Does the Neighborhood Area of Residence Influence Non-Attendance in an Urban Mammography Screening Program? A Multilevel Study in a Swedish City

Background and aim The public health impact of population-based mammography screening programs depends on high participation rates. Thus, monitoring participation rates, as well as understanding and considering the factors influencing attendance, is important. With the goal to acquire information on the appropriate level of intervention for increasing screening participation our study aimed to (1) examine whether, over and above individual factors, the neighborhood of residence influences a woman’s mammography non-attendance, and (2) evaluate, whether knowing a woman’s neighborhood of residence would be sufficient to predict non-attendance. Methods We analyze all women invited to mammography screening in 2005–09, residing in the city of Malmö, Sweden. Information regarding mammography screening attendance was linked to data on area of residence, demographic and socioeconomic characteristics available from Statistics Sweden. The influence of individual and neighborhood factors was assessed by multilevel logistic regression analysis with 29,901 women nested within 212 neighborhoods. Results The prevalence of non-attendance among women was 18.3%. After adjusting for individual characteristics, the prevalence in the 212 neighborhoods was 3.6%. Neighborhood of residence had little influence on non-attendance. The multilevel analysis indicates that 8.4% of the total individual differences in the propensity of non-attendance were at the neighborhood level. However, when adjusting for specific individual characteristics this general contextual effect decreased to 1.8%. This minor effect was explained by the sociodemographic characteristic of the neighborhoods. The discriminatory accuracy of classifying women according to their non-attendance was 0.747 when considering only individual level variables, and 0.760 after including neighborhood level as a random effect. Conclusion Our results suggest that neighborhoods of residence in Malmö, Sweden (as defined by small-area market statistics (SAMS) areas) do not condition women’s participation in population based mammography screening. Thus, interventions should be directed to the whole city and target women with a higher risk of non-attendance.


Dear Editor,
An established area of research in social epidemiology and public health concerns the [1]. Researchers aim to identify contextual influences of the neighbourhood purpose, multilevel analysis of variance is a fundamental methodology that allows appropriate measurement and interpretation of contextual effects [2,3]. However, many studies continue to focus on estimating and interpreting only measures of association (e.g., odds ratios) between specific contextual characteristics and individual health outcomes [4]. Unfortunately, this may lead to incorrect inferences and, thereby, incorrect conclusions. Though, multilevel analysis of variance is technically more complex than standard analyses and this may have deterred many researchers from applying it. This research article therefore proposes an innovative and accessible three-step approach to conducting multilevel analysis of variance in neighbourhood and health studies. Our approach distinguish We provide and compare different measures of (observational) contextual effects and introduce the area under the receiver operating characteristic curve (AU-ROC) as an intuitive measure to quantify general contextual effects.
While our contribution is fundamentally methodological, we illustrate our three-step approach by performing real empirical analyses paying special attention to describe and explain the applied methodology. Furthermore, we present our ideas in a didactic and conceptual fashion, rather than a mathematical one, in order to make our arguments and methods accessible to as broad a readership as possible.
Our team has considerable experience in the analysis and interpretation of multilevel analyses of variance and we have also published several tutorials on other aspects of multilevel modelling. We believe our study fills a gap in the current literature on multilevel analysis and it will therefore be received with interest by many researchers. We hope that our work will facilitate and improve the use and interpretation of multilevel regression analyses in Public Health which, in turn, will ultimately lead to improvements in public health practice.
(" Considering these ideas, we can identify at least three different analytical approaches in social associations (e.g., ORs) between specific contextual level variables and individual health (17), !%" adjusting for neighbourhood clustering. Finally, the multilevel analysis of individual !&" heterogeneity approach combines both the multilevel analysis of associations for estimation !'" of specific contextual effects and the multilevel analysis of variance (e.g., the degree of !(" clustering, ICC) for the investigation of general contextual effects (i.e., non-specific !)" contextual influences on health) (3) (2). The small area variation approach typically applied !*" in Public Health represents a refinement of classical ecological studies on aggregated data.

