RESEARCH ARTICLE

Body mass index and childhood

symptoms of depression, anxiety,
and attention-­deficit hyperactivity
disorder: A within-­family Mendelian
randomization study
Amanda M Hughes1,2*, Eleanor Sanderson1,2, Tim Morris1,2, Ziada Ayorech3,4,
Martin Tesli5,6, Helga Ask3,5, Ted Reichborn-­Kjennerud5,7, Ole A Andreassen6,7,
Per Magnus8, Øyvind Helgeland9, Stefan Johansson10,11, Pål Njølstad12,13,
George Davey Smith1,2, Alexandra Havdahl1,2,3,4,5†, Laura D Howe1,2†,
Neil M Davies1,2,14†
1
Medical Research Council Integrative Epidemiology Unit, University of Bristol,
Bristol, United Kingdom; 2Population Health Sciences, Bristol Medical School,
University of Bristol, Barley House, Oakfield Grove, Bristol, United Kingdom;
3
PROMENTA Research Centre, Department of Psychology, University of Oslo,
Oslo, Norway; 4Nic Waals Institute, Lovisenberg Diaconal Hospital, Oslo, Norway;
5
Department of Mental Disorders, Norwegian Institute of Public Health, Oslo,
Norway; 6Norwegian Centre for Mental Disorders Research (NORMENT), Division of
Mental Health and Addiction, Oslo University Hospital, Oslo, Norway; 7Institute of
Clinical Medicine, University of Oslo, Oslo, Norway; 8Centre for Fertility and Health,
Norwegian Institute of Public Health, Oslo, Norway; 9Center for Diabetes Research,
*For correspondence: Department of Clinical Science, University of Bergen, Bergen, Norway; 10Department
amanda.hughes@bristol.ac.uk of Clinical Science, University of Bergen, Bergen, Norway; 11Department of Medical
†
These authors contributed Genetics, Haukeland University Hospital, Bergen, Norway; 12Mohn Center for
equally to this work Diabetes Precision Medicine, Department of Clinical Science, University of Bergen,
Competing interest: See page
Bergen, Norway; 13Children and Youth Clinic, Haukeland University Hospital, Bergen,
16 Norway; 14K.G. Jebsen Center for Genetic Epidemiology, Department of Public
Health and Nursing, NTNU, Norwegian University of Science and Technology,
Funding: See page 16
Høgskoleringen, Norway
Preprinted: 22 September 2021
Received: 29 September 2021
Accepted: 07 November 2022
Published: 20 December 2022
Abstract
Reviewing Editor: Mashaal
Background: Higher BMI in childhood is associated with emotional and behavioural problems, but
Sohail, National Autonomous
these associations may not be causal. Results of previous genetic studies imply causal effects but
University of Mexico, Mexico
may reflect influence of demography and the family environment.
‍ ‍Copyright Hughes et al. This Methods: This study used data on 40,949 8-­year-­old children and their parents from the Norwegian
article is distributed under the
Mother, Father and Child Cohort Study (MoBa) and Medical Birth Registry of Norway (MBRN). We
terms of the Creative Commons
investigated the impact of BMI on symptoms of depression, anxiety, and attention-­deficit hyperac-
Attribution License, which
permits unrestricted use and tivity disorder (ADHD) at age 8. We applied within-­family Mendelian randomization, which accounts
redistribution provided that the for familial effects by controlling for parental genotype.
original author and source are Results: Within-­family Mendelian randomization estimates using genetic variants associated with
credited. BMI in adults suggested that a child’s own BMI increased their depressive symptoms (per 5 kg/m2

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 Research article Epidemiology and Global Health | Genetics and Genomics

increase in BMI, beta = 0.26 S.D., CI = −0.01,0.52, p=0.06) and ADHD symptoms (beta = 0.38 S.D.,
CI = 0.09,0.63, p=0.009). These estimates also suggested maternal BMI, or related factors, may
independently affect a child’s depressive symptoms (per 5 kg/m2 increase in maternal BMI, beta =
0.11 S.D., CI:0.02,0.09, p=0.01). However, within-­family Mendelian randomization using genetic vari-
ants associated with retrospectively-­reported childhood body size did not support an impact of BMI
on these outcomes. There was little evidence from any estimate that the parents’ BMI affected the
child’s ADHD symptoms, or that the child’s or parents’ BMI affected the child’s anxiety symptoms.
Conclusions: We found inconsistent evidence that a child’s BMI affected their depressive and ADHD
symptoms, and little evidence that a child’s BMI affected their anxiety symptoms. There was limited
evidence of an influence of parents’ BMI. Genetic studies in samples of unrelated individuals, or
using genetic variants associated with adult BMI, may have overestimated the causal effects of a
child’s own BMI.
Funding: This research was funded by the Health Foundation. It is part of the HARVEST collabo-
ration, supported by the Research Council of Norway. Individual co-­author funding: the European
Research Council, the South-­Eastern Norway Regional Health Authority, the Research Council of
Norway, Helse Vest, the Novo Nordisk Foundation, the University of Bergen, the South-­Eastern
Norway Regional Health Authority, the Trond Mohn Foundation, the Western Norway Regional
Health Authority, the Norwegian Diabetes Association, the UK Medical Research Council. The
Medical Research Council (MRC) and the University of Bristol support the MRC Integrative Epidemi-
ology Unit.

