A. Measuring variance to evaluate the boundaries defining collective level of analysis

Individual bodies, collective bodies and Frankenstein

Researchers traditionally investigate average characteristics of individuals (eg blood pressure) or of areas (eg social cohesion), but seldom question the “boundaries” that define the units of analysis. These boundaries are often accepted a priori. At the individual level, the limits that define the human body are very apparent, and so is the intra-individual correlation of the individual parts. Without question there is a generalised individual effect that maintains a sophisticated homeostasis among an array of cellular and physiological processes (eg blood pressure level) within the physical boundaries of human skin. As a result, when performing multiple measurements of individual variables in a group of subjects, a great proportion of the variance between measurements is at the individual level. From an epidemiological perspective, this intra-individual correlation is a nuisance that, for statistical reasons, needs be accounted for when analysing such things as repeated blood pressure measurements, diseases of the eyes or teeth, or multiple bone fractures. However, as the boundaries of human bodies are so well delineated, they are taken for granted. Instead, the present research mainly focuses on whether exposure to a variable (ie antihypertensive medication) has an effect on, or changes, the mean of the distribution of another variable (ie lowering of blood pressure).

Ever since the days of Durkheim17, it has been known that when individuals adhere to each other and form a coherent community, a relational18 and collective effect emerges that becomes more that the sum of each individual action. On some occasions this collective effect may have arisen because of sharing of common geographic environments,19 and not necessarily as a result of a voluntary individual decision to form a social group. In any case, this general collective effect is to some extent analogous to the general individual effect mentioned above. Like multiple measurements, individuals within a collective are themselves more similar to one another than they are to individuals outside of their group because insiders share common social boundaries and contextual influences.10 As in the case of the individual body, the collective body maintains a social homeostasis that balances numerous social processes. However, lacking a covering skin such as human bodies possess, the collective body’s geographical or cultural limits (eg “neighbourhood”) are more difficult to discern. A further source of complexity exits: unlike the parts of a human body,20 individuals often belong to several collectives,21 22 both in a cross-sectional and in a life course perspective.23 Sometimes, however, collective boundaries are relatively easy to recognise, as in the case of schools or health care centres when investigating pupil outcomes24 or medical treatments.25

Although the existence of contextual effects on individual health is rather obvious,26 the validity of many administrative boundaries for defining collective bodies27 28 requires more investigation.18 In fact, the possibility cannot be excluded that many of the “neighbourhoods” studied are – like contextual Frankenstein's creatures – constructed by assembling parts from different collective bodies. Paraphrasing Duncan, Jones, and Moon: “the hierarchical definition of the levels could be criticized as an inappropriately formalistic and mechanistic attempt to capture the cultural geography of lifestyle”29 (p. 732).

Can appropriate collective boundaries be identified for investigating contextual effects?

Whereas a number of collective bodies (eg neighbourhoods) are assumed to be exclusively delimited by geographical boundaries, other cultural or relational criteria (either alone or combined with geographical information) may be more appropriate for identifying collective bodies.18 30 31 In any case, if such a collective body exists, one might anticipate finding a correlation in the health of the individuals within it.10 Moreover, the closer the boundary definition corresponds to the boundaries of the hypothesised collective body, the greater one may expect the clustering of the health outcome of interest to be.10 32 Based on this assumption, attempts can be made to identify geographical collective boundaries in one of two ways: either by (a) scanning a geographical surface to identify clusters of the outcome (eg specific diseases), or by (b) using a priori defined sociogeographical areas and quantifying the observed clustering of disease outcomes within these areas.

In the first instance above, cluster recognition analysis33 34 may help to identify geographical clusters of the outcome of interest (eg the incidence of cholera). Once the relational18 boundaries that include the clusters have been identified, investigations can be made into what makes them different from the rest of the geographical surface (eg the water supply), and thereby relevant information can be obtained for drawing causal hypotheses and planning public health interventions. This idea is close to John Snow’s approach in his seminal work on cholera.35 In the second scenario (b), the most common procedure is to employ geographical divisions found in administrative databases (eg census tracts). Alternatively, such areas may be combined on the basis of certain characteristics31 36 37 or by using Geographic Information Systems (GIS) techniques.34

Measures of variance and clustering (eg intra-class correlation,15 38 median odds ratio9 39 40 or parwise odds ratio32) allows us to identify the scale (eg local neighbourhoods, parishes or municipalities)41 42 on which contextual influences operate with different health outcomes.43 For example, in 1999 Boyle and Willms performed an unconventional multilevel analysis exclusively based on measures of intra-class correlation and places defined by administrative boundaries.44 They observed that place effects were generally small and were influenced by both the size of the geographical area used to define place and the health indicator selected for study. The authors questioned the usefulness of carrying out health needs assessment surveys within large administrative areas, and cast doubt on the utility of these geographic boundaries for studying place effects. Boyle and Willms based their conclusions not on means-centric measures of association, but on the analysis of variation, and they raised questions about the context as a whole. Their work has resulted in some criticism (see, for example, Blakely45 p. 373).