#+"
The multilevel analysis of associations approach follows the conventional approach in #!" probabilistic risk factors epidemiology, while the multilevel analysis of individual ##" heterogeneity approach adopts a multilevel perspective for understanding heterogeneity of #$" individual responses around the average risk in a group (18). It is this last approach which we #%" develop and promote in this study.
Interestingly, in spite of their independent origins and areas of application, the multilevel !" analysis of individual heterogeneity approach has many analogies with that adopted in other #" fields of epidemiology concerned with the identification of new candidate risk factors and $" biomarkers and the evaluation of diagnostic and screening test. In those research fields, it is %" well known that measures of average association like ORs provide limited information for &" gauging the performance of a diagnostic, prognostic, or screening marker (19). Accordingly, '" the rule is that measures of association need be interpreted together with measures of (" discriminatory accuracy such as net reclassification improvement (NRI), integrated )" discrimination improvement (IDI) (20-22) and, especially, the area under the receiver *" operating characteristic curve (AU-ROC) (23, 24). Analogously, the multilevel analysis of !+" individual heterogeneity approach argues that estimates of specific contextual effects (i.e.,

!!"
average measures of association) provide insufficient information if they are not accompanied by measures of general contextual effects (i.e., degree of clustering) (1, 2, 18).

!$"
In the multilevel analysis of individual heterogeneity approach the ICC for hierarchical !%" multilevel structures (25) is a fundamental measure for quantifying general contextual effects.

!&"
As a concept, the ICC (i.e., the share of the total outcome variance which lies at the context !'" level, having adjusted for any covariates) is rather intuitive for continuous responses since the !(" individual-and contextual-level variances are both estimated and defined on the same scale.

!)"
However, the ICC proves less straightforward to understand and calculate when analysing been proposed to quantify the extent of general contextual effects. These include the pairwise #" odds ratio (PWOR)(14) and measures of heterogeneity such as the median odds ratio $" (MOR) (28,29). In any case, it is important to realize that the ICC is itself a measure of %" discriminatory accuracy (30, 31). Therefore, taking advantage of the analogy between the &" concept of discriminatory accuracy and the notion of general contextual effects, a simple but '" innovative approach is to express general contextual effects by means of measures of (" discriminatory accuracy like the AU-ROC (32, 33). The AU-ROC measure is well established among epidemiologists, public health practitioners and physicians and its computation is *" straightforward using standard statistical software.

!+"
In the current study, we present a novel three-step approach for the systematic investigation of !!" observational multilevel (e.g., individual and neighbourhood) effects on binary measures of !#" individual health and health care utilization, distinguishing between specific and general !$" contextual effects. To make our approach as accessible as possible, we present a conceptual !%" and didactic treatment of the issues rather than a technical and mathematical one. We

!&"
introduce and then demonstrate the utility of AU-ROC as a measure of general contextual !'" effects and we compare it to the ICC and the MOR. We illustrate our approach by analysing !(" two different binary outcomes: (i) use of psychotropic medication, which is related to both !)" psychological health and access to medication; and (ii) individual choice of a private vs. a !*" public general practitioner (GP), which is a behavioural outcome.

#+"
Population and methods personal identification numbers to ensure the anonymity of the subjects. The Regional Ethics !%" Review Board in southern Sweden as well as the data safety committees from the National Board of Health and Welfare and from Statistics Sweden approved the construction of the !'" LOMAS database.

!("
For the purpose of our study we created a fully anonymized sample that completely prevents !)" the identification of individuals using a combination of variables. This fully anonymized !*" sample is provided in the Online Supplementary Materials.

#"
To illustrate our three-step approach, we carried out two empirical analyses. In the first $" analysis the outcome variable was defined as use (= 1) or not (= 0) of psychotropic sedatives) and N06A (Antidepressants). In the second analysis, the response variable was practice (GP) during the year.

*"
Individual characteristics !+" In order to illustrate our approach as clearly as possible, we considered only three individual- level covariates: age categorized into five age groups, 35 39, 40 45, 50 54, 55 59, and 60 !#" 65 years, using the youngest age group as the reference category in the model specifications; sex that compared men (=1) with women (=0); !%" less that the median income in Malmö, psychotropic medication the reference category was high income while in the analysis of private GP choice !'" the reference category was low income. These choices are cosmetic, but ensure that we !(" estimate positive rather than negative associations between the outcome and income which are easier for readers to interpret (psychotropic medication use is higher among the poor while !*" private GP use is higher among the rich). The median income in Malmö was derived from boundaries which are constructed to maximise the internal homogeneity of housing tenure.

%"
The resulting neighbourhoods have an average population of around 1000 individuals.

