The effects of area deprivation on the incidence of child and adult pedestrian casualties in England

Accident Analysis and Prevention 37 (2005) 125–135

The effects of area deprivation on the incidence of child andadult pedestrian casualties in England

Daniel Graham∗, Stephen Glaister, Richard Anderson

Department of Civil and Environmental Engineering, Centre for Transport Studies, Imperial College London, London SW7 2AZ, UK

Received 26 January 2004; received in revised form 29 June 2004; accepted 16 July 2004

Abstract

This paper analyses child pedestrian casualties in England, focusing on the influence of socio-economic deprivation. It develops an area-based model of pedestrian casualties and presents estimates based on data for the English wards. The results detect an association betweenincreased deprivation and higher numbers of pedestrian casualties across England. The deprivation effect is strong both for all child casualtiesand for children killed or seriously injured. Estimates for adult casualties also reveal a positive and significant association with increasingdeprivation, but the magnitude of the effect is smaller than for children. The paper concludes by outlining some of the implications of ther©

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eywords:Deprivation; Pedestrian; Child; Adult; Negative binomial

. Introduction

The relationship between child pedestrian accidents andhe socio-economic characteristics of victims has received

great deal of attention in the literature. Researchers haveemonstrated the greater incidence of road accidents involv-

ng children from deprived or disadvantaged backgrounds.Christie, 1995andWhite et al., 2000provide comprehen-ive reviews of this literature).

White et al. (2000)cite literature demonstrating that theisk of death for child pedestrians is related to socio-economiclass, parental circumstances, and ethnicity. Their reviewhows that children of the lowest socio-economic status arever 4 times more likely to be killed on the road than those ofhe highest socio-economic status. It also indicates that ratef child mortality resulting from road accidents have declined

ess amongst the manual social classes than the non-manualocial classes, and as a consequence, the socio-economicortality differentials have increased.

∗ Corresponding author. Tel.: +44 20 7594 6088; fax: +44 20 7594 6107.

An earlier survey byChristie (1995)suggests several resons why there are a greater number of pedestrian roaddent victims from deprived backgrounds. These includearguments that children of a disadvantaged socio-econstatus are at a greater risk due to higher exposure ratfewer parents own cars), that they have less adult supervin the traffic environment, and that educational disadvanis prevalent in understanding issues of road safety.Christie(1995) also cites evidence showing that deprived childexhibit different behavioural patterns that increase theirceptibility to road traffic accidents.

Previous articles have developed models of road acciin relation to costs and traffic flows (for exampleDickersonet al., 2000; Peirson et al., 1998; Jansson, 1994; Jones1990; Jones-Lee et al., 1985; Persson and Odegaard,Vitaliano and Held, 1991).

Here we take up the broad theme of deprivation and petrian accidents and test the hypothesis that the level of seconomic well-being influences child accident rates.analysis is concerned with accidents across England iyears 1999 and 2000. We compare the effects of depriv

E-mail addresses:d.j.graham@ic.ac.uk (D. Graham),.glaister@ic.ac.uk (S. Glaister), richard.anderson@ic.ac.uk (R. Anderson).

on the number of pedestrian casualties suffered by childrenand by adults.

001-4575/$ – see front matter © 2004 Elsevier Ltd. All rights reserved.oi:10.1016/j.aap.2004.07.002

126 D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135

Our approach differs from that of previous studies. Insteadof focusing upon the socio-economic status of the victim, wetake a small area-based approach to the analysis of pedestrianaccidents. We develop a model that attempts to explain spatialvariation in accident numbers according to a wide range oflocation specific characteristics, a sub-set of which representslocal socio-economic conditions. It is easy to see in the “raw”data that there is an apparent strong relationship betweencasualty numbers and measures of deprivation. However, oneshould not jump to the conclusion that this is a straightforwardrelationship between deprivation and casualties. It might bethat deprivation is more commonly found in dense urban areasand accidents happen more frequently in dense urban areas.It could be that areas of similar density but differing levelsof deprivation suffer similar casualty numbers. Or it couldbe that areas of similar density have very different casualtynumbers, depending on the levels of deprivation. Deprivedareas may tend to have more children in them, so highercasualty numbers would not necessarily be to do with levels ofdeprivation. Thus, we seek to disentangle the effects of ‘areatype’ from the influence of socio-economic characteristics.

This paper is structured as follows. Section2 introducesthe data sources we have used and describes the spatial frame-work for analysis. Section3presents some background statis-tics on child pedestrian accidents in England. Our pedestrianc ed inS ut onS sedi

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The STATS 19 data provide a very rich source of accidentdata but are prone to under-reporting. A study comparingpolice records with hospital records estimated that approx-imately one quarter of child pedestrian casualties were notrecorded on STATS 19 (Tunbridge et al., 1988). There hasbeen little analysis of this under-reporting but we must recog-nise that there may be some form of bias.

Using the grid references given in the STATS 19 data weallocated the child pedestrian casualties to each of the 8414wards of England. We chose this particular spatial frameworkfor our analysis because we wish to make use of the relativelyfine grain variation in local characteristics. The wards of Eng-land are small spatial units with an average area of 14 km2.But they are also areas for which a variety of data is availableto allow us to construct a spatial model of child pedestriancasualties. In our choosing the unit for spatial analysis thereis a trade off. Increasing geographical disaggregation wouldperhaps allow for more accurate modelling of local ‘environ-mental’ characteristics, but it is also associated with dimin-ishing data availability. The choice of wards as the unit ofanalysis provides sufficient data to develop a tractable modelof spatial variance in child pedestrian casualties, but one thatis still able to incorporate a high level of variation in localcharacteristics.

