ARTICLE IN PRESS

Health & Place 16 (2010) 140–146

Contents lists available at ScienceDirect

Health & Place

1353-82

doi:10.1

n Corr

for Chil

Subiaco

E-m

journal homepage: www.elsevier.com/locate/healthplace

Vector fields of risk: A new approach to the geographical representation ofchildhood asthma

Gavin Pereira a,b,c,n, A.J.B.M. De Vos a,b, Angus Cook a,b, C. D’Arcy J. Holman a,b

a School of Population Health M431, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australiab Cooperative Research Centre for Asthma, Sydney, Australiac Telethon Institute for Child Health Research, Centre for Child Health Research, University of Western Australia, 100 Roberts Road, Subiaco, WA 6008, Australia

a r t i c l e i n f o

Article history:

Received 14 April 2009

Received in revised form

9 September 2009

Accepted 9 September 2009

Keywords:

Asthma

Vector field

Child

Mapping

92/$ - see front matter & 2009 Elsevier Ltd. A

016/j.healthplace.2009.09.006

esponding author at: Telethon Institute for C

d Health Research, University of Western A

, WA 6008, Australia. Tel.: +61 8 9489 7725.

ail address: pereirag@gmail.com (G. Pereira).

a b s t r a c t

One of the major challenges in health studies with a spatial dimension is to produce valid and

meaningful geographical representations of risk. This issue has arisen in our research on childhood

asthma and proximity to traffic in Perth, Western Australia. To illustrate the spatial variation in risk over

the study area, we developed a method for constructing a ‘‘risk field’’ map and applied this method to

our study population. Cases and controls aged 0–19 years were defined using emergency department

presentations from 2002 to 2006. For each asthma case, two matched controls were obtained. Geocoded

residential addresses were used to calculate ‘‘vectors’’ or arrows of risk across the study area. This allows

a rapid interpretation, with the risk of asthma greatest in the direction of the head of the vector relative

to the vector’s tail. This approach clearly indicated that the risk of asthma presentation at hospital

emergency departments is higher for children living closer to the major urban city centers. Application

of our method to the study population suggests that the ‘‘vector’’ approach may be useful as an

exploratory tool for the spatial investigation of risk of other health outcomes.

& 2009 Elsevier Ltd. All rights reserved.

1. Background

One of the major challenges in epidemiological studies with aspatial dimension is to produce a valid and meaningful geogra-phical representation of risk. The issue of mapping risks has arisenin our current research on childhood asthma and proximity totraffic in Perth, Western Australia. Despite earlier conflictingopinions (Heinrich et al., 2004), recent reviews have highlightedassociations between asthma and traffic exposure and possiblecausal mechanisms (Brugge et al., 2007; Holguin, 2008; Salam etal., 2008). This health issue is of increasing concern in parts ofPerth following recent rapid population growth of the city.

For our study, we sought to explore the risk of asthmaEmergency Department (ED) presentation of children and youngadults living in the south-west metropolitan area of Perth.Typically, a spatial analysis would begin with an exploratoryinvestigation of asthma risk, then proceed to formal statisticaltests. To visualize how asthma varies with residential location, weinstead developed a new method for constructing a ‘‘risk field’’map. The risk field is best conceptualized as a field of vectors that

ll rights reserved.

hild Health Research, Centre

ustralia, 100 Roberts Road,

‘‘point’’ in the direction of maximal risk, analogous to other vectorfields in the physical sciences (e.g. electro-magnetic fields). Theuse of vector fields in geographic information analysis has alreadybeen identified, and vector fields such as velocity fields, electro-magnetic fields and gravitational fields are commonly used tomodel phenomena having a location, magnitude and direction(O’Sullivan and Unwin, 2003). For instance, velocity fields can beconstructed by modeling of the speed and direction of fluid flowsuch as wind flow in a street canyon (DePaul and Sheih, 1986).