&"
For simplicity, we categorized neighbourhoods according to whether the '" proportion of low income individuals in each neighbourhood was below the median across all (" neighbourhoods in the city. Paralleling the way we entered individual income into our models, in the analysis of psychotropic medication we set the reference category for neighbourhood *" income to be rich neighbourhoods while in the analysis of private GP we set the reference !+" category to be poor neighbourhoods.

!!"
Multilevel analysis of heterogeneity !#" The data have a two-level hierarchical structure with individuals (level 1) nested within !$" neighbourhoods (level 2). For the analysis we applied a three step-approach consisting of !%" fitting, interpreting and contrasting the results of three consecutive multilevel logistic GP) for individual ( ) in neighbourhood ( ).

!*"
Step 1 -T he individual effects model: Step 1 simply consists of fitting a conventional #+" single-level logistic regression for including only the individual-level covariates; neighbourhoods are completely ignored. In terms of our two illustrative applications, the ##" covariates are age, sex and income. The model is therefore written as (1) where denotes the probability that individual in neighbourhood uses psychotropic #" medication (or private GP) given their individual characteristics , and .

$"
The regression coefficients measure the associations between the log-odds of the %" health outcome and each covariate all else equal and when exponentiated these are translated &" to ORs. For ease of illustration we have entered age into the model linearly, but we shall relax '" this assumption when we fit the model. Post-estimation, predicted probabilities are (" calculated for each individual and are used to calculate the AU-ROC for the model.

)"
The AU-ROC (32, 33) is constructed by plotting the true positive fraction (TPF) (i.e., Step 2 T he general contextual effects model: Step 2 consists of extending the Step 1 !*" model from a conventional single-level logistic regression model to a two-level individuals- within-neighbourhoods logistic regression model. This extended model is written as #!" (2) ##" where denotes the random effect for neighbourhood . These effects are assumed normally #" distributed with zero mean and variance , a parameter to be estimated.

$"
Postestimation, values can be assigned to these effects via empirical Bayes prediction. These associated with very small neighbourhoods. The statistical uncertainty surrounding these *" predictions can also be calculated and communicated via error bars (e.g., 95% confidence !+" intervals). This uncertainty must be taken into account when ranking neighbourhoods, for (37-39). More generally, the interpretation of neighbourhood rankings needs be done in !%" relation to the general contextual effect (see elsewhere for empirical examples)(2).

!&"
The general contextual effect is appraised using the estimated between-neighbourhood !'" variance as this quantifies the variability in unobserved influences on the health outcome !(" common to individuals living in in the same neighbourhood. Thus, is assumed to reflect variation in any direct effects of neighbourhood context captured by the neighbourhood in an observational study, it might also #+" reflect neighbourhood compositional differences in unmodelled individual characteristics #!" (e.g., unobserved selection of individuals into neighbourhoods). We calculated three different information alone for identifying individuals with, or without the outcome, the predicted #" probabilities from the Step 2 model are based on both the individual-level covariates and the $" predicted neighbourhood random effect . Consequently, the AU-ROC of the Step 2 model %" can be compared with that from Step 1 to quantify the added value of having information on &" the neighbourhood of o identifying the outcome of the '" individuals. Therefore, in this approach the general contextual effect of the neighbourhood is (" appraised by quantifying the increase in the AU-ROC achieved when adding general )" neighbourhood information to the individual level predictions calculated in the Step 1 model.

*"
The larger this difference, the greater the general neighbourhood effect is.

!+"
(ii) We chose to calculate the ICC based on the latent response formulation of the model as it is the approach most widely adopted in applied work. This formulation assumes a latent !#" continuous response underlies the observed binary response and it is this latent response for which the ICC is calculated and interpreted. The higher the ICC, the more relevant neighbourhood context is for understanding individual latent response variation (10, 12, 25).

!&"
The ICC is calculated as values from two different neighbourhoods, and comparing the one from the higher risk #" neighbourhood to the one from the lower risk neighbourhood. In simple terms, the MOR can $" be interpreted as the median increased odds of reporting the outcome if an individual moves %" to another neighbourhood with higher risk. Therefore, the higher the MOR the greater the &" general contextual effect. The MOR is calculated as where represents the inverse cumulative standard normal distribution function. In )" absence of neighbourhood variation (i.e., ), the MOR is equal to 1.

*"
Step 3 T he specific contextual effects model: Step 3 consists of adding the neighbourhood !+" covariate of interest to the model in order to estimate the specific OR for a contextual !!" variable. In our case we are interested in the effect of neighbourhood income (i.e., rich or !#" poor) on each outcome. The step 3 model can be written as where denotes the additional neighbourhood covariate.