For our study we also require data on the level of depriva-t iceso imeM ciala landa de-fid iveni aini cov-e , andg mul-t andc epri-v

y de-t pec-t thed n ca-s tionS eachp havet eacho

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asualty model and the reasoning behind it is describection4. Model results and estimation issues are set oection5. Conclusions and policy implications are discus

n the final section.

. Sources of spatial data

The principal source of data available for our analysedestrian casualties describes road accidents in the U

he years 1999 and 2000. These data are based on rompleted by police officers each time a road accident oublic highways is reported to them. The individual poecords are collated and processed by the UK Departmeransport (DfT) as “Road Accident Data – GB”, genernown as the STATS 19 data base.

A vast range of information is reported surroundingarticular circumstance of each accident recorded in ST9. For instance, the time of day, month of year, chara

stics of the road, weather conditions, and a range of veharacteristics. Crucially for our analysis, the STATS 19lso records the age of the casualty,1 the grid reference o

he location of the accident, and whether the casualty wedestrian. Of additional use is the classification of the clty by severity: slight, serious, or fatal, which allows unalyse incidences in which the victim was killed or serio

njured (KSIs).2

1 A “child” is defined a person under the age of 16.2 Fatal injuries include those cases where death occurs in less th

ays as a result of the accident, but do not include suicides or death

s

ion of the localities in which the accidents occur. The indf deprivation produced by the Office for the Deputy Prinister gather together a range of information on the sond economic characteristics of the population of Engt the census ward level. The current deprivation datane 8414 wards within England.3 A full description of theeprivation indices and the associated methodology is g

n DETR (2000). The data include scores on six ‘domndices’ that measure individual aspects of deprivation,ring income, employment, housing, health, educationeographical access to services. An overall index of

iple deprivation (IMD) is also produced that weightsombines the domain indices into a single measure of dation.

The ward base of the deprivation data provides a highlailed spatial cross-section of England covering a wide srum of different area types. The grid reference given inata allows us accurately to locate each road pedestriaualty on a map of the UK. Using Geographical Informaystem (GIS) software we have been able to allocateedestrian casualty to one of the English wards. We

hen counted the number of child and adult casualties inf the 8414 wards.

atural causes. Serious injuries are those that require detention in hs an in-patient and casualties that die 30 or more days after the ac

rom injuries sustained in that accident. Examples of serious injuries incractures, internal injury, severe cuts, crushing, burns, concussion, andeneral shock.

3 Separate deprivation indices are produced for Scotland and Waleo issues of incompatibility between these indices we have focused oention on England alone.

D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135 127

Fig. 1. Histogram of child pedestrian casualties in English wards, 1999 and 2000.

In order to model child accidents effectively we have con-structed additional variables for the ward cross-section. Theseinclude data on ward area, employment, child, working ageand retired population; road type and length; the number ofroad network nodes; and local weather conditions.

Thus, we have gathered together a cross-section data setthat divides England into 8414 localities and comprises roadpedestrian casualty data for the 2 years, 1999 and 2000.

3. Pedestrian casualties

The STATS 19 data record 320,283 road accidents forBritain in the year 2000.Table 1shows that of these casu-alties 24,482 were adult pedestrians and 16,184 were childpedestrians. The data we analyse in this paper describe pedes-trian casualties for the wards of England in the years 1999 and2000.Table 2below some summary statistics of these data.

Over 28,200 child casualties were recorded in Englandin 1999 and 2000, an average of 3.35 casualties per ward

Table 1Road accident casualties by road user type and severity, Britain

1999 2000

Road accident casualties 320,310 320,283P 5

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Table 2Child and adult pedestrian casualty rates, England 1999 and 2000

Childcasualties

ChildKSI

Adultcasualties

AdultKSI

Incidents 28,228 5713 42,848 10,964Incidents per ward 3.35 0.67 5.09 1.30Incidents per 1000 2.80 0.57 1.09 0.27

or 2.80 casualties per 1000 children. Of these casualties ap-proximately 20% involved KSIs. There were 42,848 adultcasualties in these 2 years, but the rate is smaller – an aver-age of 1.09 per 1000 adults. Just over one-quarter of the adultcasualties involved a KSI.

Fig. 1 shows a histogram of child pedestrian casualties.This shows how the majority of wards have very few inci-dents. The most frequent case is to have no incidents at all.However, there are a few wards, in the right hand “tail” of thediagram that have large numbers of incidents.

4. Modelling child pedestrian casualties

In this section we outline the basic structure of a model ofchild pedestrian casualties. The implementation of this modelrelies on a variety of different data, as described in Section3, to represent factors that we hypothesise to be important ininfluencing child pedestrian accidents.

The main focus of the present research is on the rela-tionship between child pedestrian accidents and deprivation.Our hypothesis is that the activity of children, and their useof the streets, is associated with deprivation such that, otherfactors being equal, children active in deprived areas have ahigher probability of being a road pedestrian casualty. There

edestrian casualties 41,682 40,66

hild pedestriansKilled 107 107Serious injured 3350 3119All severities 16,876 16,184

dult pedestriansKilled 760 750Serious injured 5461 5362All severities 24,806 24,481

128 D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135

are several aspects to the reasoning behind this hypothesis.First, that children in deprived areas may be less likely tobe driven by car by their parents and therefore more likelyto be a pedestrian. Second, that deprived areas may provideless access to gardens or open space, meaning that residentchildren are more likely to play in the street. Third there maybe factors to do with health, education, housing and localcultural differences that make a difference to casualty rates.

