A brief conceptual tutorial of multilevel analysis in social epidemiology: linking the statistical concept of clustering to the idea of contextual phenomenon. Merlo, Juan; Chaix, Basile; Yang, Min; Lynch, John; Råstam, Lennart Published in: Journal of Epidemiology and Community Health DOI: 10.1136/jech.2004.023473 2005 Link to publication Citation for published version (APA): Merlo, J., Chaix, B., Yang, M., Lynch, J., & Råstam, L. (2005). A brief conceptual tutorial of multilevel analysis in social epidemiology: linking the statistical concept of clustering to the idea of contextual phenomenon. Journal of Epidemiology and Community Health, 59(6), 443-449. https://doi.org/10.1136/jech.2004.023473 Total number of authors: 5 General rights Unless other specific re-use rights are stated the following general rights apply: Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Read more about Creative commons licenses: https://creativecommons.org/licenses/ Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 12. Aug. 2021
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A brief conceptual tutorial of multilevel analysis in social epidemiology: linking thestatistical concept of clustering to the idea of contextual phenomenon.
Merlo, Juan; Chaix, Basile; Yang, Min; Lynch, John; Råstam, Lennart
Published in:Journal of Epidemiology and Community Health
DOI:10.1136/jech.2004.023473
2005
Link to publication
Citation for published version (APA):Merlo, J., Chaix, B., Yang, M., Lynch, J., & Råstam, L. (2005). A brief conceptual tutorial of multilevel analysis insocial epidemiology: linking the statistical concept of clustering to the idea of contextual phenomenon. Journal ofEpidemiology and Community Health, 59(6), 443-449. https://doi.org/10.1136/jech.2004.023473
Total number of authors:5
General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal
Read more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.
doi:10.1136/jech.2004.023473 2005;59;443-449 J. Epidemiol. Community Health
Juan Merlo, Basile Chaix, Min Yang, John Lynch and Lennart Råstam
of clustering to the idea of contextual phenomenonsocial epidemiology: linking the statistical concept A brief conceptual tutorial of multilevel analysis in
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J Epidemiol Community Health 2005;59:443–449. doi: 10.1136/jech.2004.023473
Study objective: This didactical essay is directed to readers disposed to approach multilevel regressionanalysis (MLRA) in a more conceptual than mathematical way. However, it specifically develops anepidemiological vision on multilevel analysis with particular emphasis on measures of health variation (forexample, intraclass correlation). Such measures have been underused in the literature as compared withmore traditional measures of association (for example, regression coefficients) in the investigation ofcontextual determinants of health. A link is provided, which will be comprehensible to epidemiologists,between MLRA and social epidemiological concepts, particularly between the statistical idea of clusteringand the concept of contextual phenomenon.Design and participants: The study uses an example based on hypothetical data on systolic blood pressure(SBP) from 25 000 people living in 39 neighbourhoods. As the focus is on the empty MLRA model, thestudy does not use any independent variable but focuses mainly on SBP variance between people andbetween neighbourhoods.Results: The intraclass correlation (ICC =0.08) informed of an appreciable clustering of individual SBPwithin the neighbourhoods, showing that 8% of the total individual differences in SBP occurred at theneighbourhood level and might be attributable to contextual neighbourhood factors or to the differentcomposition of neighbourhoods.Conclusions: The statistical idea of clustering emerges as appropriate for quantifying ‘‘contextualphenomena’’ that is of central relevance in social epidemiology. Both concepts convey that people from thesame neighbourhood are more similar to each other than to people from different neighbourhoods withrespect to the health outcome variable.