Editor's evaluation
The manuscript uses genetic effects on BMI to test whether BMI affecxts childhood emotional and
behavioural problems: symptoms of depression, anxiety, and attention-­deficit and hyperactivity
disorder (ADHD) at age 8. By using a within-­family design in a large sample of children with geno-
typed parents in Norway, the study finds that previous estimates of the effect of BMI on childhood
emotional and behavioural symptoms may have been overestimated due to confounding with the
environment. Larger samples will be needed to determine whether there is a causal effect of BMI on
childhood emotional or behavioural problems, and what size it is.

Introduction
Children with high body mass index (BMI) have been found to have greater risk of emotional and
behavioural problems, including symptoms and diagnoses of depression (Lindberg et al., 2020;
Patalay and Hardman, 2019; Geoffroy et al., 2014; Quek et al., 2017) anxiety (Lindberg et al.,
2020) and attention-­deficit hyperactivity disorder (ADHD) (Cortese and Tessari, 2017; Griffiths et al.,
2011). Prior to the COVID-­19 pandemic, prevalence of childhood overweight and childhood obesity,
respectively, was 21.3% and 5.7% in Europe (Garrido-­Miguel et al., 2019) and 20.1% and 4.3% in
Norway (Glavin et al., 2014). The estimated prevalence in Europe of mid-­childhood emotional disor-
ders was around 4% (Kovess-­Masfety et al., 2016; Sadler et al., 2018) while the global prevalence of
child and adolescent ADHD was estimated at 5% (Sayal et al., 2018). These rates may have increased
considerably in the wake of the pandemic (Vizard et al., 2020). In this context, there is a clear need
to understand the relationship between these factors, but it is not known if child body weight causes
emotional or behavioural problems.
High BMI in childhood could affect emotional symptoms through social mechanisms, for example
bullying victimization (Puhl et al., 2017). An impact on ADHD has been proposed via sleep disturbance
and neurocognitive functioning (Vogel et al., 2015). However, even if children with high BMI are more
likely than normal weight children to experience these symptoms, associations may not be causal.
Aspects of the family environment may independently affect children’s BMI and their likelihood of
developing emotional and behavioural symptoms, for example socioeconomic disadvantage (Russell
et al., 2016) and parental mental health (Hope et al., 2019a; Hope et al., 2019b). Some studies have
suggested that prenatal maternal obesity may confound associations of childhood BMI with emotional
and behavioural symptoms (Sanchez et al., 2018), although the evidence is mixed (Li et al., 2020;
Arafat and Minică, 2018). Reverse causality is also plausible: depressive, anxiety or ADHD symptoms

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 Research article Epidemiology and Global Health | Genetics and Genomics

eLife digest Some studies show that children with obesity are more likely to receive a diagnosis
of depression, anxiety, or attention-­deficit hyperactivity disorder (ADHD). But this does not necessarily
mean obesity causes these conditions. Depression, anxiety, or ADHD could cause obesity. A child's
environment, including family income or their parents' mental health, could also affect a child's weight
and mental health. Understanding the nature of these relationships could help scientists develop
better interventions for both obesity and mental health conditions.
Genetic studies may help scientists better understand the role of the environment in these condi-
tions, but it's important to consider both the child's and their parents’ genetics in these analyses.
This is because parents and children share not only genes, but also environmental conditions. For
example, families that carry genetic variants associated with higher body weight might also have
lower incomes, if parents have been affected by biases against heavier people in society and the
workplace. Children in these families could have worse mental health because of effects of their
parent’s weight, rather than their own weight. Looking at both child and adult genetics can help
disentangle these processes.
Hughes et al. show that a child's own body mass index, a ratio of weight and height, is not strongly
associated with the child’s mental health symptoms. They analysed genetic, weight, and health survey
data from about 41,000 8-­year-­old children and their parents. The results suggest that a child's own
BMI does not have a large effect on their anxiety symptoms. There was also no clear evidence that a
child's BMI affected their symptoms of depression or ADHD.
These results contradict previous studies, which did not account for parental genetics. Hughes et
al. suggest that, at least for eight-­year-­olds, factors linked with adult weight and which differ between
families may be more critical to a child's mental health than a child’s own weight. For older children
and adolescents, this may not be the case, and the individual’s own weight may be more important.
As a result, policies designed to reduce obesity in mid-­childhood are unlikely to greatly improve the
mental health of children. On the other hand, policies targeting the environmental or societal factors
contributing to higher body weights, bias against people with higher weights, and poor child mental
health directly may be more beneficial.