It has to be stressed that our deprivation data describe thesocio-economic conditions of the geographical unit (ward)and not necessarily of the victim of the accident. In effect weare using the deprivation data to test hypotheses both aboutthe area and the travel patterns of children living in those ar-eas. But we do know from previous research that most childaccidents take place very close to home.Sharples et al. (1990)recorded the distance of child accidents to the home in 235cases and found that for child pedestrian casualties 34% ofthese incidents took place within 0.4 kms of residence and80% within 1.6 kms. The average area of a British ward is14 km2. In any case, preventive measures tend to be geo-graphically based and thus from a policy perspective it isas important to understand the factors underpinning spatialvariation in pedestrian casualties as it is those underpinningsocio-economic variation.

An additional dimension to the analysis of child accidentsa chil-d bero om-p ? Thisi epri-v nott rns,t thee drenm hichd

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The volume of traffic flows is not directly observable atthe ward level. Instead we use data on the employment andpopulation in each ward as basic measures of levels of ‘ac-tivity’. Specifically, we construct proxy variables for trafficflows by modelling two traffic generation characteristics ofeach ward:

i. the direct traffic generation potential of wardi – we as-sume that originating and destinating traffic is proportion-ate to the level of employment (Ei) and resident population(Pi) in any ward.

ii. the potential through traffic generation in wardi – in cap-turing this effect we wish to account for the volume oftraffic in each ward that arises from trips to employmentand population in other proximate wards. For trips gener-ated in wardi by proximate employment (PEi) and popu-lation (PPi) we have constructed the following measures:

PPi =i�=j∑

j

Pj

dij

and PEi =i�=j∑

j

Ej

dij

wheredij is the distance from wardi to ward j.4 It isworth noting that the way in which we construct thesevariables in effect introduces a spatially autoregressivestructure into the model. It does so by applying a weightmatrix based on distance from each ward to every other

able

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nd deprivation is added by comparing the results forren to those for adults. Does deprivation effect the numf adult pedestrian casualties in a similar way and to a carable degree as it does the number of child casualties

s an important question. Because if the influence of dation derives solely through environmental factors, andhrough behavioural ones or differences in travel pattehen we would expect any effect on adults to be similar toffect on children. Differences between adults and chilay allow us to speculate about the specific ways in weprivation impacts upon casualty numbers.

Clearly, deprivation is only one of many factors that wnfluence the number of child pedestrian accidents inard. In addition to deprivation, our model hypothesisespatial variation in the absolute number of child pedesccidents is a function of five local factors:

i. the absolute number of children,i. the volume of traffic flows,i. the physical nature of the local environment,. the characteristics of the local road infrastructure,. ‘other’ local specific factors.

While we can think of these conceptually as distinctors there are points of overlap in measurement. We deaach in turn.

The number of children resident in each ward is direbservable from the available data. In fact population figre available along with the deprivation data, as they aruired in order to construct the various deprivation ind

or the wards of England.

ward. We hope that inclusion of these variables areato capture any existing spatial interdependence.

With respect to the nature of the local environment,eek to model effects on child accidents arising from theent of development in the ward and from land use mixensity. Our thinking here relates to two main concerns

First, We know that wards differ in the degree to whhey are covered by built development, and therefore, iroportion of the spatial area on which traffic actually moe do not have any direct measure of the extent of this w

ach ward. Instead we create a proxy variable, whichures the number of traffic network nodes per unit of are5

Second, we hypothesise that the type and density ofse may have an impact on the number of accidents. Ftance, we may expect more child pedestrian causalitnner city areas where there is a high-density mix of resiial and economic land uses, than in low-density subureas that are predominantly residential. We are not abbtain land use density data for the wards. Instead, we

aken measures of employment per node and populatioode as indicative of the relative densities of economicesidential land uses.

To model the characteristics of the road network we henerated data on road capacity across England. Forard, we measure the length of A road, B road, minor r

4 We experimented with different exponents on the distance denomut found linear distance worked best in our models.

5 A node is defined as the meeting point of more than two links.

D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135 129

and motorway.6 Unfortunately, we do not have detailed in-formation on traffic speeds.

Finally, we have included variables to account for some‘other’ local specific factors. These include an average mea-sure of annual rainfall from one of 31 weather stations andalso thex (east–west) andy (north–south) co-ordinates ofthe geographical location of the centre of each ward. Wealso assume that there are a number of unobservable affectson pedestrian accidents that may arise at the regional level.These could include differences in public policy decisions, inpublic investment, climate, social habits, and other unknowneffects. We have attempted to represent these with a set ofdummy variables differentiating the eight standard regionsof England.

5. Estimation issues and results

In this section we present estimates of our model of pedes-trian casualties. We analyse pedestrian casualties as a wholebut have also run separate regressions for KSIs alone. Asmentioned previously, we are also concerned with compar-isons between children and adults and so present results forboth age groups below.

5

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in which λι is the expected number of events per ward, andxi a vector of regressors. Thusβj , the estimated coefficient,is the proportional change in the expected number of eventsper period from a unit change in an independent variable,xj .