B. Combining measures of variance and means-centric measures of association for a better understanding of contextual effects

Small variance but conclusive associations

It may appear paradoxical that a conclusive (“significant”) association between a contextual variable and an individual outcome can be detected alongside a very small fraction of overall variance in the outcome at the contextual (eg neighbourhood) level.46 Thus, means-centric measures of association indicate the existence of contextual effects, whereas measures of variance suggest the opposite.

In an attempt to justify this paradox,47 48 it has been commented that standardised mean differences (d) between intervention and control neighbourhoods, which programme evaluators commonly view as medium (d = 0.4) or even large (d = 0.6), translate into “small” intra-neighbourhood correlations of 4% and 8% respectively. Several criticisms can be raised to this reasoning, with the most fundamental being that there is no need for such a justification. As the present study argues, such a paradox does not exist but, rather, the question is to distinguish between the different information provided by measures of association and by measures of variance. Furthermore, it has been previously revealed that standardised coefficients47 are inappropriate measures of effect as they can be “confounded” by the variance of the specific setting where the study is performed (see Greenland49 and Cummings50 for an extended explanation). Standardised effects are actually distorted measures of association and also hide the information contained in the variance being standardised. In addition, while intra-class correlations ranging from 4% to 8% may be considered small by some,47 they may be highly relevant for others, particularly when compared with the intra-class correlations of many “neighbourhood” outcomes relevant for social epidemiology.51

The fundamental difference between measures of variation and means-centric measures of association becomes clear if one understands that the interpretation of variance is often temporospatially constrained, and that for every individual outcome there may be a pattern of variance produced by different environmental conditions.52 Thus, in seeking useful information for planning public health interventions, measures of variance and clustering from a specific context provide insight into the areas being investigated during the period of the study. By contrast, measures of association intend to provide causal information that can be generalised and applied to contexts beyond the one where the study was performed. Further illustration of this idea using a continuous contextual variable is given in figure 1 (see also a previous study11).

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Figure 1

Visualisation of a hypothetical association between a contextual variable (eg extreme poverty to extreme wealth) and individual blood pressure, based on data on from neighbourhoods in different cities around the world. In this representation the contextual variable explains 100% of the variance between neighbourhoods, as all areas are located on a regression line. However, although the regression coefficient is identical in all cities (ie a one unit increase in wealth results in an equivalent increase in health), the original neighbourhood variance before the introduction of the contextual variable was lower in city B than in city A. The original neighbourhood variance also corresponds to a much larger proportion of total individual variance in city A as opposed to city B. Consequently, a contextual public health intervention would be more efficient in city A than in city B. The key for this intervention is the size of the neighbourhood variance.

This apparent contradiction can even be clarified in an equation calculated from a two level logistic regression model. As an example, imagine individuals are nested within neighbourhoods and the aim is to analyse the relationship between neighbourhood deprivation (X) and presence of hypertension. Without loss of generality, assume the contextual variable is centred on the mean. It can be shown that the total neighbourhood variance σ²_T (as originally estimated in the simplest “empty” model with only individual nested within neighbourhoods) is a function of the regression coefficient of the contextual variable (β²_X), the variance of this contextual variable (σ²_X), and of the residual variance (σ²_u) once the contextual variable is included in the model. Therefore, it is possible to find a similar β_x with very different scenarios of variance.

σ²_T = β²_X·σ²_X+σ²_u

Failure to distinguish between the two types of measures explained above, and, particularly, interpreting means-centric measures of association as if they were measures of variance may lead to inappropriate conclusions, a situation that is unfortunately rather common in many multilevel analyses performed today. As one example, in 2001 Diez-Roux et al.53 performed a state of the art and thoroughly conducted multilevel analysis of the relationship between characteristics of neighbourhoods and the incidence of coronary heart disease. Possibly, as the samples of individuals within blocks in this Atherosclerosis Risk in Communities Study (ARIC) were very small, the authors did not estimate neighbourhood variance. They did, however, assume the existence of intra-neighbourhood correlation in the outcome, which was considered a statistical nuisance and overcome by adjusting standard errors for clustering using the statistical software SUDAAN. The size of this conjectural intra-neighbourhood correlation was never reported. The study drew two main conclusions: (1) “Neighbourhood characteristics are related to the incidence of coronary heart diseases” and (2) “Strategies for disease prevention may need to combine person-centred approaches with approaches aimed at changing residential environments”. Although these conclusions are of clear academic interest for understanding the contextual causes of coronary heart disease, they are also vague and may even be misleading. An approach aimed at changing residential environments may be effective in the ARIC context, but, as there is no information on the intra-neighbourhood correlation (or similar measures of variance), this cannot be certain. For example, although an analogous multilevel study in Malmö, Sweden,54 demonstrated a clear association between the socioeconomic characteristics of the urban areas and individual blood pressure (in agreement with the ARIC study),53 differences between these same areas explained less than 1% of the individual variance in blood pressure. Consequently, the study concluded that, with regard to Malmö, an intervention focused on urban areas with a higher mean level of deprivation would be ineffective.4 11