could cause higher BMI, for instance via disordered eating patterns or decreased physical activity
(Blaine, 2008; Martins-­Silva et al., 2019). To avoid confounding and reverse causation, recent studies
have applied Mendelian randomization (MR), a causal inference approach which uses genetic variants
as instrumental variables for putative risk factors (Davies et al., 2018). Results, principally based on
adult populations, are consistent with a causal influence of BMI on ADHD (Martins-­Silva et al., 2019)
and depression (Tyrrell et al., 2019). They are inconclusive for anxiety, reporting both positive (Walter
et al., 2015) and negative (Millard et al., 2019) predicted causal effects of body weight.
However, although MR studies avoid classical confounding and reverse causation, they can be
vulnerable to other sources of bias. Specifically, estimates from ‘classic’ MR studies – those conducted
on samples of unrelated individuals – may be affected by demographic and familial factors (Davies
et al., 2019; Morris et al., 2020). Bias can firstly arise from uncontrolled population stratification, where
systematic differences in genotype between individuals from different ancestral clusters correlates
with differences in environmental or cultural factors. This is an example of gene-­environment correla-
tion, which can lead to biased associations of genotypes and phenotypes. Secondly, indirect genetic
effects may exist whereby parental genotype influences a child’s phenotype via environmental path-
ways, termed ‘dynastic effects’ or ‘genetic nurture’ (Kong et al., 2018). Thirdly, assortative mating in
the parents’ generation, where parents are more (or less) similar to each other than would be expected
by chance, can distort genotype-­phenotype associations in the child’s generation. Recent work has
suggested that these biases may be especially pronounced for complex social and behavioural pheno-
types (Brumpton et al., 2020; Howe et al., 2022). Previously reported MR estimates of the effect
of BMI on emotional and behavioural problems may therefore partly reflect demographic or familial
biases rather than a causal influence of BMI. To investigate this, we used a ‘within-­family’ Mende-
lian randomization (within-­family MR) design. This approach uses the child’s, mother’s, and father’s
genotype data as instruments for the BMI of the child, mother, and father. Within family Mendelian

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 Research article Epidemiology and Global Health | Genetics and Genomics

randomization estimates of the effect of the child’s BMI on the outcomes are robust to demographic
and family-­level biases. We compared within-­family MR estimates with estimates from multivariable
regression of the child’s outcomes on the child’s, mother’s and father’s reported BMI, and with esti-
mates from ‘classic’ Mendelian randomization (classic MR), in which the child’s genotype data was
used to instrument the child’s BMI without controlling for the parents’ genotype.

Methods
Study population
The Norwegian Mother, Father and Child Cohort Study (MoBa) is a population-­based pregnancy
cohort study over 114,500 children, 95,200 mothers, and 75,200 fathers conducted by the Norwegian
Institute of Public Health (Magnus et al., 2016). Participants were recruited from all over Norway
from 1999 to 2008, with 41% of all pregnant women invited consenting to participate. The first child
was born in October 1999 and the last in July 2009. The cohort now includes over 114,500 children,
95,200 mothers, and 75,200 fathers (for more details see Appendix 1: MoBa study details). As of
May 2022, genotype data which had passed quality control filters was available for 76,577 children,
53,358 fathers, and 77,634 mothers. This analysis was restricted to 40,949 mother-­father-­child ‘trios’
for whom genetic data were available for all three individuals, and at least one questionnaire had been
completed.
The numbers of participants excluded are shown in a STROBE flow chart in Appendix 1—figure 1.
From all records in MoBa (N=114,030 after removing consent withdrawals), participants were excluded
if the parents had not completed any of the MoBa questionnaires used in imputation models. Of the
104,915 records remaining, there were 40,949 births for which genetic data were available and had
passed QC filters for mother, father, and child (for details see Appendix 1: Genotyping and imputa-
tion, and Appendix 1: Genetic quality control). Missing values in phenotypic information for these
participants were estimated using multiple imputation (details in Appendix 1: Multiple imputation).
Related participants were retained, but all models were clustered by genetic family ID derived using
KING software (Manichaikul et al., 2010). This genetic family ID groups first, second, and third-­
degree relatives (i.e. siblings in the parental generation and their children as well as nuclear families),
in this way accounting for non-­independence of observations.