Our risk field was constructed by modeling the odds ratiousing the latitude and longitude coordinates corresponding to theresidential addresses. Each of the vectors in the risk field isanchored at a reference subject’s residential address, and the headof the vector (‘‘the tip of arrow’’) points in the direction of elevatedrisk. In other words, there is a greater risk of the adverse healthoutcome for subjects that reside at locations in this direction basedon the locations of neighboring subjects. An illustration of riskvectors for a simplified hypothetical situation is shown in Fig. 1.This figure uses relative risk but the odds ratio could equally beapplied as a descriptor of risk. There are two aspects to any vector:a direction and a length. From the illustration it is evident that thevectors point in the direction of greatest risk and that the length ofthe vectors are proportional to the increase in risk in thisdirection.

More traditional scalar fields such as density surfaces, contourmaps, and choropleth maps of risk do not explicitly display the

ARTICLE IN PRESS

Fig. 1. Each of the vectors (arrows) plotted on the study area have a DIRECTION and a LENGTH. DIRECTION: the vectors point to the location in the study area at which RR is

highest. LENGTH: the length of the vectors are proportional to the increase in RR in that DIRECTION.

Table 1Prevailing wind direction and wind speed in Perth.

Annual Summer Autumn Winter Spring

Prevailing wind directiona

9 AM East East North-east North-east East

3 PM South-west South-west South-west South-west South-west

Wind speeda

9 AM 14.1 17.3 13.3 11 14.8

3 PM 18.6 21.5 16.4 16.1 20.4

Source: Bureau of Meteorology. Climate Statistics for Australian Locations.

Commonwealth of Australia, 2008.

a Measured at Perth Airport.

G. Pereira et al. / Health & Place 16 (2010) 140–146 141

magnitude of risk in a particular direction from a particularreference location, such as residential address. These forms ofvisualization are also less useful than a vector field of risk formaking comparisons with other predominantly two-dimensionalfields of exposure, such as prevailing wind and vehicle traffic flowin the context of asthma risk. Alternative approaches have beendeveloped that are based on the ratio of case and control kernelintensities (Bithell, 1990; Kelsall and Diggle, 1995). However, suchmethods are not always suitable for spatial epidemiologicalstudies in which cases are matched to controls. Moreover, aninherent assumption of many methods is that the ‘population atrisk’ of the disease has a continuous spatial distribution (Lawsonand Kleinman, 2005). This assumption is typically violated if thestudy area contains sections of no resident population, such aswithin industrial areas. A less obvious violation occurs whensections of the study area contain a resident population, none ofwhom are at risk of the disease.

This paper describes the development of ‘‘risk field’’ maps andprovides an application of this method to asthma ED presenta-tions. Many weaknesses of cluster identification studies and thoseincorporating statistical tests have been identified (Rothman,1990). For this reason, the risk field map was developed as anexploratory spatial tool to visually assess hypotheses formed apriori and provide a visual summary of the observed locations ofadverse health events. The method could also be applied moregenerally to other spatial analyses to enable visualization of howrisk varies geographically by subject location.

2. Method

2.1. Study design

This study is a record-based n:m matched case–control studyusing geocoded ED presentation data on children and youngadults living in the study area.

2.2. Study area

The study area included 613 census Collection Districts (CDs),encompassing eight Statistical Local Areas, within the south-western region of the Perth metropolitan area. CDs are thesmallest available geographical areas for which demographicstatistics are disseminated by the Australian Bureau of Statistics,

and on average included 225 dwellings. This particular study areawas chosen because, being traversed by major metropolitanvehicle corridors and less-trafficked local roads, it provided asufficient degree of exposure contrast. It was also representativeof the wider metropolitan area. The total population in the areawas 269,734 (2006 Census of Population and Housing).

2.3. Summary of climatic conditions

Perth is located on a narrow coastal plain between the IndianOcean to the west and the 300 m high Darling Scarp to the east.Perth has a Mediterranean climate with hot, dry summers, andmild wet winters (Sturman and Tapper, 2006). During thesummer, Perth is influenced mainly by morning easterly windsblowing across the inland desert, shifting to strong south-westerlysea breezes dominating during the afternoon (Hurley and Manins,1995) (Table 1).

