Study population and study area

Data collection was performed within the health monitoring units in Bavaria (GME, Gesundheits-Monitoring-Einheiten) which are organized by the Bavarian Health and Food Safety Authority. Main goal of the GMEs is to monitor health status of children in Bavaria. Therefore, in three consecutive years surveys with identical procedures concerning data collection were conducted within the framework of the obligatory school entrance health examination in three rural and three urban study regions. All parents gave their written informed consent. The ethics committee of the Bavarian medical council approved the procedures of data collection before the first survey [18]. There were only slight modifications of the questionnaires between the surveys.

This analysis considered 3499 children aged 5–7 years in one of the GME study regions, the city of Munich. Data were pooled from the three surveys conducted between 2004 and 2007 in Munich. The children were clustered in 18 school enrolment zones with a range of 117 – 331 children per school district. These districts were used as a proxy for the children’s close neighbourhood environment.

Measures of overweight

Weight and height were objectively measured by trained staff of the local health authority. Age–specific BMI percentile curves specific for boys and girls, respectively, were used to derive cut-offs for defining children as overweight or obese. We used the International Obesity Task Force (IOTF) cut-off values by Cole et al. [19]. In our analysis the definition of overweight did also include children with obesity.

Individual characteristics from parental questionnaires

We defined three categories of parental education. The highest level of completed education achieved either by the mother or the father was considered. ‘High’ included a final degree at university or technical college, A-levels, or advanced technical college entrance qualification. ‘Middle’ included upper secondary school certificate or adequate graduation. ‘Low’ included a lower secondary school certificate or no graduation.

Household equivalent income was calculated based on the reported monthly household net income as disposable income after taxes and social transfers weighted for age and number of household members according to the Organization for Economic Co-operation and Development-modified scale [20]. A relative poverty threshold was defined as 60 % of the median household equivalent income in Bavaria [21]. Three income groups were created: ‘low’ (<60 % of median), ‘middle’ (60 % of median – median), and ‘high’ (>median). Due to a high number of missing information on household income in our dataset we created an additional income group ‘not indicated’ including parents who did not respond on their income in order to avoid selection bias [22].

Parental working status was considered as a binary variable. Unemployment within household was applied if both parents were marginally employed at most. The category employment was applied if one parent was at least part-time employed. A binary variable of single parenthood was created by combining three answers about single parent, family status, and living together with a partner. Only responses showing consistency in all three answers were taken into account [22].

Household crowding was present if there was more than one person per room or less than 20 m² per person available. Nationality of the child was used as an indicator of migration status. Following the rationale of Schenk et al. [23], categories of German nationality and non-German nationality, including dual citizenship, were defined.

Birth weight and BMI of the mother were obtained from parental questionnaires, too. Three categories of birth weight were generated using international cut-offs from the Pediatric Nutrition Surveillance System (PedNSS) by the Centres for Disease Control and Prevention (CDC) [24]: Low (<2500 gram), normal (2500 gram - 4000 gram), and high (>4000 gram). Maternal BMI data were categorized into normal (<25 kg/m²), overweight (25 kg/m² - <30 kg/m²), and obese (≥30 kg/m²).

Neighbourhood socioeconomic variables

We considered five aggregated variables on the level of administrative primary school enrolment zones in which the children live. Averages from the years 2006 and 2007 were calculated. From the city council of Munich we obtained data on foreigners and migration background (percentage of residents with no German citizenship, and percentage of residents with a German citizenship and a migration background), and household data (percentage of single parent households). Data on education were provided by microm GmbH, Neuss, Germany (percentage of households with lower education and with vocational training).

Statistical analysis

All statistical analyses were performed using SAS statistical software package version 9.3 (SAS Institute, Cary, NC, USA).

We performed bivariate logistic regression between socioeconomic neighbourhood variables, individual variables and overweight. All individual variables which were associated with overweight with a Wald’s P <0.2 in bivariate logistic regression were included in multivariate analysis. All socioeconomic neighbourhood variables which were associated with overweight with a Wald’s P <0.2 were taken into account for principal component analysis (PCA). This cut-off is recommended for initial covariable selection [25].

PCA was used as a statistical procedure for data reduction of correlated variables because it creates non-correlated orthogonal linear combinations explaining the maximum of variance [26]. The first component explains most of the variance and was therefore used as an indicator for the socioeconomic neighbourhood environment. Higher values of the index imply a lower neighbourhood SEP. Spearman rank correlation coefficients between socioeconomic neighbourhood variables used for PCA and the first component were calculated to check how each neighbourhood socioeconomic indicator was represented in the index. Finally, the index was categorized into tertiles (high, middle, and low neighbourhood SEP).