Measures
Children’s BMI was calculated from height and weight values reported by mothers when the chil-
dren were 8 years old. Maternal pre-­pregnancy BMI was calculated from height and weight reported
at ~17 weeks gestation. Father’s BMI was calculated from self-­reported height and weight at ~17 weeks
gestation. This information was missing from around 60% of fathers, and in these cases the mother’s
report of the father’s height and weight was used instead (observed values of BMI from the two
sources were correlated at 0.98). Values of height and weight more than 4 standard-­deviations from
the mean were treated as outliers and coded to missing.
Depressive, anxiety, and ADHD symptoms were reported by the mother when the child was 8 years
old using validated measures. For depressive symptoms, the 13-­item Short Mood and Feelings Ques-
tionnaire (SMFQ) was used, for anxiety symptoms the 5-­item Short Screen for Child Anxiety Related
Disorders (SCARED) (Birmaher et al., 1999) and for ADHD symptoms the Parent/Teacher Rating
Scale for Disruptive Behaviour Disorders (RS-­DBD) (total score and subdomain scores for inattention
and hyperactivity) (Silva et al., 2005). Prorated summary scores were calculated for individuals with at
least 80% of item-­level information. Full details of all questions asked in MoBa are available at https://​
mobawiki.fhi.no/mobawiki/index.php/Questionnaires.
Blood samples were obtained from both parents during pregnancy and from mothers and children
(umbilical cord) at birth. Details of genotyping and genetic quality control are described in Appendix
1: Genotyping and imputation and Appendix 1: Genetic quality control. Polygenic scores (PGS) for
BMI were calculated using SNPs previously associated in GWAS with BMI at p<5.0 × 10–8 and weighted
using the individual SNP-­coefficients from the GWAS. We first constructed a PGS based on the largest
existing GWAS of BMI in adults (Yengo et al., 2018). Since genetic influences on BMI in childhood and
adulthood differ (Silventoinen et al., 2016) we also constructed a PGS based on a GWAS of body size
in childhood as recalled by adult participants of UK Biobank (Richardson et al., 2020). These SNPs

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have been shown in external validation samples to predict BMI in childhood better than SNPs associ-
ated with adult BMI (Richardson et al., 2020; Brandkvist et al., 2021). From the full GWAS results,
we excluded SNPs not available in MoBa, then used the TwoSampleMR package (Hemani et al.,
2018b) to identify SNPs independently associated with BMI (with a clumping threshold of r=0.01, LD
= 10,000 kb) at p<5.0 × 10–8. This left 954 SNPs associated with adult BMI, and 321 associated with
childhood body size. Full details of SNPs included in both PGSs are provided in Supplementary file
1a and b. Equivalent PGSs were derived for depression and ADHD based on SNPs previously associ-
ated with these conditions at p<5.0 × 10–8 in GWAS (Wray et al., 2018; Demontis et al., 2019). This
was not possible for anxiety, due to few known SNPs associated with these traits at p<0.05 × 10–8.
Details of the SNPs in the depression and ADHD PGSs are provided in Supplementary file 1c and d.

Statistical analysis
Among trios with genetic data, multiple imputation by chained equations was performed in STATAv16
to estimate missing phenotypic information (details in Appendix 1: Multiple imputation of phenotypes).
We used non-­genetic linear regression, classic MR, and within-­family MR to estimate the effects of the
child’s BMI on the following outcomes: depressive, anxiety, and ADHD symptoms, and subdimensions
of ADHD (inattention and hyperactivity). Non-­genetic regression models were adjusted for child’s sex,
year of birth, mother’s and father’s BMI, and likely confounders of observational associations: moth-
er’s and father’s educational qualifications, mother’s and father’s depressive/anxiety symptoms (using
selected items from the 25-­item Hopkins Checklist Hesbacher et al., 1980) and ADHD symptoms
(from the 6-­item adult ADHD self-­report scale Kessler et al., 2005), mother’s and father’s smoking
status during pregnancy, and maternal parity at the child’s birth. For comparability, these models also
included all covariates included in genetic models: genotyping centre, genotyping chip, and 20 prin-
cipal components of ancestry for the child, mother, and father (for detailed information on principal
components see Appendix 1: Genetic quality control). All MR models were conducted with two-­stage
least squares instrumental-­variable regression using Stata’s ivregress, with F-­statistics and R2 values
obtained using ivreg2. Classic MR models, which do not account for parental genotype, used the
child’s own PGS but not those of the parents to instrument the child’s BMI. Within-­family MR models
were multivariable MR models, in which we used PGSs for all members of a child-­mother-­child trio to
instrument the BMI of all three individuals (model equations are provided in Appendix 1: Model equa-
tions). Classic and within-­family MR models were adjusted for the child’s sex and year of birth, and the
genotyping centre, genotyping chip, and the first 20 principal components of ancestry for the child,
mother, and father. Given skew in outcomes variables, all models used robust standard errors (Stata’s
vce option) and thus made no assumptions about the distribution of outcomes. We report two sets of
results, in which either the adult BMI GWAS, or the childhood body size GWAS, was used to create
the BMI PGS for the child, mother, and father. Z tests of difference were used to formally compare the
classic MR and within-­family MR estimates. To assess the extent of assortative mating in the parental
generation based on phenotype data, we ran linear regression models of standardized paternal BMI,
depressive symptoms, and ADHD symptoms on standardized maternal BMI, depressive symptoms,
and ADHD symptoms. We then regressed paternal polygenic scores for BMI, depression, and ADHD
on maternal polygenic scores for BMI, depression, and ADHD. All models investigating assortative
mating adjusted for both parents’ principal ancestry components and genotyping covariates. We did
not examine correlations with polygenic scores for anxiety, due to few known SNPs associated with
these traits at p<0.05 × 10–8. All statistical tests were two-­tailed.