2.4. Study population

The cases were all individuals aged 0–19 years with residentialaddresses in the study area, who presented at the ED of any Perthmetropolitan hospital in 2002–2006, with a principal diagnosis ofasthma (J45) or status asthmaticus (J46). Each case was matchedto a gastroenteritis (A00–A09) control and an upper limb injury(S40–S69) control. Gastroenteritis and upper limb injuries werechosen as control conditions because they had no known orsuspected association with proximity to air pollution from motorvehicle traffic. Previous case–control studies have also used

ARTICLE IN PRESS

G. Pereira et al. / Health & Place 16 (2010) 140–146142

gastroenteritis as a control condition in the investigation of airpollution and associated hospitalization and ED presentation forasthma (Lin et al., 2002; Lipsett et al., 1997; Oyana et al., 2004).The control diseases were selected as they represent the spatialdistribution of the population at risk aged 0–19 years. Cases andcontrols were matched so that each case–control triad were fromthe same 5 year age group (i.e. 0–4, 5–9, 10–14, 15–19), gender andseason of presentation. Controls were obtained for the sameperiod as cases.

2.5. Retrieval of subject information

De-identified data for the period 2002–2006 were obtainedfrom the Emergency Department Information System (EDIS). Thesystem draws real time, continuously updated information on EDpresentations, including the coded primary diagnosis, from allhospitals across Perth. Only first presentations of cases andcontrols during the 2002–2006 period were included in theanalysis.

2.6. Adjustment

We adjusted for the effect of socio-economic status (SES).However, due to lack of individual level data, SES was ascertainedfrom the Socio-economic Index for Areas (SEIFA) Index of RelativeSocio-Economic Disadvantage. Adjustment for SEIFA was imple-mented by incorporating the SEIFA index corresponding to the CDof the subject’s residential address. The CD was the smallestaggregate unit for which the SEIFA index was available. The SEIFAindex is a validated and standardized metric that provided acomparative area-level measure on education, income, occupa-tion, living conditions and access to services (Australian Bureau ofStatistics, 2006). Two outlier cases and their matched controlswere removed from analyses as they exhibited values of socio-economic status (SES) far below that of the other subjects andwere considered to have arisen from a coding error.

2.7. Overview of the risk field approach

Our ‘‘risk field’’ method relies on the availability of geocodedresidential addresses of study participants. The projected latitudesand longitudes were used in their own right as predictor variablesto model risk of ED presentation for asthma. The resultant north-south and east-west effects were combined to create a singlearrow, or ‘‘vector’’, which points in the direction at which risk ismaximal. This procedure was repeated on groups of subjects toproduce a set of vectors anchored at subject residential locationsthat point in the direction of greatest risk, and consequentlyrepresents the variability in risk with residential location.

2.8. Construction of the risk field

Latitude and longitude coordinates of the residential addressesfor cases and controls were projected using a transverse Mercatorprojection into the Geocentric Datum of Australia 1994 Map Gridof Australia Zone 50 using ArcGIS 9.2 (ESRI 2008). The easting (x)and northing (y) geographic Cartesian coordinates were thenextracted for all cases and controls.

For each case, referred to hereon as reference cases, the 50 (k)nearest neighboring cases were selected along with all controlsmatched to these cases, including the controls matched to thereference case. The number of nearest-neighboring cases, k, waschosen in order to achieve the desired level of ‘‘smoothness’’, andwas also chosen to ensure that there were sufficient data toestimate the parameters in the statistical model. In the context of

the resultant vector field, smoothness relates to the consistency inthe magnitude (length) and direction of the risk vectors across thegeographic area. Larger values of k will induce greater smoothnessin the risk field. There were 603 (n1) reference cases and 1206 (n2)matched controls, yielding a total study group of 1809 (ntotal)subjects.

A n:m matched case–control analysis was performed for eachreference case using the reference case itself, the reference case’smatched controls, their 50 nearest-neighboring cases and theirmatched controls. The matched case–control analysis wasperformed using conditional logistic regression, adjusting forsocio-economic status (SES) and incorporating the projected (x,y)coordinates as predictors. The equivalence of this approach tousing the change in spatial coordinates from the reference caselocation is demonstrated in the Supplementary material. Condi-tional logistic regression was applied using SAS v9.1 (SAS InstituteInc., 2003).