This article has, on the one hand, didactic purposes and isdirected to readers disposed to approach multilevelregression analysis (MLRA) in a more conceptual than
mathematical way. Readers who wish an alternative or moreformal statistical explanation may consult any of the otherreferences on multilevel analysis published elsewhere.1–5
On the other hand, and perhaps more important, in thisessay we also develop a vision of multilevel analysis6 thatconsiders measures of health variation7 (for example,neighbourhood variance, intraclass correlation) for under-standing the distribution of health in the general populationrather than only applying measures of association (forexample, regression coefficients, odds ratios)8 to understandcontextual determinants of individual health. We believethat, so far, measures of health variation have been under-used in multilevel epidemiology.Our aim is to provide a link, which will be comprehensible
to epidemiologists, between MLRA techniques and socialepidemiological concepts, particularly the analogy betweenthe statistical concept of clustering and the social epidemio-logical idea of contextual phenomenon.It is intuitive that people from the same area may be more
similar to each other in relation to their health status than topeople from other areas. In other words, persons with similarcharacteristics may have different degrees of health accord-ing to whether they live in one area or another becauseof differing cultural, economic, political, climatic, historical,or geographical contexts.9 This contextual phenomenonexpresses itself as clustering of individual health statuswithin areas. That is, a portion of the health differences
among people may be attributable to the areas in which theyreside.6 10
The notion of contextual phenomenon has a long history inepidemiology and is included under different forms in theDurkheimian concept of social fact,11 Rose’s notion ofpopulation disease rates,12 13 and John Snow’s findings oncholera incidence.14 These three related seminal conceptionsare contextual in their nature, and support the idea thatknowledge on the distribution and determinants of popula-tion health is epistemologically multilevel15 and needs toconsider both people and areas.10 16 17
The idea of contextual phenomenon, which could beconsidered as a core notion in social epidemiology, corre-sponds to the statistical concept of clustering*—that is, inturn, the main reason for applying multilevel regressiontechniques. Statistically, it is necessary to use techniquesthat, like MLRA, consider the dependence of the outcomevariable between people from the same area. An importantassumption made in usual regression analyses is theindependence of individual measures. If this assumption isviolated, the results of the regression analysis are biased.1
However, we have previously emphasised6 that clustering ofindividual health within neighbourhoods is not a statisticalnuisance that only needs to be considered for obtainingcorrect statistical estimations, but a key concept in socialepidemiology that yields important information by itself.2 6 19–21
The more the health of the people within a neighbourhood is
alike (as compared with people in other neighbourhoods), themore probable it is that the determinants of individual healthare directly related to the contextual environment of theneighbourhood, and/or that social processes of geographicalsegregation are taking place—that is, similar types of peoplechoose or are forced to reside in a given neighbourhood.Those aspects are of high significance in social epidemiol-
ogy as they have value in the context of ideas about theefficacy of focusing intervention to reduce health inequalitieson certain geographical areas rather than on specific peopleonly. Measures of variation are important in public health tounderstand the significance of specific contexts for differentindividual health outcomes.7 Traditional measures of associa-tion, in contrast with measures of variation, do not inform onthe multilevel distribution of health.6
Without being a panacea to miraculously fix the ills of a‘‘risk factor’’ epidemiology that seems inappropriate forassessing the impact of the context,23 MLRA is a suitablestatistical technique that can be used to operationaliseconceptual schemas in multilevel epidemiology.In this essay we explain how to investigate whether a given
health phenomenon (for example, systolic blood pressure)has a contextual dimension. Using this research question, weintroduce the ‘‘empty’’ MLRA model. This model is thesimplest form of MLRA as it does not include any covariatebut focuses only on how health differences are distributedbetween people and between areas. Along the explanation ofthe empty model, we present figures that permit a visualcomprehension of MLRA concepts such as residuals, parti-tioning of variance at different levels, and the idea ofclustering and intraclass correlation.