Sensitivity analyses
To check sensitivity of results to outliers, all analyses were repeated using log-­transformed versions of
outcome measures (as all symptoms scales began at 0, we added 1 to scores before log-­transforming).
Genetic studies designed to assess causation can be biased by horizontal pleiotropy (Davies et al.,
2018). This is when genetic variants in a polygenic score influence the outcome via pathways which
do not involve the exposure. Pleiotropic effects can inflate estimated associations, or bias estimates
towards the null. Methods have been developed to test for the presence of horizontal pleiotropy by
comparing SNP-­specific associations of exposures and outcomes, although these tests themselves
rest on assumptions (Hemani et al., 2018a). We therefore performed additional robustness checks
based on associations of individual SNPs included in the polygenic scores with BMI in the GWAS,

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and associations of the same SNPs with each outcome in MoBa. It was not computationally feasible
to include individual SNPs in the imputation models, so SNP-­outcome associations in MoBa were
calculated using unimputed SNP data with imputed outcome data. For robustness checks of classic
MR models, SNP-­outcome associations were adjusted for the child’s sex and birth year, and the geno-
typing centre, genotyping chip, and ancestry principal components of the child, mother, and father.
For robustness checks of within-­family MR models, SNP-­outcome associations were adjusted for the
child’s sex and birth year, mother’s and father’s genotype, and the genotyping centre, genotyping chip,
and principal components of the child, mother, and father. We conducted inverse-­variance weighted,
MR-­Median, MR-­Mode, and MR-­Egger regression in STATAv16 with the MRRobust package (Spiller
et al., 2019). A non-­zero intercept from an MR-­Egger model indicates presence of horizontal plei-
otropy. We repeated main analyses without using imputed data in the sample of participants who
had full genetic, exposure, outcome, and covariate data. To explore nonlinearities in associations of
BMI with depression, anxiety, and ADHD symptoms, we ran non-­genetic models with the child’s BMI
divided into quintiles. Finally, MR models were run with additional adjustment for parental education.
Attenuation of classic MR estimates in these models would be consistent with confounding by aspects
of the family environment linked to parental education.

Results
This analysis was restricted to 40,949 mother-­father-­child ‘trios’ for whom genetic data were avail-
able for all three individuals, and at least one questionnaire had been completed. To assess whether
participants included in the analytic sample (N=40,949) differed from the rest of the MoBa sample
(N=72,742), we conducted t-­tests and chi-­squared tests for key characteristics at birth, BMI, and
outcomes using unimputed data. There were modest differences, described in Appendix 1: Compar-
ison of analytic sample and excluded participants. BMI did not differ for mothers, fathers or children,
but children in the analytic sample had slightly lower depressive symptoms (mean SMFQ = 1.81 vs
1.91), anxiety symptoms (mean SCARED = 1.04 vs 1.00) and ADHD symptoms (mean RS-­DBD ADHD
= 8.4 vs 8.7). Descriptive characteristics of the full MoBa sample are in Appendix 1—table 1.
Descriptive statistics of the analytic sample after multiple imputation is presented in Table 1. The
mean BMI for children was 16.3 (SD = 2.0), for mothers 24.0 (SD = 4.1), and for fathers 25.9 (SD = 3.2).
Corresponding descriptive characteristics from unimputed data are included in Appendix 1—table
2. Both polygenic scores used to instrument BMI were strong instruments, even when used in within-­
family models. For the adult BMI PGS, conditional first-­stage F-­statistics for children, mothers, and
fathers were 718.7, 1338.2, and 1272.5. The conditional R2 showed that the score explained 1.7%,
3.2%, and 3.0% of the variation in BMI for children, mothers, and fathers respectively. For the child-
hood body size PGS, conditional first-­stage F-­statistics were 919.8, 1071.8, and 960.2 for children,
mothers, and fathers, with the scores explaining 2.2%, 2.6% and 2.3% of the variation in BMI. The
correlation of the polygenic scores for adult BMI and for childhood body size was 0.38 for children,
0.36 for mothers and 0.37 for fathers.

