The present study was based on data from the Healthy Start study (ClinicalTrials.gov, ID: NCT01583335). Healthy Start was designed as a randomized intervention with the aim of preventing overweight and obesity in children aged 2–6 years, who were primarily normal weight, but predisposed to overweight because of having either a high birth weight (> 4000 grams), a mother who was overweight prior to pregnancy (BMI > 28), or a mother with low SES (educational level ≤ 10 years). The intervention was family based, and strategies included optimization of diet-, physical activity- and sleep habits, and reduced stress. The average intervention time was 1.3 years. A description of The Healthy Start Study has been given in detail previously [15].

Recruitment of participants to the Healthy Start study took place between 2009 and 2011. Information on birth weight, pre-pregnancy BMI of the mother and maternal educational level was obtained from the Danish National Birth Register and administrative birth forms on all children born between 2004 and 2007 from 11 selected municipalities in the greater Copenhagen area [15]. A total of 5,902 children met the criteria and were randomized into an intervention group, a control group, or a shadow control group. After the randomization, children were identified and checked for eligibility in the Danish Central Person Registry (CPR). Children that had requested protection from participation in statistical or scientific surveys based on data delivered from the Danish Central Person Registry, had moved to another municipality, had emigrated or died, lived in an orphanage, or that had an unknown life status were not eligible and thus excluded (n = 2,180). A total of 3722 children complied with the inclusion criteria [15].

Children in the shadow control group were followed for their weight development in registers. However, in the present study, children from the shadow control group were excluded as there was no registry information or obtained measurements on either exposure or covariates.

For those randomised into the intervention or control groups, a letter was sent to the parents inviting them to participate in the study. A total of 635 children in the intervention and control groups attended the baseline examinations. A total of 290 children from the intervention or control group were excluded due to missing information on exposure, primary outcome (change in BMI z-score) or covariates. Thus, the final population size for the present study was 345 children, of which 34 were overweight at baseline. A detailed flowchart can be found in S1 Fig.

Change in BMI z-score from baseline to follow-up was the primary outcome. Body weight was measured to the nearest 0.1 kg using a mechanical weight or beam-scale type weight (Tanita BWB-800 or SV-SECA 710). The children were measured in underwear only and were asked to urinate before the weighing. If the child was using a diaper, a new diaper was put on before the weighing. Body height was measured barefoot or in stockings to the nearest 0.1 cm using a stature meter (Soehnle 5002 or Charter ch200P) [15]. BMI was calculated as weight in kilograms per height in meters squared. BMI z-scores were generated using the Lambda-Mu-Sigma (LMS) method, which summarises the changing distributions of the dependent variable (e.g. BMI) by the median, the coefficient of variation and skew expressed as Box-Cox power [16]. Using z-scores enables comparison of a measured BMI with adequate gender- and age-specific reference values [17]. It was chosen to apply a national reference of BMI z-score to the study population, and thus, a power transformation of 0.1 years of age was used [16].

Changes in waist circumference (WC), waist-hip ratio (WHR) and body fat percentage (BF%) were used as secondary outcomes. WC was measured to the nearest 0.5 cm midway between the lowest rib and the iliac crest. Hip circumference was measured to the nearest 0.5 cm, at the place where the circumference was the largest, seen from the frontal and medial angles. Both WC and hip circumferences were measured in triplicate and a mean was calculated. WHR was calculated based on these measurements [15].

Bioelectrical impedance was measured at a resistance of 50 kHz using a SEAC Multiple Frequency Bioimpedance Meter (model SFB3 and SFB2 version 1.0), RJL or Animeter (BIA-101 and BIA-103). Moreover, skinfolds were measured in triplicate at triceps and subscapular on the left side of the child, using Harpenden Skinfold Caliper or Lange Skinfold Caliper. From this, fat free mass (FFM) was estimated using an equation described by Goran et al. in young children [18]: FFM(kg)=[0,16×(H2R)]+(0,67×weight)−(0,11×triceps)−(0,16×subscapular)+(0,43×sex)+2,41kg

Where H²/R is height²/resistance in cm²/Ω, weight is body weight in kg, triceps and subscapular are skinfold thicknesses in mm, and sex = 0 for girls and 1 for boys. Fat mass was calculated by subtracting fat free mass from body weight. BF% was calculated by dividing fat mass by body weight.