THE ‘‘EMPTY’’ MLRA MODELTo explain MLRA we use an example based on hypotheticaldata. The population of the example consists of 25 000subjects, 35 to 64 years old, living in the 39 neighbourhoodsof an imaginary city. The individual outcome variable issystolic blood pressure (SBP), and we assume that it iscontinuous and follows a normal distribution. As this articleexplains the empty MLRA model, we do not use anyindependent variable but focus only on the mean andvariance of SBP.The example was adapted from a real empirical investiga-
tion that analysed countries rather than neighbourhoods.10
This essay is based on simulated data and, therefore, theresults presented in this article should not be used asempirical evidence. For all analysis, we use the softwareMLwiN version 1.1 developed by Goldstein’s researchgroup�.24
The reason for naming this model ‘‘empty’’ is that it doesnot include any explanatory variables but only estimates the
city SBP mean and the neighbourhood and individualdifferences in SBP on the basis of the study sample. Wepresent below a very simple equation of the model that willbe clear to readers not trained to read formal statisticalnotations. Readers who wish a formal statistical explanationare referred elsewhere.2 25 26
SBPI=SBPC+EN2c+EI2c
SBPI=SBP of an individual in a neighbourhoodSBPC=Mean SBP of the cityEN2c=Difference between the city SBP mean and the
neighbourhood SBP mean (also known as neighbourhood‘‘shrunken residual’’)EI2c=Difference between the neighbourhood SBP mean
and the individual SBP value (also known as ‘‘individualresidual’’)In MLRA both people and neighbourhoods are assumed to
be randomly sampled from a population of persons and apopulation of neighbourhoods. It is assumed that theresiduals are normally distributed and that there is indepen-dence between the individual residuals and the neighbour-hood residuals. MLRA presents advantages compared withthe common analysis of variance.The model presented above shows that the SBP value of a
person living in a neighbourhood (SBPI) is equal to the meanSBP in the city (SBPC) plus the predicted neighbourhooddifference from the city mean (that is, neighbourhoodshrunken residual [EN2c]) plus the individual differencefrom the neighbourhood mean (that is, individual residual[EI2c]).
Partitioning overall differences in SBPThe presence of neighbourhood and individual residuals inthe empty multilevel model just shows that SBP varies bothat the individual and at the neighbourhood level. The mainintent of the empty model is to partition the total variance inSBP in the city (VTotal) into a variance that occurs betweenneighbourhoods (VN) and a variance that occurs betweenpeople (VI) as shown in the equation 1, illustrated in figure 1,and calculated in table 1.
In figure 1 we can visualise the empty model and theconcepts that it conveys. In this figure the neighbourhooddifferences from the city mean represent the shrunkenresiduals. The figure shows that multilevel structures conveyinformation on variability both between and within neigh-bourhoods. The variance is a summary of the differences. Thehigher the variance, the larger the differences are. In figure 1the brackets show that the total variance is the sum of thebetween neighbourhood variance and the within neighbour-hood variance.Figure 2 shows the individual and neighbourhood SBP
values used in our example. We can see that eachneighbourhood has a specific SBP mean (black dots) thatdiffers from the city mean (130 mm Hg) by a certain amountof mm Hg. This difference is the neighbourhood level rawresidual.
Single level individual studies compared with MLRAIn table 1 we can see that the empty model gives evidence ofboth between individual (VI=433.4) and between neigh-bourhood (VN=36.2) variance in SBP. If we combine thevariance from both levels to give a total variance, we see thatthis total variance (VTotal = 468.1) is similar to the variance
*According to the ideas of Durkheim (1858–1917) people belonging toa specific community share a collective conscience (common socialvalues and norms that are formed by human relations and interactionsand that generate collective feelings of solidarity and connectedness).This collective conscience operates creating what Durkheim called‘‘social cohesion’’ to bind the social structure together. Understood in thisway, the social group emerges as an independent social fact rising overand above individual circumstances, and going beyond the sum of thepeople that compose it.11 Thus collective characteristics shape the healthof the population in a way that cannot be reduced to individualcharacteristics. A classic example concerns population differences insuicide rates. Even if within each area the people at risk of committingsuicide are not the same in different time periods, the differencesbetween populations in suicide rates are fairly stable over time. This factsuggests the existence of a contextual phenomenon that conditions aclustering of individual suicide risk within areas. In other words, somepart of the total differences in health between people might be as aconsequence of the differences between the areas where the people live.Analogous consideration can be made when interpreting John Snow’sfindings on cholera incidence in different areas of London14 and theideas of Geoffrey Rose on sick people and sick populations.10 12 18
� For a review on other programs suitable for MLRA see the Centre forMultilevel Modelling, Institute of Education, London (http://multilevel.ioe.ac.uk/ softrev/index.html).