We have included quadratic terms in our estimated mod-els for certain variables where it was thought appropriate todo so. In fact, we initially ran the negative binomial regres-sions with fourth-degree polynomial terms, and subsequentlyremoved terms of order higher than two as there was no ob-served improvements in estimation. The reason for includingthe quadratic terms is that we would expect some of the rela-tionships to be non-linear and being uncertain about the exactnature of the relationships, we thought it prudent to increaseflexibility from first to second order approximations.

5.2. Dummy variables

As mentioned in Section4we hypothesised that a range ofunobservable factors that arise at the regional level may affectthe number of pedestrian casualties. However, the inclusionof dummy variables representing the eight standards regionsof England7did not provide statistical evidence that the datashould be differentiated in this way.

After fitting the models we were able to identify thosewards whose accident records seemed to be particularly badlyp mbero se itw s re-fl theo f them y be-c ts buti asest uredb ardsw upedt omeo Ty-n

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.1. Estimation issues

The discrete nature of count data and the preponderaneros and small values means that the use of linear muegression can produce inefficient, inconsistent, and bstimates. The formulations widely used to analyse mo

n which the dependent variable takes only non-negativeger values corresponding to the number of events occun a given interval are based on the Poisson regression mCameron and Trivedi, 1986, 1998). The Poisson model aumes equidispersion, that is, that the conditional meanonditional variance are the same. A related generalisathe Poisson regression is the negative binomial model, woes not require the assumption of equidispersion.

The results presented in this section for child accidedult accidents, child KSIs, and adult KSIs are based oegative binomial rather than Poisson formulation. Thecause the test statistics associated with our modelss to reject the hypothesis of equidispersion assumedoisson model, confirming the appropriateness of the n

ive binomial formulation for our data.For discrete random variable, Y, and observed freque

n ward i yi , i = 1,. . .,n the negative binomial model is:

n λi = β′xi + ε,

6 A roads are part of the trunk or principal road network being rohat are of national importance or that act as regional or local distrib

roads are part of the non-principal road network and are routes ofmportance. Minor roads are feeder roads comprising minor rural roadrban estate roads.

redicted by the model, either because the observed nuf accidents was much higher than predicted, or becauas much lower than predicted. In either case this waected in an extremely low calculated probability thatbserved number of accidents would have occurred iodel were correct. In some cases this might be purel

ause of the random nature of the occurrence of accidenn others this might well be symptomatic that in those chere was some important local factor at work, not capty our models. It was interesting to note that those with unexpectedly high casualties rates tended to be gro

ogether geographically – in London, Birmingham, and sf the cities of the Midlands, Lancashire, Yorkshire andeside.

We experimented with the use of individual dummy vbles to “account” for these extreme outliers.8 For each o

he four models we selected the 20 wards with the lorobability of the observed number of accidents and deummy variables specifically relating to that ward. Of couhen the models were re-run including these dummiesoefficients on the dummies were highly significant. Hver, we found that the other model coefficients wereffected, and the overall goodness of fit statistics werelittle improved. We decided not to continue using th

7 The eight standard regions are East Anglia, East Midlands, North,est, South East, South West, West Midlands, and Yorkshire and Hu

ide.8 A general discussion of procedures for treating outliers can be f

n Judge et al. (1980).

130 D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135

dummies in the interests of clarity and computational parsi-mony, and we have not reported any results involving dummyvariables.

6. Results

Since the basic results from the negative binomial modelsdescribe proportional changes in the expected number of ca-sualties for a unit change in the independent variables, andsince quadratic terms are sometimes included, meaningfulinterpretation of the actual coefficients requires informationabout the mean value of the regressors. For this reason wepresent two types of result below.

First, we give the full estimation results from the neg-ative binomial models including the estimated coefficients(βi ’s), the associated standard errors, and thet-statistics,as well as the likelihood ratios for the models. These areuseful in demonstrating the degree of statistical signifi-cance we have achieved with respect to our independentvariables.

Table 3Estimated negative binomial regressions for child and adult pedestrian casualties

Child pedestrian casualties Adult pedestrian casualties

b

C −I 0PP 80P −E −E 3( −( −( 00( −( 55( −P −PP 9P −A 8A −BB −M −M 7M 0.529 −0.011 0.013 −0.815MRSxy

NLRχ

α

Second, we use these estimated coefficients, and the meanvalues of the regressors, to calculate model coefficients foreach independent variable (∂ ln λ/∂ ln xj) that incorporatequadratic effects, and also the relevant elasticities. The elas-ticities allow us to address the scale issue that impedes inter-pretation of the raw ‘unit-change’ results.

Table 3presents results from the negative binomial regres-sion for child and adult pedestrian casualties.

The negative binomial regression above is based on 8413observations; we had missing data for only one ward. Thealpha statistic associated with our estimation allows us to re-ject the hypothesis of equidispersion and, therefore supportsthe negative binomial formulation.

