxication 0.0001 — no 0.5452 — yes

a P-value stands for the significance level. It gives the probability of committing a Type I error, which means rejecting the true hypothesis.

In Table 7 the odds ratio is given in the last column.From Eq. (5) it follows that the odds ratio is equal tothe ratio of probability for outcome S or F undercondition that attribute k has the value of 1 (is true)and probability for outcome S or F under conditionthat attribute k has the value of 0 (is not true).

Now we present some comments on the estimationresults, grouped by attributes as detailed at the begin-ning of this section.

5.1. Attributes of participants

Among variables corresponding to the type of the‘vulnerable’ participant, the one corresponding to mo-torcyclist is the reference one. Pedestrian-related vari-able is positive, meaning that the odds of a pedestrianto fall a victim to FS is 1.2 times the odds of amotorcyclist. The hazard of a cyclist to fall a victim toFS is only 0.7 times that of a motorcyclist.


The hazard of a PCM to fall a victim to FS when usinga protection device (helmet) is 0.97 times that of a PCMnot using one. This is a surprising value (not expectedto be so close to 1) for which we have no seriousexplanation.

The hazard of a PCM to fall a victim to FS in anaccident where the involved car driver’s age equals 25 orless, is 1.26 times higher than when the car driver isolder.

Among PCMs the most risky group includes thoseaged 60 and more (those in the reference category). Thelikelihood that a PCM aged from 20 to 29 years mightfall victim of the aforementioned circumstances is only0.32 times in comparison with the reference-aged PCM.

The likelihood that a PCM might fall a victim to FSin an ACCID2 type of accident — where the car driveris not intoxicated — is 0.55 times the likelihood whenan intoxicated driver is involved. If the PCM is intoxi-cated the corresponding factor is 0.71.

5.2. Attributes related to the road

PCMs that are involved in an accident taking place ina settlement are 0.6 times less likely to fall a victim toFS than PCMs that are involved in an accident takingplace out of settlement. Among different roads settle-ments with a street system pose the smallest risk toPCMs if compared to settlements without streets (asreference category). PCMs involved in ACCID2 acci-dents on local, regional and main roads run a risk offalling victims to FS approximately 0.9 times that ofPCMs becoming victims of an accident in settlementswithout a street system. The highest risk is associatedwith accidents on motorways (with odds ratio equalling1.2).

5.3. Dynamic situation specific aspects

Accidents at night and those that happen because ofpedestrians’ improper action are the most risky ones forPCMs. PCMs that are involved in an ACCID2 type ofaccident caused by excessive driving speed are 1.5 timesmore likely to fall a victim to FS than those involved inaccidents with other causes (reference class). The corre-sponding odds ratio connected with pedestrian’s im-proper action is equal to 1.2. The most risky days areSunday and Saturday (as reference category).

As already mentioned, our model was estimated tak-ing into account the available data covering the period1994–1998. Parameters are therefore characteristic forthe situation in that period. We also made an attempt totest the model on another year’s data as well, i.e. on

preliminary data for the year 199920. There are differentmethods available for this purpose. Let us mention thosebased on likelihood, then measures of ordinal associa-tion and cross validation. We chose cross validation.Using the cross validation method we put the model atwork on 1999 data, making predictions on a case-by-casebasis. For each case we computed the predicted proba-bility of event occurrence (FS outcome of accident). Ifit is higher than 0.5 the case is classified as belonging tothe FS category, otherwise it is classified as NTL. Wethen compared predicted and actual classification on thedependent variable in the validation sample and countedthe number of errors made by using the model to predictFS occurrence. Usually the error rate is given as finalmeasure.

Testing the model on data covering the period 1994–1998 (the same data as used for estimation purpose)resulted in misclassification error rate equalling 0.228,meaning that the model had wrongly21 predicted 22.8%of all cases. Testing the same model on 1999 — coveringdata produced a misclassification error equal to 0.199.This means that the model wrongly classified 19.9% ofall cases. Prediction quality of the model thus proved tobe even better in case of 1999 than in case of 1994–1998.

6. Conclusion

In the paper we try to quantify the effect of factorswhich — in road accidents involving a pedestrian/cy-clist/motorcyclist and a car — cause a fatal or seriousinjury of the former. We had at our disposal the Ministryof Interior’s database, providing us with data on all roadaccidents reported by police. A quantitative model isproposed that uses the method of logistic regressionwhich seems to be appropriate for this purpose.

The following high risk attributes of ACCID2 type ofaccidents are found on the basis of 1994–1998-relateddata:1. pedestrians and motorcyclists are at higher risk than

cyclists;2. cyclists and motorcyclists that use crash helmets run

a lower risk (though insignificantly) of falling victimto FS in ACCID2 — when they are involved in one— than those that do not use them;

3. PCMs getting hit by a car whose driver is aged 25years or less, are more likely to become FS victims

20 Data used cover the whole year 1999 but are not yet final. InJuly 1998 a new road classification system was introduced but wasused only in a very small number of police reports on road accidents.We treated such accidents as having missing values for the attribute‘type of road’. For 1999 we had to transform new codes for the typeof road into old ones, probably making some mistakes.

21 This means that either an FS outcome is predicted for an actualNTL outcome or an NTL outcome for an actual FS outcome.


than those getting injured by cars driven by olderdrivers;

4. older PCMs (60 years and more) are the mostexposed group;

5. intoxication of PCM or car driver increases thehazard of FS outcome for PCM in ACCID2 type ofaccidents;

6. accidents of ACCID2 type are especially dangerousif they happen out of settlements and onmotorways;

7. accidents that happen at night are much more seri-ous than those taking place during daytime;

8. Saturday and Sunday are the most risky days forPCMs;

9. pedestrian’s improper action or excessive drivingspeed of car driver result in a high risk in terms ofa severe injury or fatality (when PCMs are involvedin ACCID2).

We are aware that the aggregate approach to pedestri-ans, cyclists and motorcyclists in one group may con-ceal some safety issues of one specific group. In ourpaper we try to find common factors that influence theoutcome of an accident — with fatal or serious injuriescaused to the group as a whole, while specific issues areonly taken into account through dummy variables re-lated to different groups. A separate analysis for spe-cific groups would necessitate inclusion of additional(specific) attributes.

The primary goal of any traffic safety policy shouldbe to decrease the total number of road traffic acci-dents. Our analysis concentrated on factors that distin-guish a fatality or severe injury from a slight or noinjury caused by accident when it happens. Havingidentified the most risky attributes of ACCID2 type ofaccidents one should look for policy measures to influ-ence them. In our paper we do not treat thesequestions.

Our ambition, amongst others, is to provide theMinistry of Interior with some feedback on the quality

of their data. We propose passengers-related data to becomplemented by data describing the vehicle in whichpassengers were found after the accident, and theirposition in it. It should furthermore be investigatedwhich data are of no proper use and could be omitted;and which ones should be included. This process shouldbe guided by (positive) foreign experience. Finally wepropose a more thorough examination of the FS typeof accidents, where the introduction of some additionalattributes might be of some help.

Acknowledgements

The paper was prepared as part of the researchproject ‘Quantitative basis for transport policy manage-ment’, financed by the Ministry of Research and Tech-nology of Slovenia (Contract 3411-99-22 0881). Theauthor wishes to thank the editor and referees for manyhelpful comments and suggestions.

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Documents

Road accidents in Slovenia involving a pedestrian, cyclist or motorcyclist and a car