Associations of BMI with depressive, anxiety, and ADHD symptoms at

age 8
Depressive symptoms (SMFQ)
In adjusted non-­genetic regression models (Figure 2, Appendix 1—table 3), children’s higher BMI at
age 8 was associated with slightly higher depressive symptoms. Per 5 kg/m2 increase in BMI, SMFQ
score was 0.05 standard deviations (SD) higher (95% CI: 0.01,0.09, p=0.02). Classic MR using the adult
BMI PGS suggested that for each 5 kg/m2 increase in the child’s BMI, the child’s SMFQ score increased
by 0.45 SD (95% CI: 0.26,0.64, p<0.001). Within-­family MR using the adult BMI PGS also provided
some evidence for an effect (beta: 0.26 SD, 95% CI: –0.01,0.52, p=0.06), but the within-­family MR
estimate was less precise (70% as precise as the classic MR estimate, and 15% as precise as the OLS
estimates, from the ratio of standard errors). A z test for the difference (p=0.26) indicated that the
within-­family MR estimate was consistent with the classic MR estimate. Using the childhood body size
PGS (Figure 3, Appendix 1—table 4) there was little evidence that a child’s own BMI affected their
depressive symptoms from either classic MR (beta: 0.08 (95% CI: –0.07,0.22, p=0.29) or within-­family

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Table 1. Descriptive characteristics of analytic sample (N=40,949)*.

Continuous variables mean SD

Maternal age at child’s birth (years) 30.2 4.4

Paternal age at birth (years) 32.6 5.1

Maternal depressive/anxiety symptoms, Hopkins

Symptoms Checklist-­25 (SCL-­25)† 1.2 1.9

Paternal depressive/anxiety symptoms, Hopkins

Symptoms Checklist-­25 (SCL-­25) ‡ 1.1 2.1

Maternal ADHD symptoms: adult ADHD self-­report

scale § 6.7 3.4

Paternal ADHD symptoms: adult ADHD self-­report

scale ¶ 8.3 3.1
2
Maternal pre-­pregnancy BMI (kg/m ) 24.0 4.1
2
Paternal BMI (kg/m ) 25.9 3.2
2
Child’s BMI at age 8 (kg/m ) 16.3 2.0

Child depressive symptoms age 8: Short Mood and

Feelings Questionnaire (SMFQ)** 1.9 2.5

Child anxiety symptoms age 8: Screen for Child Anxiety

Related Disorders (SCARED)†† 1.0 1.2

Child ADHD symptoms age 8: Parent/Teacher Rating

Scale for Disruptive Behaviour Disorders (RS-­DBD) ‡ ‡ 8.6 7.2

Child ADHD symptoms (inattention) age 8: Parent/

Teacher Rating Scale for Disruptive Behaviour Disorders
(RS-­DBD) § § 5.0 4.1

Child ADHD symptoms (hyperactivity) age 8: Parent/

Teacher Rating Scale for Disruptive Behaviour Disorders
(RS-­DBD)§ § 3.6 3.9

Categorical variables Category %

Male 51.1

Child’s sex Female 48.9

9 year elementary education 2.0

Up to 2 years further education 4.1

Further education: vocational 12.2

Further education: general studies,

sixth form 14.9

Higher education: college/university,

up to 4 years 42.8

Higher education: college/university,

Maternal educational qualifications over 4 years 24.0

Paternal educational qualifications 9 year elementary education 3.4

Up to 2 years further education 5.6

Further education: vocational 25.1

Further education: general studies,

sixth form 12.9

Higher education: college/university,

up to 4 years 28.4

Higher education: college/university, 24.4

over 4 years
Table 1 continued on next page

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Table 1 continued
Continuous variables mean SD

0 46.8

1 35.7

2 14.0

3+ 2.7

Maternal parity at child’s birth 4+ 0.7

Married/registered partner 97.4

Mother’s marital status at birth single 2.6

never 51.0

Stopped before week 17 42.0

Currently, sometimes 2.4

Mother’s smoking status during pregnancy Currently, daily 4.5

*The reasons for exclusions and numbers in each case are shown in Appendix 1—figure 1.
Missing data in BMI, outcomes and covariates was imputed using multiple imputation by
chained equations. Descriptive statistics for the unimputed data are shown in Appendix 1.
†
Based on 5 items. Possible range: 0–15.
‡
Based on 8 items. Possible range: 0–24.
§
Possible range: 0–24.
¶
Possible range: 0–24.
**Possible range: 0-­26.
††
Possible range: 0–10.
‡‡
Possible range: 0–54.
§§
Possible range: 0–27.