A contextual analysis should not be avoided because the area variance or the intra-class correlation is very small, as means-centric associations between contextual variables and individual health may still be detected. On the other hand, neither can one recommend a contextual public health intervention based on a “significant” means-centric association if the clustering of individual health within areas is unknown or very low. Means-centric measures of association do not provide sufficient information for deciding to launch public health interventions at some specific areas but not at others. In fact, if clustering is small, a public health intervention directed to concrete areas would be ineffective, even where a contextual variable is associated with the individual outcome and serves to explain 100% of the area variance. As Singer has stated “You can explain a large amount of very little”,55 p. 332. A different scenario is also possible in which a clear association is observed between the contextual variable and the individual outcome side by side with a very large residual area variance. In this case, if the contextual variable does not go very far toward explaining the original area variance, a public health intervention aimed at changing this contextual variable would not be very effective.

As discussed earlier, measures of variance and clustering are useful for identifying boundary limits of the “collective body” that it is assumed influences the outcome under study. In this section the aim was to demonstrate that such collective boundaries (ie “the geographic scale”) cannot be properly identified solely by means-centric measures of association. For this purpose, means-centric measures of association must be combined with measures of variance and clustering.

New analytical approaches – solving the paradox

In an earlier publication,9 empirical examples of the two scenarios depicted above were given, and a pair of useful measures proposed by Larsen et al. were applied:9 40 the median odds ratio (MOR) and the interval odds ratio (IOR) (for an extended explanation of these measures, see39). The MOR quantifies neighbourhood variance on the odds ratio scale, and the IOR incorporates both the means-centric effect (ie odds ratio) and neighbourhood variance in one interval, allowing for a more detailed description of the means-centric effect.

In a previous study,9 it was found that administrative neighbourhoods of Malmö were very suitable for identifying the “collective body” that conditions certain individual behaviours, such as choosing to visit a private rather than a public physician. For this condition, the area variance (SE) with adjustment for age and individual education was 1.815 (0.278) and the correspondent MOR = 3.61. However, the same neighbourhoods seemed inappropriate for identifying the “collective body” that conditioned hospitalisation for ischaemic heart disease, as the corresponding variance (SE) was only 0.028 (0.025) and the MOR = 1.17. In the same study, the socioeconomic characteristics of the neighbourhood appraised by aggregated educational achievement (low vs high) were, however, associated with both outcomes. Nevertheless, in spite of this observed association (and disregarding concerns about counter-factuality), it was concluded that a possible public health intervention directed to specific neighbourhoods would be ineffective in either instance. In the case of hospitalisation for ischaemic heart disease, the inefficiency would depend on the very low neighbourhood variance. Finding such a low area variance in cross-sectional studies is rather common for chronic diseases, which, like arteriosclerosis, develop over a whole life-course and have little to do with the place where an individual may be currently residing. When it comes to change an individual’s choice of physician, a neighbourhood intervention would similarly be ineffective because of the large variance that remains unexplained after including the variable “neighbourhood level of education” in the model. The latter expressed itself in a very broad IOR = 0.28–27.3. There is little doubt that the current neighbourhood context influences individual behaviour much more than chronic disease, but “neighbourhood educational level” – in spite of being associated with the choice of physician – does not explain very much in the city of Malmö.

Combining variance-based measures with means-centric measures of association provides useful and complementary information on contextual effects. These considerations may be relevant when attempting to determine the efficacy of focusing intervention on places rather than on people. For example, imagine that a City Council has been informed that average blood pressure is higher in deprived neighbourhoods than in wealthy neighbourhoods. As a consequence, decision makers are considering the allocation of resources in the most deprived neighbourhoods for the creation of new health care centres specialising in blood pressure control. However, if the neighbourhood variation represents only a very small part of the total individual variation in blood pressure, then many people with high blood pressure would be ignored simply because they reside in wealthy neighbourhoods. When the clustering of individual health status within neighbourhoods is small, focusing intervention on specific places may be a rather inefficient strategy.4 11 Using the words of Clarke: “without knowledge of the random components, the interpretation of area-level fixed effects parameters becomes decontextualized”37 (p. 315).