The statistical modeling resulted in a set of 603 parametercoefficient pairs (ai,bi) where ai and bi are the respectiveparameter coefficient estimates of the eastings (x) and northings(y) components of the model for reference case i. For fixed SEIFA,the natural logarithm of the odds ratio (OR) took the form:loge(ORi)=aix+biy. Intuitively, the parameter coefficient pairs(ai,bi) inherently indicate the direction of maximal risk. A detailedillustration of the optimization of each risk vector’s direction issupplied in the Supplementary material.

A vector for each reference case was constructed with themagnitude and direction as described, with the vector’s tailpositioned at the residential location of the reference case (xi,yi).As the log-risk component (ai,bi) and location component (xi,yi)operated in different units, these initial vectors were all equallyscaled to ensure visibility on the geographic map of the studyarea. The mandatory scaling process had the follow-on effect thatvectors could be taken to represent the change in risk for any fixedunit of distance, rather than the 1 m increment initially con-sidered. Untransformed risks could also be used, but exponentia-tion would result in different risk fields for each increment size.The log-risk vectors indicated the direction of maximal risk of EDasthma presentation, and the length of any two vectors repre-sented the increase in log-risk relative to each other. The resultfrom the above procedure is a geographical map displaying a riskfield at reference case residential locations.

A sensitivity analysis was conducted by applying the methodon all cases using k=30 nearest neighboring cases. Subanalyseswere conducted to observe the effects by season, although forthese estimates, only k=30 nearest-neighboring cases were usedgiven the reduction in sample size after stratification by season.

2.9. Ethical approval

Ethical approval was obtained from The University of WesternAustralia Human Research Ethics Committee (RA/4/1/1511) andthe Department of Health Western Australia Human ResearchEthics Committee, formerly called the Confidentiality of HealthInformation Committee (#200622).

3. Results

3.1. Demographics

The study population consisted of 603 asthma cases and 1206age and gender-matched controls. Table 2 shows a demographiccomparison between asthma cases and controls. More subjectswere male (n=1023, 57%). The largest number of subjects was in

ARTICLE IN PRESS

Table 3

G. Pereira et al. / Health & Place 16 (2010) 140–146 143

the 0–4 years age group (n=672, 37%), followed by the 5–9 yearsage group (n=528, 29%).

3.2. Subject locations

The study area along with jittered case and control locations isshown in Fig. 2, although this process rendered some of the tags atimprobable locations the figure illustrates that the controls,representing the distribution of the underlying population atrisk, were located further south and slightly further west than thecases, which were more evenly distributed across the study area.

3.3. Risk estimates based on single-predictor models

In addition to matching by age, gender and season of event ofthe corresponding matched case, SEIFA, eastings (x) and northings(y) were included in future models. Ethnicity was dropped fromfuture analyses as models did not suggest the significance of thisvariable once SEIFA was included. The SEIFA index was collapsedinto categories 1–6 (Table 3), with the reference category 1representing the most disadvantaged, and category 6 representingthe least disadvantaged CDs. A higher risk of asthma EDpresentation was observed moving in an easterly direction,northerly direction, and in the less disadvantaged comparedwith the most disadvantaged subjects. A 1 km eastward

Table 2Demographic comparison between asthma cases and controls, Perth, Western

Australia.