!("
Specific contextual effects measure the associations between contextual characteristics of the neighbourhood (e.g., rich or poor neighbourhood) and the individual outcome. As in the case !*" of individual-level observational effects, specific contextual effects are estimated using #+" measures of average effect such as ORs. However, an extended misunderstanding when #!" ##" OR of contextual variables (10, 28, 29).
The point is that the multilevel regression provides regression coefficients for individual !" variables that are adjusted for the neighbourhood-level random effects. That is, they reflect #" the association between individual level variables and the outcome within a specific $" neighbourhood. They are %" ORs. However, in multilevel logistic regression, a contextual OR can hardly be interpreted in &" this way since the contextual variable is constant for all individuals in the neighbourhood. The '" contextual OR can at best be interpreted as contrasting two neighbourhoods differing in the the neighborhood variance in the quantification of a contextual OR.

!!"
The lower and upper bounds of the IOR-80% for are calculated as The IOR-80% is defined as the middle 80% range of the distribution of ORs formed by !%" making random pairwise comparison between neighbourhoods exposed and non-exposed to the contextual variable. The IOR-80% interval is narrow if the between-neighbourhood !'" variance is small, and it is wide if the between-neighbourhood variance is large. If the !(" IOR-80% interval contains 1, then for some neighbourhoods the association is in the opposite direction to the overall OR (28) (10).

!*"
An alternative to the IOR-80% is the Proportion of Opposed Odds Ratios (POOR). That is, the proportion of ORs with the opposite direction to the overall OR (10). The values of the #!" POOR extend between 0% and 50%. A POOR of 0% means all ORs have the same sign. A

##"
POOR of 50% means that half of the ORs are of the opposite sign and so the association is very heterogeneous. For our binary measure of neighbourhood income, the POOR is !" calculated as #" .

$"
Observe that in Step 2 we calculated the AU-ROC as a way of quantifying neighbourhood %" general contextual effects. In Step 3, we included a specific contextual characteristic of the obtained by combining the available individual information and the neighbourhood identity.

*"
The latter captures the totality of potentially observable, but also unobservable neighbourhood factors. The inclusion of a specific neighbourhood contextual variable as a fixed-effect !!" covariate will explain some of that neighbourhood variance (that is, decrease the average absolute size of the neighbourhood estimates) and, thereby reducing the predictive role of !$" the neighbourhood random effects. However, this change to the model specification !%" simultaneously improves the model prediction through the addition of the regression coefficient for the neighbourhood income variable. Because of this balance the discriminatory !'" accuracy of the Step 2 and 3 models will be effectively the same.

!("
Step 3 provides a way of understanding the mechanism behind the observed general adding the specific neighbourhood effect (i.e., neighbourhood income variable) in Model 3 In our case, a large PCV would suggest that the general contextual effect is substantially !" mediated by the neighbourhood income variable.

#"
Summary of the multilevel analysis of heterogeneity approach $" In multilevel analysis of heterogeneity, we need a joined analysis that includes individual %" variables, neighbourhood boundaries, and neighbourhood characteristics. We need to include &" measures of association, variance and discriminatory accuracy. The simpli '" approach based on the calculation of ORs alone is insufficient (" In our two example studies we perform a series of three consecutive regression models. )" We start with Model 1 (Step 1) that only includes individual-level covariates in a standard *" (i.e., single-level) logistic regression. The selection of these individual variables is based on the assumption that they condition the outcome and also the neighbourhood of residence. For instance, age is associated with use of psychotropic medicine and individuals may move to !#" certain neighbourhoods when they become older. That is, we aim to prevent compositional In Model 2 ( Step 2) we quantify the added value of having neighbourhood level information.

!)"
We only include the neighbourhood boundaries without specifying any neighbourhood !*" characteristic. We analyse the change in the AU-ROC compared with Model 1. We also #+" interpret the ICC and the MOR. This information tells us about the size of the general #!" contextual effect.