Treating first the results for child casualties inTable 3we can see immediately that the estimation accords a highdegree of significance to the deprivation score. As depriva-tion increases there is an increase in the expected numberof child accidents and thet-statistic is high, 26.38. As wewould expect the absolute number of children in any ward isalso positively associated with the expected number of casu-alties and the associatedt-statistics is 6.26. Of the remaining

b S.E.

onstant −1.230 0.238MD score 0.017 0.001opulation < 16 0.154 0.025opulation 0.252 0.008opulation2 −0.006 0.000mployment −0.004 0.003mployment2 4.7E−05 1.3E−05

Population/node) −1.320 0.892Population/node)2 −4.934 3.056Employment/node) 5.034 0.527Employment/node)2 −9.396 1.751Node/area) 0.882 0.082Node/area)2 −0.363 0.046roximate employment −12.003 1.578roximate employment2 7.458 1.150roximate population 5.181 0.644roximate population2 −1.192 0.240-road 0.017 0.005-road2 −0.001 0.000-road 0.002 0.005-road2 −2.5E−04 1.6E−04inor road −0.017 0.001inor road2 6.1E−05 7.6E−06otorway 0.007 0.014

0.140 0.006

/S.E. b S.E. b/S.E.

5.158 −0.239 0.230 −1.04026.377 0.010 0.001 15.996.256 −0.301 0.026 −11.44933.097 0.287 0.007 42.733.248 −0.004 0.000 −16.7741.520 0.012 0.003 3.529.724 3.6E−05 1.9E−05 1.8981.480 −12.507 0.868 −14.4051.614 28.371 2.968 9.5599.551 14.358 0.538 26.7

5.368 −30.628 1.554 −19.71510.698 1.383 0.094 14.7

7.844 −0.530 0.061 −8.7127.606 −4.567 1.692 −2.7006.484 1.871 1.248 1.499

8.050 0.700 0.693 1.004.969 1.336 0.252 5.3103.252 0.054 0.005 10.082.654 −0.002 0.000 −6.5060.487 0.010 0.006 1.7631.594 −4.2E−04 3.3E−04 −1.28612.649 −0.017 0.001 −11.349.991 5.6E−05 1.0E−05 5.611

.043 0.003 0.001 2.561

.924 5.7E−04 1.2E−04 4.6773.209 −7.2E−06 1.2E−04 −0.060.844 1.5E−04 1.6E−04 0.9612.778 −7.0E−04 1.0E−04 −6.724

8413−17379−196794600.50

23.167 0.229 0.007 32.966

D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135 131

Table 4Coefficients and elasticities from the negative binomial models for child and adult pedestrian casualties

Child casualties Adult casualties

Coefficient Elasticity Coefficient Elasticity

IMD score 0.017 0.378 0.010 0.226Population < 16 0.154 0.184 −0.301 −0.361Population 0.184 1.084 0.245 1.440Employment 2.2E−04 0.001 0.012 0.027Population/node – – −8.408 −0.607Employment/node 4.567 0.113 12.839 0.318Node/area 0.706 0.171 1.125 0.273Proximate employment −8.929 −1.840 −4.567 −0.941Proximate population 4.000 1.981 1.323 0.655A-road 0.012 0.048 0.041 0.155B-road – – – –Minor road −0.014 −0.347 −0.014 −0.343Motorway – – 0.002 0.001Rainfall 7.1E−04 0.488 5.7E−04 0.394Sunshine −3.8E−04 −0.552 – –x-coordinate 6.2E−04 0.281 – –y-coordinate −3.0E−04 −0.083 −7.0E−04 −0.190

independent variables entered into the child casualty modelthree do not perform well, population density (pop/node),the absolute length of B-road, and the length of motorway inwards.

For adults, the number of casualties is also strongly associ-ated with the IMD score. Thet-statistics, 16.0, is smaller thanthat for children but still high. The only variables that do notperform well in the adult casualty model are the length of B-road, the amount of sunshine, and thex-coordinate. All otherexplanatory variables are significant with 95% confidence.

Mysteriously, there seemed to be a positive relationshipbetween child pedestrian casualties and grid reference, withwards to the east experiencing, on average, higher rates andwards to the north experiencing lower rates. This was afterincluding all the other expansion factors used in the modelso there must be systematic but unexplained factors at work.

Table 4below shows the coefficients for each independentvariable, incorporating quadratic effects, and also the relevantelasticities. A missing value in any cell indicates statisticalinsignificance. Note that the elasticities have been calculatedat the point of means.

The elasticity associated with the IMD score for childrenis 0.378. Thus, a 10% increase in the deprivation score acrossthe wards is associated with a 3.8% increase in the expectednumber of accidents. For adults, the deprivation effect is alsoc 10%i ith a2 ts.

corem lcu-l rianc rivedw es-t theg roba-

bility of pedestrian casualties between the least and the mostdeprived wards.

It would therefore appear that, in addition to the other vari-ables included in our models, area deprivation can explainsome of the variation in child and adult pedestrian casual-ties. To provide a further test of whether deprivation reallyprovides an ‘additional’ explanation in our models we havecalculated likelihood-ratio tests between the restricted mod-els (without the deprivation variable) and unrestricted models(with the deprivation effect). This test is designed to identifywhether the inclusion of the deprivation variable significantlyimproves the log-likelihood function (e.gGreene, 2003). Forthe child model we calculate a log-likelihood ratio of 594and for adults 162. The 1% significance point for theχ2-distribution with 1 degree of freedom is 6.63, and thus inboth cases we can reject the hypothesis that the inclusion ofthe deprivation variable has not improved the log-likelihoodfunction.

Thus, a central conclusion we must take from our resultsis that having included the other factors that we believe to beimportant in influencing numbers of pedestrian casualties, wecan still determine a distinct deprivation effect. Furthermore,this effect is present for both children and adults, but to amuch larger extent for children.