Stratum Age group (years) Gender Cases Controls Total

1 0–4 Male 126 252 378

2 0–4 Female 98 196 294

3 5–9 Male 107 214 321

4 5–9 Female 69 138 207

5 10–14 Male 68 136 204

6 10–14 Female 44 88 132

7 15–19 Male 40 80 120

8 15–19 Female 51 102 153

Total 603 1206 1809

IndianOcean

FremantlePort

1

Fig. 2. Study area in the south-west metropolitan area of Perth, Western Australia. [Ca

[Google Maps web site]. Available at hhttp://www.maps.google.com.aui Accessed 16 Fe

www.spatialepidemiology.neti Accessed 16 February 2009]. (For interpretation of the r

this article.)

movement of the residential address resulted in a 6.8% increasein risk (OR 1.068, 95% CI 1.051–1.084). In the northerly direction, a1 km movement resulted in a 17.1% increase in risk (OR 1.171, 95%CI 1.148–1.195). All but the second SEIFA category exhibited aconvincing association with the risk of asthma ED presentationrelative to the first category representing the most disadvantagedsubjects. Risk of asthma ED presentation in SEIFA category 4 wasup to 3 times greater than that in the most disadvantaged subjects(OR 3.000, 95% CI 1.791–5.023).

3.4. Risk fields

The multivariate analysis performed on all subjects demon-strated a statistically significant increase in risk in the northerlydirection only (OR 1.157/km, 95% CI 1.130–1.186). The OR for a 1 kmincrease in the easterly direction was close to unity (OR 1.008, 95%CI 0.990–1.027). The least disadvantaged (SEIFA category 6) had a55% increase in risk of asthma ED presentation, but this effect wasalso statistically non-significant (OR 1.550, 95% CI 0.904–2.650).

There were 603 risk vectors, comprising 110 for summer eventcases, 172 for autumn event cases, 192 for winter event cases, and129 for spring event cases. Due to the infeasibility of presentingORs for such a large number of models, the information was best

Perth CBD

5km

11km

se (red) and control (yellow) locations have been jittered. Software Source: Google

bruary 2009, Aanensen D [Spatialepidemiology.Net web site]. Available at hhttp://

eferences to color in this figure legend, the reader is referred to the web version of

Risk estimates for ED presentation for asthma based on SEIFA categories.

p-Value ORn 95% CI

SEIFA category (index)

1 (536–885) (referent) (referent) (referent)

2 (886–950) 0.1216 1.527 0.894–2.608

3 (951–1011) 0.0003 2.614 1.546–4.420

4 (1012–1064) o0.0001 3.000 1.791–5.023

5 (1065–1102) 0.0002 2.690 1.605–4.507

6 (1103–1161) 0.0006 2.529 1.487–4.301

x

1 km east o0.0001 1.068 1.051–1.084

y

1 km north o0.0001 1.171 1.148–1.195

ARTICLE IN PRESS

380000 385000 390000 395000 400000 405000

6450000

6455000

6460000

6465000

West−East (m)

Sou

th−N

orth

(m)

Fig. 3. Risk field for ED presentation for asthma using 50 neighboring cases.

[Adjusted for SEIFA].

380000 385000 390000 395000 400000 405000

6450000

6455000

6460000

6465000

West−East (m)

Sou

th−N

orth

(m)

Fig. 4. Risk field for ED presentations for asthma using 30 neighboring cases.

[Adjusted for SEIFA].

G. Pereira et al. / Health & Place 16 (2010) 140–146144

represented in the geographical form of the risk fields themselves.The risk field for all seasons using 50 nearest-neighboring cases isdisplayed in Fig. 3. The direction of maximal risk moves clockwisefrom vectors pointing north-west on the westerly extreme of thestudy area, through north in the middle of the study area,culminating in vectors pointing north-east on the north-eastextreme of the study area and south-east on the south-eastextreme of the study area. The magnitudes of the vectors alsoincreased in these directions

A sensitivity analyses was performed using a smoothingparameter of 30 neighboring cases (k=30) to produce a lesssmooth risk field (Fig. 4). The general patterns in direction andmagnitude of the risk fields for k=30 and 50 were comparable.

Analyses were also stratified by season of the matched caseevent (Fig. 5). The figures contrasted the autumn and winter riskfields, which resemble that of the annual risk field, to the springand summer risk fields. In the spring and summer risk fields, thevariability in risk magnitude and direction are attenuated.