A Danish single-sided version of the Strengths and Difficulties Questionnaire (SDQ) was used. SDQ is a brief questionnaire screening for behavioural problems [19]. It is validated and has a high test-retest reliability and has been used in several large studies [6]. SDQ was an integrated part of a large questionnaire completed by the parents at baseline [16]. The questionnaire contained about 25 items related to the child’s behaviour, some positive and others negative. These 25 items are divided into 5 scales (“Emotional symptoms”, “Conduct problems”, “Hyperactivity/inattention”, “Peer relationship problems”, and “Prosocial behaviour”) [20]. The scores within all categories except “Prosocial behaviour” were summed to a Total Difficulties score (SDQ-TD score) and used as an exposure variable. The scale on Prosocial Behaviour was not incorporated into the SDQ-TD score, as absence of prosocial behaviours differs conceptually from the presence of psychological difficulties [19]. Therefore, the Prosocial Behaviour score (SDQ-PSB score) was used as an exposure variable by itself. In the present study we used the English scoring syntax for pre-school children available from the SDQ-webpage [21]. The exposure variables were included both as continuous and binary variables. The continuous SDQ-TD score variable ranged from 0–40 and SDQ-PSB score ranged from 0–10. For the binary SDQ-TD score and SDQ-PSB score variables, a category consisting of children above the 90^th percentile and a category of the remaining children was generated. This categorization was selected as a previously published cross-sectional study from the Healthy Start study suggested a higher BMI z-scores among children with an SDQ-TD score above the 90^th percentile [11].

The parents completed a large questionnaire on life style and demographic factors at baseline and follow-up [15]. Based on this questionnaire, the following variables were included as covariates. The mother’s physical activity level in leisure time over the past year with response options in 4 categories: 1) “Regular and vigorous physical activity several times a week”, 2) “some physical activity” (cycling to work, performing heavy gardening or similar a minimum of 4 hours per week), 3) “light exercise” (e.g. walking or light gardening a minimum of 4 hours per week), and 4) “sedentary activities” (e.g. reading or watching television). In the questionnaire the mother’s height and weight was self-reported and BMI was calculated based on this information. Maternal level of completed education was reported in 9 categories. Due to very few individuals in some of the groups, we recoded it into 4 categories: 1) “Primary and lower secondary”, “upper secondary”, “one or more short courses”, “skilled worker”, 2) “short-term further education [< 3 years]” or “medium- term further education [3–4 years]”, 3) “long-term further education [< 4 years]”, “research level” and 4) “others”. The parents were asked whether their child likes to be physically active with 5 possible answers. For this study, the 5 possible answers were recoded into the following 3 categories: 1) “The child never thinks it is fun being physically active” or “the child rarely thinks it is fun being physically active” or “the child sometimes thinks it is fun to be physically active”, 2) “the child usually thinks it is fun to be physically active”, and 3) “the child always thinks it is fun to be physically active”.

Information on the child’s total energy intake (MJ/day) was calculated based on a 4-day dietary record (Wednesday-Saturday) completed by parents, applying a picture book as guidance in reporting portion sizes. Finally, we included information on child sex, baseline age (years), and intervention status (intervention or control).

The Healthy Start study complied with the Helsinki declaration and approved by the Danish Data Protection Agency regarding participant's data protection (j. no. 2015-41-0530). The Scientific Ethical Committee of the Capital Region in Denmark decided that The Healthy Start Study was not a bioethics project and as a result did not need approval from the Danish Bioethics Committee (j.no. H-A-2007-0019). Written informed consent to use the collected data for research purposes was obtained from all parents of the participants [15].

Linear regression was used to examine the associations between SDQ-TD score and SDQ-PSB score and changes in BMI z-score and secondary outcomes (body fat percentage, WC and WHR) during follow-up. The statistical analyses were conducted in a stepwise manner using the following structure:

Model controls (i.e., investigating linearity of the relationship between outcomes and predictors, consistency with a normal distribution of the residuals, and variance homogeneity) were performed for the fully adjusted models. In the analyses of the primary outcome, possible effect modification by sex, intervention status or baseline level of outcome was examined by adding product terms to the models.

All statistical tests were two-tailed with a significance level at 0.05. Analyses were performed using Stata SE 14 (StataCorp LP, College Station, TX, USA; www.stata.com).

Body fat percentage is a relative measure and thus changes in absolute values of lean and fat mass may occur independently of changes in the body fat percentage. Thus, as a sensitivity analyses, we further explored the associations between SDQ-scores and subsequent changes in fat mass index [fatmass(kg)height(m)2] and fat free mass index [fatfreemass(kg)height(m)2].