The variance inflation factor (VIF) (VIF _i  = 1/T _i ) was used to assess multicollinearity between the covariables. The VIF is calculated with the tolerance (T) (T _i  = 1 − R _i ² ). R _i ² is the calculated variance of each covariate associated with all other independent variables. A VIF higher than 10 indicates a serious problem of multicollinearity [27–29].

We applied multilevel logistic regression modelling with school districts as random intercepts to correct for clustering of individuals within the same school district [30]. Our calculated index of neighbourhood SEP was modelled as a 2nd level variable. All individual level variables were considered on the 1st level. Multilevel modelling enables to estimate variance between school districts separately from residual variation between individuals. Thus, this modelling approach makes quantification of overweight variance between neighbourhoods being explained by our calculated neighbourhood SEP index possible. The GLIMMIX procedure in SAS was used for calculating multilevel models.

In a first empty null model only school districts were modelled as random intercepts in order to assess the covariance parameters for the random intercept variance of overweight between school districts. In a second model individual level variables were included to analyse how these variables were associated with overweight, and how much of the variance between school zones was explained by these factors. In the full third model the index of neighbourhood SEP was added to assess if there was an independent association between neighbourhood SEP and overweight. For multivariate analysis observations with missing values in any independent variable were not taken into account, except for household income. The category ‘not indicated’ was generated because of a high number of missing values for this variable. For all other variables considered for multivariate analysis the amount of missing values was acceptable (≤7 %).

Multilevel models were adjusted for the three survey years considering each survey as a dummy variable and maternal BMI and birthweight. For the neighbourhood intercept variance estimates covariance tests were performed and p-values and confidence intervals were calculated. Based on the neighbourhood intercept variance estimates we calculated the proportional change in variance (PCV) in percent according to the following equation by Merlo et al. [31, 32]: PCV = ((V_a-V_b)/V_a) × 100. V_a is the between neighbourhood variance of the empty model and V_b is the between neighbourhood variance including covariables, in the individual model and the full model respectively. As a sensitivity analysis, we performed multiple imputation for missing values for household income. Multiple imputation of hierarchical data is still a research area with remaining issues and there is still no standard procedure to pool covariance estimates from the random intercepts [33]. Therefore, we performed multiple imputation for fixed effects only in order to check if estimates differed to our models considering missing values as an additional income category. We applied cumulative logistic regression imputation within the PROC MIANALYZE procedure in SAS which is appropriate for ordinal variables [34–36]. In order to consider our clustered data structure, school zones were taken into account as dummy variables within the imputation procedure.

Characteristics of study population

Principal component analysis and neighbourhood SEP index

On the neighbourhood level, except of the percentage of single parent households, all other four aggregated socioeconomic variables were associated with overweight in bivariate logistic regression (Wald’s P <0.2) and were therefore used for PCA (results not shown). The four neighbourhood variables percentage of foreigners, percentage of German residents with migration background, percentage of households with lower education, and percentage of households with vocational training were significantly correlated with the neighbourhood SEP index derived from the first principal component. Spearman rank correlation coefficients ranged between 0.69 and 0.97 and had p-values <0.05 (results not shown). According to our calculated neighbourhood SEP index, 39.3 % of the study population lived in school districts with a low neighbourhood SEP (Table 1).

Multilevel logistic regression

Multicollinearity analysis was performed with the neighbourhood SEP index and all eligible individual variables for multivariate analysis. The values of the VIFs showed acceptable values ranging from 1.0 to 1.8 (results not shown).

The full model including neighbourhood SEP explained additional 19.1 % between neighbourhood variance of overweight. However, the neighbourhood intercept variance estimates from which the PCV was calculated showed wide confidence intervals.

Our sensitivity analysis with multiple imputed data for missing values on household income revealed similar estimates for individual variables and contextual neighbourhood SEP. Therefore, we reported our multilevel results without multiple imputation of the ordinal income variable because we would like to guarantee valid covariance parameter estimates of our variance components (see methods for further details). Moreover, we analysed potential interactions between our significant fixed estimates of our final model and no significant interactions were detected (results not shown).

Availability of data and materials

The dataset supporting the results of this article may be requested from the Bavarian Health and Food Safety Authority, steering committee of the health monitoring units in Bavaria, Munich, Germany.