4. Discussion

Our method enabled us to explore how risk of asthma EDpresentation varied by residential location. Although the computa-tional process appears complex, these vectors have a simpleinterpretation: based on the locations of neighboring cases andcontrols, the risk of an asthma event is greatest in the direction

specified by that vector. Fig. 2 showed that the case locations weremore evenly distributed across the study area than the controls,which clustered in the southerly and perhaps westerly end of thestudy area. The risk fields provided further insight into the case andcontrol locations after accounting for age, gender, season of EDpresentation, and level of socio-economic disadvantage. The methodrevealed that risks were higher for children living closer to theroadways that converged on major urban centers, and was thereforesuccessful as an exploratory tool for the spatial investigation of risk.Risk fields could have a role in contributing to the interpretation ofspatially relevant exposures, such as traffic hotspots.

The risk vectors diverge from the centre of the study areatoward the major urban centers of Perth and Fremantle, with anincrease in vector magnitude with proximity to these twolocations. This field is similar to that expected from a traffic flowmodel. The risk vectors appeared to be directed toward themetropolitan hubs of the major urban centers (particularly Perth’sCBD and the port of Fremantle), while at the same time beingaligned with the limited number of major motorways that provideaccess to these centers. Motor vehicle traffic in the morning ispredominantly directed toward these two urban centers andtherefore traffic accumulates as these urban centers are ap-proached. The vectors in the centre of the study area alignconsistently with the Kwinana Freeway, which is the only freewayin the study area (Fig. 6). Just as motor vehicles are constrained tothe major vehicle corridors that serve the urban centers, so too arethe directions of the risk vectors, which do not directly point tothe urban centers, but are also ‘‘pulled’’ toward the access routes.Accordingly, other major arterial roads such as Canning Highwayand Leach Highway, which run across the study area, may inducethe observed fanning effect in the risk field. In a larger sample,varying the smoothness parameter k, might also assist inidentifying possible vehicle corridor funnels, which would existat major intersections and more easily identifiable further fromthe urban centers.

With respect to the air pollutants arising from these trafficroutes, the converging streams of traffic towards the major urbanareas tend to slow down significantly and congest, contributing toelevated emissions. This may explain the increase in magnitude ofthe vectors with proximity to the urban centers, as exposure to theemissions from motor vehicles would also increase in this spatialdirection. In contrast, the peak traffic period at the end of theweekday would not prove as influential since traffic disperses tomultiple residential location ‘‘sinks’’ across the city. Moreover, themorning peak traffic flow is potentially confined to a shorterperiod of time with the ‘‘rush’’ at the start of the business day.

The seasonal analyses revealed slight dissimilarity between thespring–summer risk fields and the autumn, winter and annual riskfields. This dissimilarity may have been imposed artificially by thelower number of cases in spring and summer (n=239 cases)compared to autumn and winter (n=364 cases), but may alsorelate to the influence of meteorological factors. Given theabsence of major topographic troughs, natural barriers andanthropogenic barriers in the study area, the stronger winds inspring and summer (Table 1) would have shifted the vehicleemissions, largely along an east–west axis. This dynamic mayhave resulted in softening the degree to which the orientation ofthe risk vector would otherwise be directed in favor of the globalmean direction, which in this case was northward.

ARTICLE IN PRESS

Spring Summer

Autumn Winter

Fig. 5. Seasonal risk fields for ED presentation for asthma using 30 neighboring cases. [Adjusted for SEIFA].

385000 390000 395000 400000

6450000

6455000

6460000

6465000

West−East (m)

Sou

th−N

orth

(m)

Kwinana Fwy

Canning Hwy

Leach Hwy

South St

Stock RdRoe Hwy

Albany Hwy

Fig. 6. A random sample of 100 risk vectors with main roads annotated. [used 50

nearest neighboring cases, adjusted for SEIFA].