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obtained by a simple individual level analysis using descrip-tive statistics. Reading table 1, you can understand intuitivelythat a portion of the individual level variance is in factneighbourhood level variance.Imagine that figure 3 represents the distribution of
individual SBP in the population of the city described inthe example. As in individual single level analysis we haveindividual data only, the fact that people are grouped withinneighbourhoods is neglected. In figure 3 we merely seedifferences between the individual SBP values and the meanSBP value of the whole city (the single level individualresiduals). We are unable to distinguish the differencesbetween the mean blood pressure in each neighbourhood andthe overall mean blood pressure in the city. In single levelindividual based designs, we tend to neglect possible
neighbourhood effects. This oversimplified approach hasbeen termed the individualist fallacy.27
Single level ecological studies compared with MLRATable 1 also shows the between neighbourhood varianceobtained by an ecological analysis performed by aggregationof the individual SBP values at the neighbourhood level. Inthe ecological analysis we estimate the mean SBP for eachneighbourhood from the sample of people in each neigh-bourhood, and then we compute the variance of theseestimated means. The ecological variance computed in thisway overstates the neighbourhood variance because italso includes variation attributable to sampling error (impre-cision) in the estimates of each neighbourhood meanSBP.
Individualvariance
City mean
Neigbourhoodlevel residual
Neigbourhoodvariance
Totalvariance
Individualvariance
Individuallevel residual
Individualvariance
IndividualvarianceIndividual
variance
Figure 1 Multilevel information. In thisfigure the neighbourhood residualsare represented by the length of thepillows between the city SBP mean,represented by a grey colour, and theneighbourhood SBP means representedby thick black horizontal lines. Theindividual residuals are represented bythe length of the vertical lines betweenthe neighbourhood means and theindividual SBP values represented byblack circles at the top of thin lines. Inthis figure we do not have anyexplanatory variable (that is, this figurecorresponds to an ‘‘empty’’ model) aswe are only interested in analysing howindividual blood pressure differencesare partitioned in a variability thatexists between people from the sameneighbourhood and a variability thatexists between neighbourhoods. In thisfigure we can imagine that theneighbourhood means (short thick lines)pull up or pull down all the individualSBP values belonging to the sameneighbourhood, even if individuallevel variability remains withinneighbourhoods. The mathematicalexpression of the intraclass correlationcan be visually understood in figure 1.Figure 1 is a graphic combination offigures 3 and 4.
Table 1 Multilevel, individual and ecological linear regression analysis of systolic bloodpressure (SBP) in 25 000 people living in the 39 neighbourhoods (hypothetical data)
Multilevel regressionanalysis (empty model)
Single level individualanalysis*
Single level ecologicalanalysis�
Fixed effectsMean SBP of the city 130.2 130.2 130.0Random effectsMultilevel measures of healthvariationVariance (SE)Between neighbourhoods 36.2 – 37.0Between individuals 433.4 468.1Intraclass correlation (ICC) ICC = 0.08 – –
Deviance (goodness of fitof the model)`
222764 224532 –
‘‘Fixed effects’’ and ‘‘random effects’’ are expressions that are often used in MLRA. In very simple terms, fixedeffects are used to model means whereas random effects are used to model variance. *In the individual levelanalysis we ignore the existence of the neighbourhood level. �In the single level ecological analysis we aggregatethe individual level information on SBP to the neighbourhood level, neglecting the existence of the individual level.`The deviance expresses the goodness of fit of the model, and was calculated using the 226log likelihood (IGLS).The Bayesian deviance information criterion (DIC) gave similar results. The multilevel models fit the data muchbetter than the single level individual analysis. The ecological analysis is not comparable as it is based on 39neighbourhoods rather than on 25 000 people. We refer elsewhere for an extended explanation of the deviancestatistic.44 45