C. Investigating the causes of health variation

Epidemiologists commonly understand causation in terms of group means, so the statement “X causes Y” is taken to imply that, ceteris paribus (see references14 48 56 57 for a discussion on this aspect), an increase in the value of X changes the mean of the distribution of Y. However, many independent variables of interest in epidemiological studies may cause a change in the variance (not the mean) of the distribution of the dependent variable2 3 4 5 6 (see figure 2).

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Figure 2

Visualisation of an imaginary association between the interval of time after the start of a contextual intervention in a hypothetical city and mean individual health measured across (1) the entire city (thick line) and (2) in each of the city’s neighbourhoods (thin lines). The measure of association (regression coefficient β) is positive; it is similar in I and II and shows an increase of the overall mean from the start of the intervention. However, health inequalities (ie neighbourhood variance) do not change along the time axis in scenario I, but are considerably reduced in scenario II. The regression coefficient (β) is zero in both III and IV, which might be interpreted as an absence of contextual effects, as the intervention does not seems to influence health. However, although the health inequalities represented by neighbourhood variance have not changed in scenario III, they have been greatly reduced in scenario IV.

The distinction between the variance altering and means-centric altering approaches is still not widely observed in social epidemiology; most researchers only discuss classic means-centric measures of association. This means-centric reductionism goes hand in hand with an epidemiology mostly concerned with risk factors58 and drug safety, and creates a paradoxical situation, as social medicine is not only interested in increasing the (mean) health of the population, but also in decreasing health inequalities (variance). Likewise, it is of major relevance to understand and prevent inappropriate health care variation, as it leads to inefficient resource utilisation. Modelling variance itself as a dependent variable may provide useful information on health inequalities and suggest a different kind of contextual effect.6 13 25 59

When investigating such variance-altering causation in contextual analysis, a fundamental independent variable is the definition of boundaries that used to operationalise collective bodies (as was attempted to be shown in the first section above). For example, “neighbourhood” is included as a random term in multilevel regression analyses. The boundaries that define a specific level of analysis can be considered as an independent variable in an equation that models variance. In this way, investigations can be made into (potential) causation where the chosen boundaries – assuming they delimit a true collective body – “cause” a certain pattern of individual differences/similarity. This has been the approach adopted, for example, by Boyle and Willms,44 Reijneveld,60 Petronis and Anthony32 and the present authors6 25 46 54 as well as recently by Uthman, Moradi and Lawoko61 and by Naess et al.62 This last work explores area variation across a life-course as a way of elucidating potential (causal) influence of area on mortality.

Modelling individual and area variance may yield valuable information on how contextual factors shape health inequalities for different individuals. In a previous study based on the MONICA project,6 contextual effects on individual systolic blood pressure were investigated, and variance modelled as a function of antihypertensive medication use and body mass index. Among other results, it was found that contextual effects were particularly strong in overweight women on antihypertensive medication. Actually, around 20% of the individual differences in blood pressure were conditioned by the MONICA population where these women were included. This contextual phenomenon possibly reflects disparities in the effectiveness of antihypertensive treatment among different national health care systems (see figure 3 in reference6).

In a recent study,25 variance altering causes were explicitly investigated and a conceptual illustration presented showing that a change in the characteristics of a context (eg the implementation of a decentralised health care budget) not only changes the mean of the distribution of the variable studied (ie increasing compliance with prescription guidelines), but also alters the variance between the collective units as well (ie decreasing inequality between health care centres). Downs and Rocke2 and Braumoeller5 also provide illustrative examples in their work.

Conclusions

Both measures of variance and means-centric measures of association need to be included when performing contextual analyses. However, more research is needed to (a) indentify appropriate boundaries for collective bodies like neighbourhoods, (b) develop statistical methods that facilitate the use of measures of variance in social epidemiology, (c) identify variance-altering causes and their mechanisms, and (d) comprehend the relationship among the degree of clustering of individual health within administrative areas, the size of means-centric measures of association, and the possible efficiency of public health interventions.

Seeking causal explanations in social epidemiology is a challenge in itself,63 but focusing on the (causal) circumstances that condition variance reveals a neglected theoretical dimension for understanding health disparities in social epidemiology. The variance approach, a new aspect of contextual analysis that cannot be interpreted in means-centric terms, allows perspectives to be expanded.