Data on children’s height and weight were extracted from the Register of Primary Health Care Visits (Avohilmo), maintained by the Finnish Institute for Health and Welfare (THL) [16]. Avohilmo includes real-time data on primary healthcare visits, including measured height and weight, collected via automatic data transmission from electronic health records of primary health care units. The data extraction criteria were that a child had visited a child health clinic, school health care or student health care between 1st of January 2018 and 31st of December 2018 and both height and weight were recorded during the visit (n = 397,047). Indicators extracted for the current study included date of birth, sex, age and height and weight measurements with their respective measurement dates. The exact age at measurement was calculated based on the child’s date of birth and the date of health care visit.

The data were validated as follows; 1) deviation statistics for height and weight values were calculated using the Finnish growth standard as reference values (relative to weight by sex and height, height by sex and age, body mass index (BMI, kg/m²) by sex and age, children’s BMI corresponding to the adult BMI (ISO-BMI kg/m²) [17], 2) children with deviation values outside the [-4,4] boundary were excluded, 3) height and weight measurements resulting in ISO-BMI ≥50 were excluded. In addition, 1,537 children were excluded because valid height and weight measurements were not available in 2018. As a result, the data included 395,510 children who were 2–17 years old and had at least one valid height and weight measurement in 2018.

Avohilmo’s data on children’s height and weight were linked on an individual level with Statistics Finland’s data from 1 January 2014 to 31 December 2018 on adults’ (both parents’) socioeconomic position (SEP) living in the same address as a child using deterministic linkage and personal identification code.

Data on parents’ SEP were not found for 7,887 children. In addition, siblings and half-siblings and families with two female or two male adults were excluded from the analysis (n = 193,200). As a result, each parent was included in the data only once, as was only one child from each family. The number of families with two female or two male adults was 374. The final data included 194,423 (100,216 boys and 94,207 girls) children with measured height and weight and information on parents’ SEP.

Overweight and obesity were defined according to the WHO growth reference for children [18, 19]. For children from two to five years of age, the definition for overweight and obesity were a BMI-for-age value greater than +2 SD and +3 SD above the WHO Child Growth Standard median, respectively [18, 20]. For children over 5 years old, overweight and obesity were defined as a BMI-for-age value greater than +1 SD and +2 SD above the WHO Growth Reference median, respectively [19, 21].

The prevalence of overweight (including obesity) and obesity in boys and girls by parents’ SEP are presented in Supplementary Tables S1, S2.

The following parents’ SEP indicators were selected for analyses; mother’s and father’s educational level of highest qualification/degree, household’s disposable monetary income, and in addition, the father’s and mother’s age and municipality group of municipality of domicile according to the 2016 regional division.

The SEP variables had several categories. For the analysis the SEP variables were re-categorized as follows: 1) Parental age was classified into six categories: <30, 30–34, 35–39, 40–44, 45–49, ≥50 years and 2) child’s age classified into four categories: 2–6.99, 7–12.99, 13–15.99 and 16–17.99 years. 3) Father’s and mother’s educational level of highest qualification/degree was classified into three categories: low, medium and high. The category of low education included parents who did not have a degree, i.e., they had completed at most primary school. The category of medium level of education included parents who had completed secondary or high school or vocational school. The category of high education included parents who had a bachelor’s degree, master’s degree or higher degree. 4) Household’s disposable monetary income was calculated considering the size of the household as follows: Each household’s yearly disposable monetary income/12/weighting coefficient. Weighting coefficient: 1.0 to the first adult, 0.5 to the second and each subsequent person aged 14 years and over, 0.3 to each child aged under 14 years, 0.4 to each child of unknown age [22]. Household’s disposable monetary income was classified into three categories: low (<1,525 euros per month), middle (from 1,525 to 4,065 euros per month) and high (>4,065 euros per month). 5) Municipality of domicile according to the 2016 regional division was classified into three categories: urban, semi-urban and rural municipalities. In urban municipalities at least 90% of the population lives in urban settlements or the population of the largest urban settlement is at least 15,000. In semi-urban municipalities, 60%–90% of the population lives in urban settlements and the population of the largest urban settlement is at least 4,000 but less than 15,000. In rural municipalities, less than 60% of the population lives in urban settlements and the population of the largest urban settlement is less than 15,000 or 60%–90% of the population lives in urban settlements and in which the population of the largest settlement is less than 4,000 [23]. Data characteristics are shown in the Table 1.

Before categorizing, most of the SEP indicators were imputed. If no previous individual data were available (preferably in 2017 or secondly in 2014–2016), data from 2018 were used. Parents’ education was imputed using values from previous years. For continuous predictors, individual trends were fitted and used for prediction of missing values. For continuous predictor data with only one observation, one trend line was fitted and used for prediction of missing values.

The analyses were carried out using a randomly selected training data (n = 155,479, 80% of the data; 80,216 boys and 75,263 girls) and left out data (n = 38,944, 20% of the data; 20,000 boys and 18,944 girls), which was used for model testing and validation.

Risk ratios for bernoulli-distributed overweight (RR_OW) and obesity (RR_OB) according to SEP were estimated using generalized linear models and using the log -link function.

Generalized linear models for overweight (including obesity) and obesity were fitted for boys and girls separately. The effects of four predictor indicators (father’s education, mother’s education, household’s disposable monetary income and municipality group of municipality of domicile) were analyzed by adjusting for child’s, mother’s and father’s age. As a first step, the univariate effect of four predictor indicators were analyzed using adjustments. In the second step, alternative multivariate main effect models were analyzed. Finally, all predictor and adjusting indicators were tested for interactions.