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The ecological variance is rather similar to the betweenneighbourhood variance in SBP obtained by the MLRA. Itis patently clear that the single level ecological analysisneglects the existence of individual level variance. Figure 4illustrates that in an ecological analysis we are unable toobserve differences between people (variation in bloodpressure within a neighbourhood), but we can distinguishdifferences between the mean blood pressure of eachneighbourhood and the mean blood pressure of the wholecity (that is, the neighbourhood residuals of an ecologicalanalysis).In single level ecological analysis, we consider all informa-
tion as if it were at the neighbourhood level, neglectingpossible individual components (this oversimplified approachhas been termed the sociological fallacy).27
Today it is well known that neither single level individualnor ecological analyses are suitable for effectively investigat-ing contextual effects.22
The intraclass correlation (ICC) or variance partitioncoefficient (VPC)It is seen in figure 1 that all people living in the sameneighbourhood share a common level of blood pressure thatdiffers from the city mean in an amount that corresponds to
the neighbourhood residual. Therefore, we often speak about‘‘differences between neighbourhoods’’ and ‘‘differencesbetween people within neighbourhoods’’. Together theindividual and the neighbourhood variance componentsrepresent the total differences in SBP. We can see that aportion of the total individual SBP difference is at theneighbourhood level, and in the empty model we canquantify this aspect by computing ICC. As equation 2 shows,the multilevel ICC is the proportion of the variance in SBPthat occurs at the neighbourhood level. In this sense the ICCis a variance partition coefficient (VPC).1
It can be seen in figures 3 and 4 that in single level analysiswe are unable to calculate the ICC, because information onhow variance is partitioned at different levels is not available.The ICC equation is intuitive and can also be understood by
observing figure 1.
In this formula VI is the variance between people from thesame neighbourhood (1st level variance) and VN is thevariance between neighbourhoods (2nd level variance).
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Figure 2 The figure shows the actualSBP values used in our example. Thelarge black dots represent theneighbourhood means. The smallcircles represent the individual SBPvalues within neighbourhoods. Thehorizontal black line represents the citySBP mean.
City meanblood pressure
Individual levelresidual
Individualvariance
Figure 3 Single level individualinformation. This figure represents thedistribution of individual SBP in thepopulation of the city when we haveonly single level individual basedinformation. The fact that people aregrouped within neighbourhoods isneglected, as we only have individuallevel data. In this figure the length of thethin vertical line from the black spot tothe thick horizontal line represents theindividual differences in blood pressurecompared with whole city mean (theindividual level residuals). Theindividual variance in single levelindividual studies is an averagesummary of these differences. In singlelevel individual analysis we consider allinformation as if it were at theindividual level neglecting possibleneighbourhood components.
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As variance can only be positive, according to equation 2the ICC is necessarily between 0 and 1. Table 1 shows that theICC, which measures individual SBP clustering at theneighbourhood level, is equal to 0.08. Therefore, in ourexample 8% of the total individual differences in SBP are atthe neighbourhood level. On these grounds, we mightconclude that there is some evidence for a possibleneighbourhood contextual phenomenon shaping a com-mon individual SBP level. Alternatively, this clusteringmight be attributable to the different composition ofneighbourhoods.The name ‘‘correlation’’ suggests that the ICC expresses the
similarity in health status (in our example SBP) between twopersons in the same neighbourhood. An ICC equal to 1 wouldinform us that all the people in a neighbourhood have anidentical SBP level (that is, 100% of the total individualdifferences are at the neighbourhood level), and an ICC equalto 0 that the people do not share any neighbourhood relatedcommon level of SBP.A high ICC value informs us that neighbourhoods are very
important in understanding individual differences in health.On the other hand, an ICC of 0 would suggest that theneighbourhoods are similar to random samples taken fromthe city and suggest that neighbourhoods are not relevant tounderstanding SBP differences. Snijders also gives a didacticexample of this concept (page 18).2 When the ICC is 0, thesuitability of performing a multilevel analysis is less obvious.