##"
In the final model, Model 3 ( Step 3), we include specific neighbourhood information explains a large share of (PCV is high) the IOR-80% will be narrow and the POOR low. '" This case illustrates a situation where the neighbourhood context conditions the outcome (i.e., (" high and ICC). It also demonstrates that this influence appears mediated by the contextual )" variable (neighbourhood high income) so the contextual variable is not only strongly *" associated with the outcome but it also explains the neighbourhood variance and thereby shows a narrow IOR-80% or a low POOR. In other words, the conclusion would be that the since was low from the beginning, the IOR-80% would also be narrow and the POOR low. associated with the outcome and the IOR-80% is narrow.

#+"
Model estimation #!" The models were estimated using Markov chain Monte Carlo (MCMC) methods as ##" implemented in the MLwiN multilevel modelling software (40). We specify diffuse (vague, that the lengths of these periods are sufficient. The Bayesian deviance information criterion $" (DIC) was used as a measure of goodness of fit of our models (41). The DIC considers both %" the model deviance and its complexity. Models with smaller DIC are preferred to models with &" larger DIC, with differences of five or more considered substantial"(42).

'"
Online supplementary materials We also provide the saved MLwiN worksheet for each model and an Excel sheet for the *" calculation of the ICC, MOR, 80%IOR and the POOR. A Stata do-file and dataset is also made available for users of that software. personal identification numbers to ensure the anonymity of the subjects. The Regional Ethics

!'"
Review Board in southern Sweden as well as the data safety committees from the National LOMAS database.

!*"
For the purpose of our study we created a fully anonymized sample that completely prevents

!"
Characteristics of the population (Table 1) #" In the study sample, use of psychotropic drugs was more frequent in individuals with low $" income and in poor neighbourhoods while the opposite was true for visiting a private GP.

%"
Rich neighbourhoods had a higher percentage of people 55 years or older and a slightly lower &" percentage of men than poor neighbourhoods. Analysis of the use of psychotropic drugs (Table 2) $"

%"
The individual level population average Model 1 shows that use of psychotropic drugs &" increases monotonically with age and was more frequent for women and among people with '" low income. These individual characteristics, however, were not sufficient for predicting  In Model 3 we observed that, over and above individual income, age and sex, living in a low $" income neighbourhood conclusively increased the individual probability of use of %" psychotropic drugs (i.e., OR= 1.29). However, the 80%-IOR included 1 and the percentage of &" ORs of opposite direction was considerable (POOR=11%). In Model 2, The ICC and the MOR were low (i.e., 1.1% and 1.20 respectively) which #" indicated that the neighbourhoods, as defined by the SAMS geographical boundaries, do not  (Fig. 1).

)"
In Model 3, inclusion of the neighbourhood income variable explained 42% of the whole city sample as reference. Fig. 2A represents the values obtained from a model   neighbourhoods, which expressed itself as a substantial overlapping of the confidence #" and need to be $" interpreted side-by-side with measures of general neighbourhood effects. Indeed, the ICC was %" very low in both models.

&"
Analysis of choosing a private vs. a public specialist physician in general practice (Table 3) '" for men and women, and that they were somewhat higher among individuals aged 50 to 64 *" than among younger individuals. High individual income clearly increased the odds of in Model 1 was capturing not only a modest within neighbourhood association but also a !(" stronger between neighbourhood association, A situation that was confirmed in Model 3 (see

!)"
Specific contextual average since the neighbourhood income was, on !*" average, strongly associated to choosing a private GP.

#%"
Model 3 shows that high neighbourhood income was, on average, strongly associated with !" visiting a private physician (OR= 3.50). So the customary interpretation would be that, over #" and above individual income, age and sex, living in a high income neighbourhood strongly $" increased the individual probability of visiting a private physician. However, this contextual %" variable only explained a small share (PCV= 11%) of the initially large neighbourhood &" variance. Therefore, unmodeled variability between neighbourhoods remained large as '" expressed by the wide IOR-80% = 130.28 -0.09. Also the POOR indicated that 33% of the likelihood of visiting a private GP than an individual from a low income neighbourhood. That

*"
is, the average OR hides strong heterogeneity around the average association. individual will choose a private versus a public GP (see Figure 3).