Therefore, we can say that the effect of deprivation on then caused withm ture.T e andb er ofp

n ina edes-t ve ah g the

lear though less marked. The elasticity indicates that ancrease in the ward deprivation score is associated w.2% increase in the expected number of adult acciden

Using the estimated coefficients and the ward IMD saximum (83.77) and minimum (1.16) values, we can ca

ate the ‘gradient’ increase in the probability of a pedestasualty occurring. For child casualties, the most depard is over four times more likely (4.07) to have a ped

rian casualty than the least deprived ward. For adultsradient is less steep, with an increase of 2.28 in the p

umber of pedestrian casualties does not simply arise beeprived wards happen to be those with more traffic, orore dense urban development, or with more infrastruchere does appear to be a real deprivation effect aboveyond these factors that serves to influence that numbedestrian casualties.

As we would expect, the absolute number of childreny ward has an influence on the expected number of p

rian casualties. Wards with more children will tend to haigher number of child pedestrian casualties. Increasin

132 D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135

child population (under 16) of the ward by 1000 will on aver-age be associated with an increase of 15.4% in the number ofpedestrian casualties. Likewise, in the adult results, we findthat for wards in which children form a higher proportion ofthe population there will be less adult accidents.

The next four variables in the table are those that wereincluded to represent the volume of traffic flows in each area.Population and employment were used as proxy variables toreflect the direct traffic generation potential of each ward,while the proximate employment and population variableswere included to represent the ‘through traffic’ generationpotential of each ward.

The scale of population in the wards has a strong effect onthe expected number of child and adult pedestrian accidents.Increasing the total population by 1000 people will on aver-age be associated with an increase of 18.4% in the numberof child pedestrian casualties and 24.5% in the number ofadult pedestrian casualties. Note that since we have alreadyaccounted for the absolute number of children, this popula-tion effect is simply showing that where more people live andare active, both as drivers and as pedestrians, more pedestriancasualties take place.

The employment effect appears less important in explain-ing pedestrian casualties. The scale of employment in thewards has a very small influence on child accident rates, whilef jobsi ber ofa , lessl ts inl

flowo rksi . Ast mbero ase.T . A1 soci-a wardsa casu-a tion.T n is1 thatf gheri ntiala ploy-m ildrent

mentp of thel nt ofb den-s lties.A ases( r) by1 n av-e ults.

The density of population (per node) is not a significantfactor in explaining numbers of child pedestrian casualties,but it is important for adult accidents. An increase in popula-tion density of 10% is associated with a 6.1% decrease in thenumber of adult accidents. The elasticity of pedestrian casu-alties with respect to employment density is 0.318 for adults.For children the employment density effect is smaller, but stillpositive with elasticity of 0.113. Thus, adults are less likely tobe knocked down in dense residential wards but are, perhaps,more likely to be knocked down in wards with higher em-ployment densities, whereas for children population densitymakes no substantial difference, but they are more at risk inwards with higher employment densities. This perhaps sup-ports the hypothesis that predominately residential suburbanareas tend to be safer for children than mixed used inner-cityareas.

The next four variables included in our model representinfrastructure volume in each ward measured by length ofroad type. For child casualties, the length of A-road has apositive and significant effect while the length of minor roadhas a negative effect. However, in both cases the elasticitiesare relative small, 0.012 for A-road and−0.014 for minorroad. The lengths of B-road or motorway are not statisticallysignificant.

For adults the elasticities associated with A-roads and mi-n th ofA reasei whilea iatedw lties.S ands

ulds d fora rdsw

our‘ t thev tivee easeo soci-a cci-d shinem s buti en trianK

ighd SIs,b thet thee cans se int alsow ousi

or adults our estimate indicates that an increase of 1000n a wards would on average increase the expected numdult accidents by 1.2%. Thus children are, on the whole

ikely to be involved in pedestrian road casualty incidenarge employment centres.

Next in the table we have our variables reflecting thef through traffic. The proximate population variable wo

n a different way to the proximate employment variablehe number of jobs proximate to wards increases, the nuf child and adult pedestrian casualties will tend to decrehe elasticity is much larger for children than for adults0% increase in proximate employment is on average asted with a 18% decrease in child casualties across thend a 9% decrease in the number of adult pedestrianlties. The population effect works in the opposite direche elasticity of child casualties to proximate populatio.981 for children and 0.655 for adults. Thus we find

or both adults and children, casualty numbers are hin wards surrounded by large-scale populations (residereas), but lower in those surrounded by large-scale ement centres. Both these effects are more intense for ch

han for adults.The node density, population per node, and employ

er node variables were included to represent the natureocal environment. For both adults and children the exteuilt development within any ward, as measured by nodeity, has a positive effect on the number of expected casuas the density of network nodes across the wards incre

or as the extent of built development becomes greate0% the expected number of pedestrian accidents will orage increase by 1.71% for children and by 2.73% for ad

or roads are much larger. A 10% increase in the leng-road across the wards is associated with a 1.5% inc

n the expected number of adult pedestrian causalities,n increase of 10% in the length of minor roads is associth a−3.4% decrease in the expected number of casuaurprisingly, the length of motorways is also positiveignificant for adults, but the elasticity is small, 0.001.