In the absence of a multilevel structure, a single levelindividual analysis is appropriate.We may be interested in knowing if the ICC is statistically
different from 0. The simplest method would be to perform astatistical test of the neighbourhood variance.1–3 When theneighbourhood level variance is not significant, there is nojustification for computing the ICC. However, when testingthe neighbourhood variance you need to consider thestatistical power in MLRA considering that it depends moreon the number of neighbourhoods than on the number ofpeople.2 Remember that absence of evidence is not evidenceof absence.28
If the ICC is 0, it does not necessarily mean that theneighbourhood context is not important compared withindividuals’ factors. Rather, an alternative reason could bethat the geographical boundaries we use to define the actualneighbourhoods do not correspond with the boundaries thatshape the relevant environment for the concrete individualhealth outcome. An ICC close to 0 in an empty model mayhide considerable neighbourhood variability that would onlyappear in more complex models. Moreover, a small ICC doesnot prevent the existence of significant associations betweenneighbourhood variables and individual health as compara-tively small variance between neighbourhood means maygive enough contrast of exposure to detect associations.6 25
These aspects are more extensively discussed in companionpapers.29 30
All neighbourhoods(city mean blood pressure)
VN = variance of meanblood pressure betweenneighbourhoods
VN
Specific neighbourhood(mean blood pressure)
Figure 4 Single level ecologicalinformation. In this figure all individualSBP values are aggregated at theneighbourhood level to obtain theneighbourhood mean. We candistinguish differences between themean blood pressure of eachneighbourhood and the mean bloodpressure of the whole city (theneighbourhood residuals). Theseresiduals are represented by thick blackhorizontal lines at the top of a pillow.The neighbourhood variance is asummary of the differences betweenneighbourhoods. We are unable toobserve differences between people(variation in blood pressure withinneighbourhoods). In single levelecological analysis we consider allinformation as if it were at theneighbourhood level neglectingindividual components.
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Figure 5 Here neighbourhoods areranked according to the mean SBPusing the whole city mean SBP asreference in the comparisons. Theneighbourhood values are the‘‘shrunken residuals’’ (black circles) andthe raw residuals (white circles). Weprovide 95% confidence intervalsobtained in the multilevel regressionanalysis.
Understanding multilevel analysis in social epidemiology 447
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‘‘Shrunken’’ neighbourhood level residualsAn extra comment on how neighbourhood level residuals arecalculated in MLRA is necessary as these residuals are oftenused in epidemiology and community health studies to ranksecond level units (for example, hospitals) and investigategeographical differences in health.31–33
In the simplest case, the raw residual is the differencebetween the city and the neighbourhood mean SBP. Theshrunken neighbourhood residual (EN2c) obtained with themultilevel regression is then calculated a posteriori bymultiplying the raw neighbourhood residual by a shrinkagefactor (SF) shown in equation 3:
Obviously SF has a value between 0 and 1. Theneighbourhood ‘‘shrunken’’ residual is calculated by weight-ing the raw residual with SF as in equation 4:
The neighbourhood ‘‘shrunken residuals’’ are computedusing the raw residuals, the estimated variances, and thenumber of people in the neighbourhood (Nn). MLRA can beperformed even when the number of people (1st level units)within each neighbourhood (2nd level unit) is very different.The fewer the number of people in a neighbourhood, or thehigher the variability within neighbourhoods as comparedwith the variability between neighbourhoods, the moreimportant the shrinkage and the more the value of theneighbourhood residual will be shrunken towards 0. Thevalue (SBPc+EN2c) is also termed ‘‘posterior mean’’.1
Computing these shrunken residuals may be viewed asdisentangling the proportion of each residual that may beattributed to true variations between neighbourhoods fromthat proportion that might better be attributed to randomvariations.34 Rather than only considering the neighbourhoodlevel variance as a summary of the variations that existbetween neighbourhoods, the shrunken residuals inform
how each specific neighbourhood differs from the citymean.In figure 5 we have ranked the neighbourhoods according
to their shrunken residual as explained above. The rawresiduals are represented by white circles and in our exampleare very similar to the shrunken residuals due to the highnumber of individuals in each neighbourhood. The barsaround each neighbourhood residual represent the 95%confidence intervals. It can be concluded that in thesehypothetical data many of the neighbourhoods present a SBPthat differs from the city SBP mean (represented by a dottedline).