!*"
If the large observed general neighbourhood effect were mediated by neighbourhood income  We observed a bimodal distribution for the neighbourhood differences with two groups of (" neighbourhoods, one smaller group with a higher probability of visiting a private GP, and )" another larger group with a lower probability. This bimodality reflects the underlying nature *" of private GP use. In our case, it revealed that over and above age, sex and individual income,

!%"
This bimodality was not a concern for the statistical analysis as the number of reduced the bimodality and it is assumable that the bimodality might be further reduced by #" modelling neighbourhood income in a more flexibly way (e.g., by entering a continuous $" measure of income as a polynomial). The pattern of neighbourhood differences also suggests %" the existence of spatial correlation which could be conditioned by the segregation of private &" practices in specific geographical areas. It is possible to allow for spatially correlated random '" effects in multilevel logistic regression, but this is beyond the scope of the current article. segregation"(47-49). Applying those ideas to our data, we fit a separate multilevel logistic !+" regression analyses, modelling low individual income as the response variable. We estimated !!" a neighbourhood variance of 1.032 which corresponds to an ICC of 24% and substantial !#" segregation. Therefore, adjusting neighbourhood income for individual income is based on !$" strong extrapolations since there are few individuals with high income living in poor !%" neighbourhoods as well as few individuals with low income living in rich neighbourhoods. private physician in 1999 (i.e., ICC = 33%, MOR= 3.36) (28) but a minor general #" neighbourhood effect for use of anxiolytic-hypnotic drugs (i.e., ICC= 1.7%, MOR = 1.25) in $" 1991-1996 (50).

%"
We question the current probabilistic, risk factor epidemiological approach based on the &" simple interpretation of ORs for specific individual and contextual (e.g., neighbourhood) '" characteristics in isolation (18). We promote a three-step multilevel analytical approach.
Step covariates, then evaluating the ORs and calculating the discriminatory accuracy (e.g., AU-*" ROC) of these variables.
Step 2 consists of extending the model to two-levels (by adding the !+" neighbourhood random effect) and then assessing the importance of general contextual effects !!" using the ICC and AU-ROC.
Step 3 consists of adding specific neighbourhood characteristics !#" (i.e., specific neighbourhood effects) to the model and interpreting their ORs jointly with the !$" size of the initial general contextual effect and the size of the neighbourhood variance Applying our three-step approach to psychotropic drug use, we observed that sex, increased !*" age, and individual low income were associated with the use of this medication. However, the #+" information provided by these individual characteristics did not allow users of psychotropic #!" drugs to be distinguished from non-users with any degree of accuracy (AU-ROC= 0.616). We

##"
also observed a very small general contextual effect since accounting for neighbourhood of #$" residence only increased the AU-ROC by 0.014 units and both the ICC (i.e., 1.1%) and the #%" ! #*" MOR (i.e., 1.20) were very low. In fact, our results suggest that SAMS neighbourhoods were !" more similar to simple random samples from the population of Malmö, than to meaningful #" contexts influencing individual psychotropic drug use.

$"
The low AU-ROC of the neighbourhood context (i.e., the low general contextual effects) %" needs to be considered when interpreting the small but conclusive association between low &" neighbourhood income and individual use of psychotropic drugs. One could argue that this '" neighbourhood variable explained 42% of the neighbourhood variance, but as such variance POOR informed that 11% of the time the positive association between low neighbourhood *" income and individual psychotropic drug use was in the opposite direction with a decreased, !+" rather than increased, propensity of using psychotropic drugs in the low income neighbourhoods.

!#"
Paradoxically, when the neighbourhood variance is low (i.e., there is a weak general !$" or the !%" contextual variables (i.e., specific contextual effect). This situation happens because we assign words, the less neighbourhood boundaries matter for the outcome, the easier it is to get outcome.

!*"
assume that there is a strong intra-neighbourhood correlation. However, we need to check this

#+"
assumption and always interpreted the specific contextual effect (i.e., OR and 95% confidence #!" interval) considering the size of the initial general contextual effects (e.g., ICC or AU-ROC).

##"
Following the three-stage approach promoted in this article ensures a more appropriate The low general neighbourhood effects could be related to the fact that psychotropic drug use !" may be conditioned by other kind of contexts like the physicians or the Primary Health Care #" centres where the individuals are treated. The SAMS areas were relatively easy to obtain but $" their definition was not based on robust theory related to the contextual processes and %" mechanisms that may condition use of psychotropic drugs (or, for that matter, the choice of a &" private GP). In fact, the relevant context may not be at the neighbourhood level at all.

'"
Prescription of psychotropic drugs is homogenously regulated all over Sweden (51), which (" may reduce the influence of the neighbourhood on individual use of this medication.