The following alternative multivariate models were fitted: 1. Full model of main effects (four predictors and three adjusting indicators), 2. Models to exclude one of the predictors (four submodels), 3. Models to include one twoway interaction between predictors or between one predictor and one adjusting indicator (18 submodels).

All models were fitted in training data and submodels were tested in left out data. Deviance residuals were predicted for full model and all submodels. The sum of squared deviance residuals (D) in left out data was used as a test statistic to test the model against full model. The difference of D-statistics were considered as chi-square distributed with the number of freely estimated parameters dropped as degrees of freedom.

Chi-square statistic for main effects: Chi-square = (D-statistic of the full model of main effects) - (D-statistic of submodel).

Chi-square statistic for interactions: Chi-square = (D-statistic of model with one interaction) - (D-statistic of the full model of main effects).

The final model was validated by comparing Area under the ROC curve (AUC) in training and left out data.

The nonsignificant result from the test for equality of AUC between training and left out data was considered a valid model for obesity or overweight.

Stata/MP 17.0 statistical software was used for all data management and statistical analyses. The significance level was 0.001 for all tests.

For boys and girls, all main effects were significant for obesity and overweight models, except for household’s disposable monetary income for girls’ overweight and obesity models. None of the tested interactions were significant. All final models were valid with no significant differences in AUCs between training and left out data (Tables 2–5).

In multivariate models the risk for obesity was lower in boys in families with higher household’s disposable monetary income (RR_OB 0.76, 99.9% CI 0.61–0.94) compared to boys in families with low income. The risk for overweight was higher in boys in middle-income families (RR_OW 1.08, 99.9% CI 1.03–1.14) compared to boys in low-income families. The risk for overweight and obesity was lower in boys and girls whose father had high education (boys: RR_OW 0.72, 99.9% CI 0.68–0.77, RR_OB 0.58, 99,9% CI 0.51–0.65; girls: RR_OW 0.72 99.9% CI 0.66–0.77, RR_OB 0.54 99.9% CI 0.46–0.63, respectively) compared to children with a lowly educated father. Comparison of the highest with the lowest level of mother’s education showed decreased risk for overweight and obesity in boys (boys: RR_OW 0.79, 99.9% CI 0.74–0.84, RR_OB 0.58, 99.9% CI 0.51–0.65, respectively) and in girls (RR_OW 0.78 99.9% CI 0.72–0.84, RR_OB 0.56 99.9% CI 0.48–0.65) in children with highly educated mothers (Tables 2–5).

Risk for overweight and obesity was lower in boys and girls living in urban areas (boys: RR_OW 0.85, 99.9% CI 0.80–0.89, RR_OB 0.77, 99.9% CI 0.70–0.85; girls: RR_OW 0.80 99.9% CI 0.75–0.85, RR_OB 0.69 99.9% CI 0.61–0.78, respectively) compared with boys and girls in rural areas (Tables 2–5).

The main strength of the study is the large and comprehensive data from two administrative registers: the register of Primary Health Care Visits (Avohilmo) and Statistics Finland providing objective measures for both children’s height and weight and parents’ SEP. Parents’ SEP was found for almost all children (98%). Altogether, our data included measured height and weight and parents’ SEP for almost 200,000 children. As far as we know, there is no similar, large registry-based data available in other countries on both childhood obesity and parents’ SEP. Statistics Finland’s data on SEP is collected from various national registers, for example from the Population Register and the Income Register, making the data more comprehensive and reliable than data collected through questionnaires. The advantage of using register data is that there is no response-bias such as lower participation to surveys by people with obesity or low SEP [53]. In addition, there are not so many missing values, as there may be when asking children, or asking adults about information that they may consider sensitive, such as education and income.

However, there are also some limitations in the study. First, although the Avohilmo data collection has covered all outpatient primary health care delivered in Finland since 2011, the coverage of data on children’s height and weight was approximately 40% in 2018. Because most children and families attend to health check-ups and children are measured regularly, the low coverage of height and weight data is mainly due to problems with the electronic health records and technical data transmission in use [52]. The future challenge is to improve the coverage of Avohilmo data on the height and weight to it’s full potential, over 90%. It requires good collaboration between public health service providers, producers of patient’s electronic health records, and THL.

In addition, according to Statistics Finland’s data on adults living at the same address as a child, it is not always possible to verify if adults are parents, biological parents, or stepparents of the child. It is also difficult to ensure, whether the family is a nuclear family or a stepfamily. One limitation is also that Statistics Finland’s indicator “educational level of the highest qualification/degree” includes only degrees in secondary education or higher. However, very few people in Finland have no basic education. Therefore, if a person did not have a degree in secondary education, we assumed that the person had primary education. Another limitation is that the registry data used in the present study does not include information on health behavior such as diet and physical activity.

While no causal conclusions can be drawn from this cross-sectional study, our findings have important public health implications in Finland. The study showed that it is possible to develop the Finnish monitoring system on overweight and obesity in children to cover several aspects of parents’ SEP, as well as the degree of urbanization of the municipality of domicile. Our results also emphasize that primary prevention of obesity is essential, including identification of children at increased risk of obesity. Obesity prevention requires wide collaboration and a health-in-all-policies approach to improve children’s health and health equity.

Parents’ low SEP, measured with several indicators, was associated with overweight and obesity in children in Finland.

Linking data of administrative registers on children’s growth and parents’ SEP is a potential, feasible and valid approach to monitor the prevalence of overweight and obesity in children by parents’ SEP.