CONCLUSIONSWe have shown in a basic way that the simple investigationof how differences in SBP are partitioned between theindividual level and the neighbourhood level providesrelevant epidemiological information. Both the statisticalidea of clustering (that is, ICC) and the social epidemiologicalconcept of contextual phenomenon convey that people fromthe same neighbourhood are more similar to each other thanto people from different neighbourhoods with respect to thehealth outcome variable. For this reason epidemiologicalmeasures of clustering as the ICC emerge as appropriate foridentifying and quantifying ‘‘contextual phenomena’’,6 35
which is of central relevance in social epidemiology.6 7 36
In companion articles we explain more complex MLRAmodels that include individual and neighbourhood levelvariables.29 37 In these articles we illustrate that the impor-tance of the context for understanding health differencesmay differ for people with different characteristics. We alsoclarify that contextual factors may modify the effect ofindividual characteristics on health, and that individual andcontextual factors can be used to explain compositional andcontextual neighbourhood differences in health. We explainthat measures of association between contextual character-istics and individual health, being important for under-standing multilevel causal pathways, do not allow forassessing the multilevel distribution of health outcomes.Studying multilevel health variation presents compara-
tively few complications and yields measures that areintuitively easy to understand when the outcome of interestmeets the conditions for linear regression analysis. However,when the outcome is not continuous, interpreting measuresof variation is less easy and it is the subject of thisinvestigation.38 39 Appropriate measures are, however, alreadyavailable,20 35 40–43 and we explain these measures in a
What this paper adds
N We provide a link—comprehensible to epidemiolo-gists—between multilevel regression techniques andsocial epidemiological concepts, particularly the ana-logy between the statistical concept of clustering andthe social epidemiological idea of contextual phenom-enon.
N We develop a vision of multilevel analysis thatconsiders measures of health variation (for example,neighbourhood variance, intraclass correlation) forunderstanding the distribution of health in the generalpopulation rather than only applying measures ofassociation (for example, regression coefficients, oddsratios) to understand contextual determinants ofindividual health.
N Measures of health variation have been underused inmultilevel epidemiology.
N Statistical measures of clustering emerge as appro-priate for quantifying ‘‘contextual phenomena’’, whichis of central relevance in social epidemiology.
Policy implications
N It is important that political decisions are grounded inappropriate analysis. This study explains a modernmethodology of analysis that can be applied in thiscontext.
N Multilevel analyses can be used to identify therelevance of the neighbourhood or other societalboundaries for understanding health inequalities.
N Our study has value in the context of ideas about theefficacy of focusing intervention to reduce healthinequalities on certain geographical boundaries ratherthan on people only.
N Politicians should always consider the fact that thehealth of the citizens may depend on their context,which deserves to be investigated and accounted forwhen planning public health interventions.
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companion paper. In any case, most epidemiological conceptsthat can be operationalised by multilevel linear regressionanalysis are of general validity and can be applied to any typeof health outcomes.Our essay may help to provide more insight into the use of
measures of health variation based on the random effects ofthe multilevel models, and emphasise the decisive part theyshould play in social epidemiology and community healthresearch. Statistical measures of clustering emerge as appro-priate for quantifying ‘‘contextual phenomena’’, which is ofcentral relevance in social epidemiology.
ACKNOWLEDGEMENTSWe thank Klaus Larsen for his comments on the manuscript andBeatriz Gonzalez Lopez-Valcarcel and other anonymous referees fortheir constructive critics.
J Merlo, L Rastam, Department of Clinical Sciences (CommunityMedicine), Malmo University Hospital, Lund University, Malmo, SwedenB Chaix, Research Team on the Social Determinants of Health andHealthcare, National Institute of Health and Medical Research, Paris,FranceM Yang, Institute of Community Health Sciences, Queen Mary Universityof London, London, UKJ Lynch, Department of Epidemiology, Center for Social Epidemiologyand Population Health, University of Michigan, Ann Arbor, USA
Funding: this study is supported by grants from FAS (Swedish Council forWorking Life and Social Research) for the projects ‘‘Development andapplication of multilevel analysis in pharmacoepidemiology and socialmedicine’’ (principal investigator: Juan Merlo, number 2002-054) and‘‘Socioeconomic disparities in cardiovascular diseases - a longitudinalmultilevel analysis’’ (principal investigator: Juan Merlo, number 2003-0580).
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