Therefore, regarding the infrastructure variables it woeem that pedestrian casualties, both for children andults, have a higher probability of taking place in waith greater A-road capacity.Finally inTable 4we have the variables we included in

other local specific factors’ category. As we would expecolume of rainfall (measured in millimetres) has a posiffect on the number of pedestrian casualties. An incrf 10 cm in rainfall per annum across the wards is asted with an increase of 7.1% in the number of child aents, and of 5.7% in the number of adult accidents. Sunakes a difference in reducing child pedestrian casualtie

s not significant for adults.Table 5shows results from thegative binomial regression for child and adult pedesSIs.As for all casualties, the IMD index also shows a h

egree of statistical significance for both child and adult Kut to a larger degree for children. Indeed for children-statistic of 14.7 is the largest associated with any ofxplanatory variables included in the model. Thus, weay that not only is deprivation associated with an increahe probability of a pedestrian casualty taking place, butith an increased probability of incidents involving a seri

njury or a fatality.

D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135 133

Table 5Estimated negative binomial regressions for child and adult KSIs

Child KSIs Adult KSIs

b S.E. b/S.E. b S.E. b/S.E.

Constant −4.203 0.466 −9.017 −2.556 0.358 −7.147IMD score 0.018 0.001 14.699 0.011 0.001 10.880% Population <0.128 <0.047 2.707 <−0.268 <0.036 <−7.527Population 0.211 0.015 14.057 0.225 0.010 21.736Population2 −0.005 0.000 −10.704 −0.002 0.000 −7.363Employment 0.002 0.007 0.308 0.008 0.004 1.926Employment2 2.6E−06 4.8E−05 0.055 1.6E−05 2.7E−05 0.585(Population/node) 4.086 2.061 1.983 −8.728 1.446 −6.036(Population/node)2 −21.383 7.636 −2.800 20.688 5.113 4.046(Employment/node) 3.206 1.250 2.565 11.259 0.794 14.180(Employment/node)2 −5.451 4.462 −1.222 −22.325 2.540 −8.789(Node/area) 0.529 0.181 2.924 1.414 0.136 10.425(Node/area)2 −0.231 0.118 −1.958 −0.532 0.078 −6.799Proximate employment −3.441 2.763 −1.246 0.124 2.311 0.054Proximate employment2 1.732 2.079 0.833 −0.424 1.689 −0.251Proximate population 2.678 1.151 2.327 0.524 0.970 0.540Proximate population2 −0.986 0.466 −2.116 0.234 0.364 0.643A-road 0.026 0.011 2.419 0.083 0.008 10.488A-road2 −1.4E−03 5.3E−04 −2.570 −0.003 0.000 −7.505B-road 0.007 0.010 0.630 0.023 0.008 2.917B-road2 −6.7E−04 5.0E−04 −1.335 −5.7E−04 3.8E−04 −1.509Minor road −0.011 0.003 −4.135 −0.009 0.002 −4.562Minor road2 6.4E−05 1.5E−05 4.234 3.4E−05 1.2E−05 2.858Motorway −0.013 0.028 −0.482 −0.004 0.018 −0.207Motorway2 6.2E−04 3.3E−03 0.189 0.003 0.002 1.774Rainfall 8.1E−04 2.2E−04 3.748 4.9E−04 1.9E−04 2.635Sunshine −1.3E−04 2.1E−04 −0.623 −2.6E−06 1.7E−04 −0.015x-coordinate 1.4E−03 2.9E−04 4.851 9.9E−04 2.5E−04 4.025y-coordinate 4.9E−04 2.1E−04 2.354 −2.8E−04 1.7E−04 −1.686

Number of observations 8413 8413Log likelihood function −7638.4 −10251.0Restricted log likelihood −7686.5 −10507.6χ2 96.2 513.0α 0.181 0.022 8.262 0.218 0.014 15.451

Again, conducting likelihood-ratio tests between the re-stricted models (without the deprivation variable) and un-restricted models (with the deprivation effect) we obtain alikelihood ratio of 212 for the child KSI model and 103for the adult KSI model. Both these values are greaterthan the 1% significance point for theχ2-distribution andwe can thus reject the hypothesis that the inclusion of thedeprivation variable has not improved the log-likelihoodfunctions.

Of the other explanatory variables entered into our modelswe find that employment, proximate employment, the lengthof B-road, the length of motorway, and the amount of sun-shine do not show statistical significance in for child KSIs. Foradults, statistically insignificant variables include proximateemployment, proximate population, the length of motorway,and the amount of sunshine.

The coefficients for each independent variable incorporat-ing quadratic effects (∂ ln λ/∂ ln xj), and the relevant elastic-ities, are shown inTable 6. A missing value in any cell in-dicates statistical insignificance. Again, the elasticities havebeen calculated at the point of means.

The elasticity of child KSIs with respect to the IMD scoreis 0.40, much higher that the elasticity for adults of 0.234.In terms of the probability ‘gradient’ the results indicate thatthe most deprived ward in England is 4.4 times more likelyto have a child KSI and 2.5 times more likely to have an adultKSI than the least deprived ward. Therefore, the IMD effectsestimated for KSIs are not substantially different from thosefor pedestrian casualties.

In fact, most of the results for KSI from our model are verysimilar to those for pedestrian casualties as a whole. The maindifferences are:

i. proximate employment does not explain variation in childKSIs or adult KSIs

ii. proximate population is insignificant for adult KSIs butis positive and significant for adult casualties

iii. the length of B-road is significant for adult KSIs, with anelasticity of 0.053.

iv. the grid references are statistically significant for bothchild and adult KSIs. Moving north or east increases theprobability of a KSI taking place.