G. Pereira et al. / Health & Place 16 (2010) 140–146 145

Socio-economic status may provide another explanation forthe patterns observed in the risk fields. The control conditions,gastroenteritis and upper limb injury, are more likely exhibited bysubjects of a lower SES. Therefore, the risk vectors may representgradients in SES. It is also possible that the effect of SES on the riskof asthma ED presentation is either not fully characterized by themeasure of disadvantage used in this study at the ecological level,or that the effect of SES can be observed beyond mere adjustmentfor SEIFA in the multivariate model and therefore was not suitableto overcome the effects of SES. Lack of disadvantage (that is,greater affluence) was strongly positively associated with asthmaED presentation with a moderate to strong effect size of up to athree-fold increase (Table 3). However, a prominent exception was

the eastern extreme of the study area, where the risk field wasconsistently directed toward the more disadvantaged areas.Consequently, risk of asthma ED presentation is more likelyexplained by both a socio-economic deprivation effect as well asan urban centre – traffic effect. Other exposures, such as airpollution from industrial sources and wind dispersal of bioaller-gens (such as pollens) have a geographic distribution that differsfrom the risk field, and thus are less likely explanations for theobserved pattern of asthma ED presentation. The method wastherefore successful as an exploratory tool for the spatialinvestigation of asthma risk.

Despite the potential usefulness of the risk field method as anexploratory tool in the identification of patterns of risk across thestudy area, a number of important methodological considerationsshould be noted. Exposure misclassification may have beeninduced due to lack of information on the daily mobility of thestudy population. However, differential exposure misclassificationacross the case and control groups in relation to mobility wouldbe required in order to have a notable effect on the study results.Nonetheless, it is important that the results of the application ofour method to the risk of asthma ED presentation are interpretedin the context of residential location.

Different numbers of neighboring cases (k) may be required togenerate the risk vectors depending upon the number of factorsincluded in a particular model. In brief, as we include moreadjustment variables as factors and covariates in the model, thelarger the number of ‘‘neighbors’’ required to estimate the riskvector. This requirement for more neighbors (that is, a highervalue for k) necessarily increases consistency among the vectorsand thus also increases the degree of ‘‘smoothness’’ in the finalspatial pattern.

Another consideration relates to the locations of the riskvectors. In this paper, the ‘‘tail’’ of each risk vector was anchored atthe residential location of its reference case. Hence, the coverageof the risk vectors across the area was related to the spatialdistribution of the case locations. Placing these estimated riskvectors at the reference point is perhaps consistent with other

ARTICLE IN PRESS

G. Pereira et al. / Health & Place 16 (2010) 140–146146

techniques, but one could decide to place the risk vectors at thecentroid of all cases or even all subjects for risk fields constructedin this way. These alternative options were not implemented inthis study, as doing so would shrink the vector space albeitinducing an edge-effect. We therefore considered that each riskvector to be an attribute of its reference case and should bepositioned accordingly. However, we acknowledge the fact thatthe vectors may be justifiably placed at other positions based onthe locations of the contributing subjects depending uponthe context of the application and intended interpretation of therisk field.

A common alternative approach to that described would be toperform the estimation based on a geographic area, such as aregular grid. We decided against this option for a number ofsignificant methodological and theoretical reasons, described inthe Supplementary material. Briefly, the spatial changes in risk areattributes of the subject population based on their geographiclocations, rather than attributes of the locations themselves.Furthermore, the control population represents the backgroundpopulation at risk. The locations of the subjects are thereforerepresentative of ‘‘allowable’’ locations of events and this propertyis violated when estimation is performed based on a geographicwindow.

Finally, the issue of edge-effects should be kept in mind wheninterpreting the risk field close to the boundary of the study area.This issue relates to the unavailability of subjects outside thestudy area. Consequently, the magnitude and direction of riskvectors close to the study boundary were overly influenced bysubjects residing farther within the study area. This edge-effectmay be minimized using a number of valid adjustments to themethod. For instance, one could only display risk vectors at least acertain distance from the boundary. However, this shrinks thevector field (or effective study area) and the size of the vector fieldis greatly influenced by the method of estimation of this cut-offdistance. Another option would be to anchor the vectors at thecentroid of subject locations, as discussed previously. Under ourapproach, the risk vectors close to the study boundary have thesame interpretation: based on the neighboring subjects, there is agreater risk of the adverse health outcome for subjects that resideat locations in this direction. However, a consequence of ourapproach is that a risk vector very close to the boundary maypoint in a direction in which it is not possible to encounter a case(such as toward the coast in our application). Given theinevitability of an edge-effect in this situation, we believe thatour approach is justifiable as the vectors close to the boundarywill be consistent with their neighboring vectors.