)"
However, larger contextual effects might be observed when studying countries with different *" health care systems and therapeutic traditions or where psychotropic drugs are available over !+" the counter. We have previously observed such a situation in the context of studying blood pressure. We identified a very low general contextual effect of the city areas in Malmö (6), but this effect was much higher when analysing countries with different health care systems !%" In summary, we were not able to identify with accuracy the factors that predict psychotropic drug use. What we did find was that individual age, sex, and low income appeared to be poor predictors for identifying users of psychotropic drugs, and additionally including !(" neighbourhood of residence did not alter this situation. That is, the neighbourhood context had only a negligible influence on individual use of psychotropic drugs.

!*"
Choice of a private vs. a public GP neighbourhood income) was, on average, associated with choosing a private GP (OR = 3.50).
(" However, this specific neighbourhood variable only explained 11% of the large )" neighbourhood variance in Model 2 (i.e., = 4.479). In fact, in as much as 33% of *" comparisons between rich and poor neighbourhoods, the OR for neighbourhood income was !+" in the opposite direction so high neighbourhood income was associated to a lower rather than !!" a higher propensity of choosing a private GP.

!#"
We observed that, on average, utilization of private GPs was higher among high income !$" people and in high income neighbourhoods than in the low income categories, which deserves might depend on cultural preferences rather than solely on economic reasons. It is known, for !*" example, that choice of sector also carries a symbolic meaning (54) and high income #+" individuals have been argued to intrinsically prefer private care. However, an alternative analysis, for instance, the degree of private GP provision in each neighbourhood might go (" some way to explaining the observed general contextual effects. )" Public Health implications

*"
Our results are relevant when planning public health interventions. For example, policies to !+" improve psychological health or reduce the use of psychotropic drugs in the city of Malmö, would need to realize that focusing on specific neighbourhoods would not be effective !#" because of the low discriminatory accuracy of this information. In fact, the same is true for the individual characteristics we analysed: age, sex, and income. Put differently, neither !%" neighbourhood of residence nor the individual characteristics studied provided accurate information for identifying target groups. If policy makers do choose to focus on those !'" individuals and neighbourhood with a higher average risk of using psychotropic drugs (which !(" would be the normal procedure in risk factors epidemiology), they need to be aware that many psychotropic users would be labelled as -users of psychotropic !*" drugs would be labelled as -only high risk groups would #+" unnecessarily expose many individuals to an intervention they do not need and would leave #!" many individuals untreated because they belong to low risk groups. Perhaps a better approach ##" would be to launch an intervention on the whole population. In any case, considering the #$" balance between harms and benefits, an intervention with low discriminatory accuracy #%" conveys that the principle of primum non nocere must be an absolute condition.
The public health implications of our second analysis are very different. Here, policies to !" increase the use of public GP services should mostly focus on specific neighbourhoods,

#"
perhaps by opening local public GP alternatives.

$"
Multilevel analysis of heterogeneity and risk factors epidemiology %" The multilevel analysis of heterogeneity we present in our study is rather innovative (18).

&"
Most studies analysing the role of individual or contextual variables on health adopt a '" probabilistic perspective based on the analysis of differences in average risk between exposed (" and unexposed groups (55) but without recognizing the value of analysing variance (56) . This )" *" analyses have only focused on the identification of contextual risk factors such as !+" neighbourhood social capital and neighbourhood deprivation. From this perspective small or !!" even tiny effects (e.g., OR = 1.5 or even lower) with very low discriminatory accuracy are !#" considered relevant. The problem is that by doing so we promote population level policies and !$" interventions that may lead to both under and overtreatment, as well as unnecessary side !%" effects and costs. It also raises ethical concerns related to misleading risk communication and the perils of both unwarranted interventions and stigmatization of exposed individuals (57).

!'"
The multilevel analytical approach we propose differs fundamentally from the classical one. the ICC) (3, 10) or, analogously, the discriminatory accuracy of using the boundaries of the !" neighbourhoods in the analysis (i.e., the AU-ROC) (32, 33). The existence of individual #" dependence within neighbourhoods is not only the sine qua non for applying statistical $" multilevel analyses but also the size of this dependence provides fundamental substantive %" information (1, 18).

Strength and weaknesses
'" Our current study tries to quantify the relevance of neighbourhoods in Malmö for neighbourhoods as this is the most common design in neighbourhood and health studies.