MR (beta: 0.02 (95%CI: –0.20,0.23, p=0.88). In summary, evidence for an effect of childhood BMI on
depressive symptoms was strongest using the genetic variants for adult BMI.

Anxiety symptoms (SCARED)

In non-­genetic models (Figure 2, Appendix 1—table 3), each 5 kg/m2 increase in BMI was associated
with a 0.07 SD lower (95% CI: −0.11,–0.03, p=0.001) SCARED score. Using the adult BMI PGS, there
was little evidence for an effect from classic MR (beta: –0.06, 95% CI: –0.25,0.12, p=0.51), or within-­
family MR models (beta: 0.01, 95% CI: –0.25,0.29, p=0.96). Again, the within-­family MR estimate
was less precise than the classic MR estimate (68% as precise), or the OLS estimate (15% as precise),
and the classic and within-­family MR estimates were consistent (p=0.54). Using the childhood body
size PGS (Figure 3, Appendix 1—table 4), MR estimates were similar (classic MR beta: –0.04, 95%:
–0.18,0.11, P=0.62, within-­family MR beta: 0.02, 95% CI: –0.18,0.22, P=0.83). In summary, there was
little evidence from any genetic model that childhood BMI affects anxiety symptoms.

ADHD symptoms (RS-DBD)

In non-­genetic models (Figure 2, Appendix 1—table 3) children’s BMI was negatively associated with
ADHD symptoms after adjusting for confounders. Per 5 kg/m2 increase in BMI, ADHD symptoms from
the RS-­DBD were 0.07 SD lower (95% CI: −0.11,–0.03, p=0.001), with similar associations observed for
the inattention or hyperactivity subscales (Figure 2, Appendix 1—table 3). Using the adult BMI PGS
there was evidence from both classic and within-­family MR models of a positive association of BMI and
ADHD. In the classic MR model ADHD symptoms were 0.35 SD higher (95% CI: 0.17,0.53, p<0.001)
per 5 kg/m2 increase in BMI; the within-­family MR estimate, at 0.36 SD (CI: 0.09,0.63, p=0.009) was
almost identical (p for difference = 0.95). A similar pattern was seen with the inattention and hyper-
activity subscales (Figure 2, Appendix 1—table 3). The within-­family MR estimate was again the
least precise (65% as precise as the classic MR estimate, 14% as precise as the non-­genetic estimate).
Using the childhood body size PGS (Figure 3, Appendix 1—table 4) there was little evidence of

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 Research article Epidemiology and Global Health | Genetics and Genomics

Figure 1. Bias in Mendelian randomization studies which do not account for parental genotype. Figure 1 is
reproduced from Figure 1; Morris et al., 2020. Population stratification due to ancestral differences (yellow lines),
dynastic effects (red lines), and assortative mating (green line). In within-­family Mendelian randomization, parental
genotype is controlled for, so effect estimates for the influence of child’s genotype on child phenotypes are
unbiased by these processes.

an association from either classic MR (beta: –0.07, 95% CI: –0.21,0.07, p=0.35) or within-­family MR
models (beta: –0.03, 95% CI: –0.22,0.17, p=0.80). Thus, as for depressive symptoms, evidence for an
effect of childhood BMI on ADHD symptoms was inconsistent and only detected using the adult BMI
polygenic score.

Association of mother’s and father’s BMI with child’s symptoms

In non-­genetic models which adjusted for the child’s BMI as well as covariates, the mother’s BMI was
associated with slightly more depressive symptoms in the child (the child’s SMFQ score was 0.05 SD
higher (95% CI: 0.03,0.07, p<0.001), per 5 kg/m2 increase in maternal BMI). Maternal BMI was also
associated with more ADHD symptoms in the child: the child’s RS-­DBD score was 0.04 S.D. higher
(95% CI: 0.02,0.06, p<0.001) per 5 kg/m2 increase in maternal BMI, with similar associations for inat-
tention and hyperactivity subscales. No such associations were seen with paternal BMI.
Within-­family MR models also provide estimates for the effect of factors linked to maternal and
paternal BMI on child outcomes, conditional on the child’s own BMI. However, compared to within-­
family MR estimates for the child’s own genotype, the interpretation of parental estimates differs. Like
classic MR estimates for the child’s BMI, within-­family MR estimates for each parent’s BMI will capture
the causal effect of the parent’s BMI on the child’s outcome, but can also reflect residual population
stratification and assortative mating in the parents’ generation or earlier. For an unbiased estimate
of parental effects, we would need to account for grandparental genotype. Within-­family MR models
provided inconsistent consistent evidence that maternal BMI affected the child’s depressive symptoms:
using the adult BMI PGS (Figure 2, Appendix 1—table 3), estimates suggested that higher maternal
BMI increased depressive symptoms in the child (0.11 SD higher SMFQ score (95% CI: 0.02,0.19,
p=0.01) per 5 kg/m2 increase in maternal BMI), but within-­family MR models using the childhood body
size PGS did not (Figure 3, Appendix 1—table 4). There was little evidence from within-­family MR of
other maternal or paternal effects on the child’s emotional or behavioural outcomes.