134 D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135

Table 6Coefficients and elasticities from the negative binomial models for child and adult pedestrian KSIs

Child KSIs Adult KSIs

Coefficient Elasticity Coefficient Elasticity

IMD score 0.018 0.401 0.011 0.234Population 0.128 0.154 −0.268 −0.321Population 0.156 0.919 0.197 1.160Employment – – 0.008 0.019Population 0.997 0.072 −5.739 −0.415Employment 3.206 0.080 10.151 0.252Node/area 0.417 0.101 1.155 0.281Proximate employment – – – –Proximate population 1.701 0.842 – –A-road 0.016 0.060 0.063 0.239B-road – – 0.023 0.053Minor road −0.008 −0.205 −0.008 −0.193Motorway – – – –Rainfall 8.1E−04 0.563 4.9E−04 0.339Sunshine – – – –x-coordinate 1.4E−03 0.647 9.9E−04 0.447y-coordinate 4.9E−04 0.134 −2.8E−04 −0.076

Thus, in conclusion to this section our models have shownthat deprivation is associated with child and adult pedestriancasualties and KSI, even after accounting for all the otherexpansion factors used in the model. The deprivation effecton children tends to be higher than on adults for casualtiesas a whole and for KSIs. Furthermore, the statistical signif-icance associated with the deprivation index is very high inthe models we have estimated.

7. Conclusions

In this paper we have explored the influence of area de-privation upon the incidence of child pedestrian casualties.Our results show a statistically significant positive and strongassociation between measures of area deprivation and the in-cidence of child casualties. Using the index of multiple de-privation score we estimate that the effect of deprivation onchildren is twice that on adults for both pedestrian casualtiesand KSIs.

Therefore, our results support the broad conclusions ofprevious research in this field. Our contribution lies in disen-tangling the effects of area type from deprivation. By doingso we are able to confirm that the reasons why children fromlower socio-economic groupings have a higher probability ofb atione ocale

ws.W orel areh andd rgee mati-c to

have higher casualty rates for adults and children, but adultsare less likely to be knocked down in dense residential areasand more likely to be knocked down in areas of dense em-ployment. As the amount of A-road increase so on averagethe number of casualties increases and the volume of rainfallis also important.

Much of the interest in child accidents has been with theexposure rates of children to traffic and with analysing the be-haviour and travel patterns of children. Research along theselines has proven extremely fruitful. But because it requiresextremely detailed data it is typically based on the analy-sis of relatively small and restricted samples with which it isextremely difficult to account for the influence of other ‘envi-ronmental’ factors. Our modelling approach differs. It is notpossible to address the issue of exposure within our frame-work, but the vast geographical area covered by our dataallows us to make use of a high degree of spatial variation indisentangling some important influences on the incidence ofchild casualties. We believe that the results of these respec-tive types of approach are complimentary; they shed light ondifferent dimensions of the problem. However, it is fair to saythat the policy implications of work on exposure have beenmore extensively discussed (White et al., 2000). It remainsfor us here to demonstrate the practical relevance of our ownmethods and findings.

locall en andt velt ar tob ofs witht havej arel tely

eing a pedestrian casualty or KSI, is due to some deprivffect, which is over and above influences arising from lnvironmental characteristics.

Other interesting results from our model are as folloe have confirmed that both adults and children are m

ikely to be knocked down where residential populationsigh and where more people are active as pedestrianrivers. Adults are more likely to be knocked down in lamployment centres but this land use effect is not systeally important for children. More built up areas will tend

The actual incidence of child casualties and KSIs at aevel is fairly small. FromTable 2we know that the averagumber of child casualties in a ward each year is 1.6

he average number of child KSIs is 0.33. At a local lehe pattern of child casualties can therefore often appee fairly random. From a policy point of view this issuecarcity is important. The authorities that are chargedhe task of reducing child pedestrian casualties typicallyurisdiction over relatively small areas. In Britain, theseocal authorities, which divide the country into approxima

D. Graham et al. / Accident Analysis and Prevention 37 (2005) 125–135 135

500 areas. At this small spatial scale it is extremely difficult toobserve the influence of local characteristics on the pedestriancasualty rate.

In reaching resource allocation decisions to reduce childpedestrian casualties transport authorities could make use ofthe type of aggregate model we have developed in this pa-per. This is because it can be used to give an indication ofwhere child accidents may take place given a range of lo-cal characteristics. In other words it gives pointers about thelocational factors that increase the probability of incidents,even if these factors have not been observed by authoritiesdue to the scarcity of casualties. Our data show that, at a lo-cal level, allocating resources to where accidents happenedin one year may not actually lead to an improvement on theincident rate the following year. Our model gives authoritiesthe chance to identify and look into the locations where highlevels of incidents are predicted for the future.

Certainly our methods and result cannot replace a detailedlocal knowledge of the transport network and of accident‘hotspots’, but they could be used in a complementary fash-ion to indicate important influences on the child pedestriancasualty rate. Socio-economic deprivation provides a partic-ularly good example of this. Our area based approach hasshown that deprivation does count and not simply due to somecharacteristics of deprived environments. For local areas it isu duet ata,l nglee

t au-t asuret thisi trat-e thatw nceo e fo-c f thep cti-c giesc ribu-

tive policy measures. Second, it suggests that authorities maywish to examine whether road safety measures are currentlyunevenly distributed with respect to their socio-economic en-vironments.

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