5. Conclusion

Our method allows the visualization of the direction of greatestrisk for a geographically defined population. In this study it wasused to explore how changes in asthma risk varied by residentiallocation. The method revealed that risks were higher for children

living closer to the major urban centers and risk vectors werealigned with peak hour morning traffic flow. This applicationsuggests that the ‘‘vector’’ approach may be useful as anexploratory tool for the spatial investigation of risk of otherhealth outcomes.

Acknowledgements

The authors would like to acknowledge CRC Asthma andAirways for financial support of the work described herein.

Appendix A. Supporting material

Supplementary data associated with this article can be foundin the online version at doi:10.1016/j.healthplace.2009.09.006.

References

Australian Bureau of Statistics. 2006. 2039.0 Information Paper: An Introduction toSocio-Economic Indexes for Areas 2039.0.

Bithell, J.F., 1990. An application of density estimation to geographical epidemiol-ogy. Statistics in Medicine 9 (6).

Brugge, D., Durant, J.L., Rioux, C., Brugge, D., Durant, J.L., Rioux, C., 2007. Near-highway pollutants in motor vehicle exhaust: a review of epidemiologicevidence of cardiac and pulmonary health risks. Environmental Health: AGlobal Access Science Source 6, 23.

DePaul, F.T., Sheih, C.M., 1986. Measurements of wind velocities in a street canyon.Atmospheric Environment (1967) 20 (3), 455–459.

ESRI, 2008. In: ArcGIS 9.2. Environmental Systems Research Institute, Redlands, CA.Heinrich, J., Wichmann, H.E., Heinrich, J., Wichmann, H.-E., 2004. Traffic related

pollutants in Europe and their effect on allergic disease. Current Opinion inAllergy and Clinical Immunology 4 (5), 341–348.

Holguin, F., 2008. Traffic, outdoor air pollution, and asthma. Immunology & AllergyClinics of North America 28 (3), 577–588.

Hurley, P.J., Manins, P.C., 1995. Meteorological modeling on high-ozone days inPerth, Western Australia. Journal of Applied Meteorology 34 (7), 1643–1652.

Kelsall, J.E., Diggle, P.J., 1995. Non-parametric estimation of spatial variation inrelative risk. Statistics in Medicine 14.

Lawson, A.B., Kleinman, K., 2005. Spatial and Syndromic Surveillance for PublicHealth. Wiley.

Lin, S., Munsie, J.P., Hwang, S.A., Fitzgerald, E., Cayo, M.R., 2002. Childhood asthmahospitalization and residential exposure to state route traffic. EnvironmentalResearch 88 (2), 73–81.

Lipsett, M., Hurley, S., Ostro, B., 1997. Air pollution and emergency room visits forasthma in Santa Clara County, California. Environmental Health Perspectives105 (2), 216–222.

O’Sullivan, D., Unwin, D.J., 2003. In: Geographic Information Analysis. Wiley.Oyana, T.J., Rogerson, P., Lwebuga-Mukasa, J.S., 2004. Geographic clustering

of adult asthma hospitalization and residential exposure to pollution at aUnited States–Canada border crossing. American Public Health Association,1250–1257.

Rothman, K.J., 1990. Keynote presentation: a sobering start for the cluster bustersconference. American Journal of Epidemiology 132 (Suppl. 1), 6.

Salam, M.T., Islam, T., Gilliland, F.D., Salam, M.T., Islam, T., Gilliland, F.D., 2008.Recent evidence for adverse effects of residential proximity to traffic sourceson asthma. Current Opinion in Pulmonary Medicine 14 (1), 3–8.

SAS Institute Inc. 2003. SAS 9.1.3 Service Pack 4. Cary, NC, USA.Sturman, A.P., Tapper, N.J., 2006. In: The Weather and Climate of Australia and New

Zealand second ed. Oxford University Press, South Melbourne, Victoria.