Data were analysed using SAS V.9.4 (SAS Institute, Cary, North Carolina, USA). The data were structured as one record per child per year, and the variables were time-dependent.

Age- and gender-adjusted admission rates were calculated for children with medical admissions in the hospital referral areas corresponding to the geographic areas served by the 18 Norwegian hospital trusts. The direct method of standardisation was applied, with three age groups (1–3, 4–9 and 10–16 years). Both annual and overall rates for the period 2008–2016 were calculated separately for parents’ educational level categories. The reference population was the annual average of all children aged 1–16 years in Norway in the period.

Independent variables included were child’s age and gender, maternal age, maternal and paternal level of education (categorical) and being an only child or not. Due to the high correlation between parents’ ages, father’s age was not included in the analysis. Restricted cubic splines (4 knots) for age with interaction terms for gender were applied, to adjust for child’s age and gender. High level of education and only child were set as reference categories. In any particular analysis, observations with relevant missing data were excluded.

Admission was a dichotomous variable for each child, and the year of the first admission was used as admission time point. For children with multiple admissions, only the year of the first admission was considered. Admission was analysed using discrete-time survival analysis (based on binary logistic regression).15

In the analysis of the number of admissions, and the cost or severity of the admission, the study population was restricted to children with admissions only, and the independent variables were defined by the year of the first admission. The number of admissions was counted for each child in the year of the first admission. As the number of admissions is a counter variable with values greater or equal to 1, truncated negative binomial regression was applied. DRG-weight of the first admission was used as a measure of cost and disease severity. DRG-weight was analysed with linear regression. DRG-weight was highly right-skewed and was therefore log-transformed. Also, the sum of DRG-weights in the first year with admission and sum of all DRG-weights throughout the period were calculated and analysed.

To control for the impact of parental level of education on geographic variation, we conducted sensitivity analyses, that is, multilevel analysis with random intercept for the hospital referral areas. This was done for the survival analysis of admission and DRG-weight. The analyses were stratified by gender and performed with restricted cubic splines (4 knots) for age. The full model with all the independent variables was compared with a reduced model without parental education.

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