!+"
However, to constrain the study of contextual effects to a single geographical level (e.g.,

!$"
Nevertheless, the analytical approach we promote can be developed for more than two levels !%" of analyses (e.g., individuals nested in households nested in neighbourhoods)(2) as well as for heterogeneity that only considers individuals nested in neighbourhoods provides a better basis !*" for informed decisions in public health than the simple ecological or spatial analyses of small #+" area variation or classical multilevel analysis of contextual risk factors (2).

#!"
The identification of causal effects in observational epidemiology and, more specifically, in poor neighbourhood means is difficult to specify and it would need a deeper sociological %" analysis. In the adjusted analysis we only considered individual age, sex and income as our &" main purpose was to illustrate the methodology. Therefore, we cannot exclude the existence '" of omitted confounding factors. Nevertheless, in neighbourhood analyses it is always a caveat (" to distinguish between confounder and mediator variables as frequently a common cause of )" both place of residence and the health outcome may also be a mediator of the neighbourhood *" effect (for instance low income is associated to using psychotropic drugs and low income !+" individuals may be segregated to poor neighbourhoods but, in turn, living in a poor !!" neighbourhood may reduce the chances of increasing an there may be problems of extrapolation (i.e., making inferences beyond the range of the data,) neighbourhood will also change the neighbourhood context). In general, drawing valid causal inferences in observational epidemiology is difficult and this is especially the case in

#!"
Correspondence between the different measures used to estimate general contextual effects

##"
There is a clear correspondence between the ICC and the AU-ROC so when the ICC is high the AU-ROC is also high. However, the ICC is not influenced by the number of individuals at #%" the neighbourhood since its calculation is based on the neighbourhood variance which, in standardized for neighbourhood size (i.e., the number of individuals in the neighbourhoods).

#"
On the other hand, the AU-ROC is based on the calculation of the TPF and FPF for different $" thresholds of the predicted probability. Since this predicted probability is an individual level %" variable, large clusters contribute with more individuals. Because of this difference, it could &" be possible to find a high ICC but a low AU-ROC if the number of individuals is relatively '" much larger in some neighbourhood than in others. This situation does not mean that the AU- expressing that most individuals have the same predicted risk, irrespective of whether they !$" visit a private GP or not, and subsequently, that neighbourhoods, in the given context, do not !%" discriminate with accuracy individuals that visit a private GP from those who do not.

!&"
Otherwise, when neighbourhoods sizes are similar there is a clear correspondence between the !'" ICC and the AU-ROC values (32, 33).

!("
There is also a correspondence between the MOR and the ICC as both are monotone functions !)" of the neighbourhood variance, and this correspondence makes the MOR a measure of general !*" contextual effects. However, the MOR is a measure of probability and not of components of #+" variance as the ICC. The MOR expresses the size of the heterogeneity between the #!" neighbourhoods and the ICC the size of the clustering within neighbourhoods.

##"
The identification of the units of analysis individual is delineated by the skin. However, this is not the case when it comes to identifying #" contextual units. For this purpose, we frequently use geographical and administrative $" boundaries delineating small areas such as neighbourhoods, blocks, census tracts, or even %" large territories such as states, counties or countries. We assume that these boundaries analyses. However, the fixed effects approach prevents the further study of contextual level ##" variables (e.g., neighbourhood low income). Besides, the model is not parsimonious. For prediction of neighbourhood effects in multilevel regression is based on empirical Bayes #" prediction which protects against this bias by being a so-called shrinkage estimator (12). More $" logistic model provides inconsistent estimates of the %" regression coefficients when the number of individuals per neighbourhood is low due to what &" is known as the incidental parameter problem (68) in which case it may be more appropriate '" to consider conditional logistic regression. ("

Summary
)" In observational epidemiology of neighbourhoods and health, there are many unsolved *" problems concerning the identification of the relevant contexts for specific health outcomes.

!+"
There are also specific difficulties for drawing causal inferences. Furthermore, in common !!" with other fields in epidemiology, the traditional approach in multilevel analysis of !#" neighbourhood and health maintains a probabilistic approach focused on the analyses of !$" associations and considers the analyses of variance as a secondary task (56). However, some !%" authors, including ourselves (2,5,7,8,28,59,60,62,63,69,70) stress that the simultaneous makers. Our study provides concepts and innovative analytical approaches like the use of the #!" AU-ROC that allow improved multilevel analysis of neighbourhood and health.

##"
Finally, performing and interpreting multilevel regression analyses is an interesting task and #$" many technical and conceptual advances have been performed during the last three decades. *" !+" !!"