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Figure 2. BMI and child’s depressive, anxiety, and ADHD symptoms, using a polygenic score for adult BMI (N=40,949 trios). Coefficients represent
standard-­deviation change in outcomes per 5 kg/m2 increase in BMI, shown with 95% confidence intervals.

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 Research article Epidemiology and Global Health | Genetics and Genomics

Figure 3. BMI and child’s depressive, anxiety, and ADHD symptoms, using a polygenic score for childhood body size (N=40,949 trios). Coefficients
represent standard-­deviation change in outcomes per 5 kg/m2 increase in BMI, shown with 95% confidence intervals.

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 Research article Epidemiology and Global Health | Genetics and Genomics

In the parents’ generation, phenotypes were associated within parental pairs, consistent with assor-
tative mating on these traits (Appendix 1—table 5). Adjusted for ancestry and other genetic covari-
ates, maternal and paternal BMI were positively associated (beta: 0.23, 95% CI: 0.22,0.25, p<0.001),
as were maternal and paternal depressive symptoms (beta: 0.18, 95% CI: 0.16,0.20, p<0.001), and
maternal and paternal ADHD symptoms (beta: 0.11, 95% CI: 0.09,0.13, p<0.001). Consistent with
cross-­trait assortative mating, there was an association of mother’s BMI with father’s ADHD symptoms
(beta: 0.03, 95% CI: 0.02,0.05, p<0.001) and mother’s ADHD symptoms with father’s depressive symp-
toms (beta: 0.05,95% CI: 0.05,0.06, p<0.001). Phenotypic associations can reflect the influence of one
partner on another as well as selection into partnerships, but regression models of paternal polygenic
scores on maternal polygenic scores also pointed to a degree of assortative mating. Adjusted for
ancestry and genotyping covariates, there were small associations between parents’ BMI polygenic
scores (beta: 0.01, 95% CI: 0.00,0.02, p=0.02 for the adult BMI PGS, and beta: 0.01, 95% CI: 0.00,0.02,
p=0.008 for the childhood body size PGS), and of the mother’s childhood body size PGS with the
father’s ADHD PGS (beta: 0.01, 95% CI: 0.00,0.02, p=0.03). We did not detect associations with pairs
of other polygenic scores, which may be due to insufficient statistical power.

Sensitivity analyses
Analyses using log-­transformed versions of the outcomes (Appendix 1—Tables 6 and 7) were consis-
tent with main results. Robustness checks based on comparing associations of individual SNPs with
BMI in the GWAS and with children’s outcomes in MoBa (Appendix 1—Tables 8 and 9) were consis-
tent with the main results. MR-­Egger models found little evidence of horizontal pleiotropy, although
MR-­Egger estimates were imprecise (Appendix 1—Tables 8 and 9). Results of analyses using the
complete-­case sample were qualitatively similar to results using imputed data (Appendix 1—Tables
10 and 11). In non-­genetic models where the child’s BMI was divided into quintiles (Appendix 1—
table 12), there was little evidence of nonlinear associations. With additional adjustment for parental
education, point estimates for depressive and ADHD symptoms in classic MR models were closer to
the null, but confidence intervals substantially overlapped (Appendix 1—Tables 13 and 14).

Discussion
In a large cohort of Norwegian 8-­year-­olds, higher childhood BMI was phenotypically associated with
slightly more depressive symptoms, but fewer anxiety symptoms and ADHD symptoms. Genetic anal-
yses using the adult BMI PGS suggested that higher BMI in childhood increased symptoms of both
depression and ADHD. This was clearest in classic MR models, but also suggested by within-­family MR
models, whose precision is lower but which account for parental genotype. Compared to associations
from non-­genetic models, effect sizes for depression and ADHD from genetic models based on the
adult BMI PGS were larger. However, these estimates were less precise, and confidence intervals for
the classic MR and within-­family MR estimates substantially overlapped for all outcomes. The child-
hood body size PGS explained more variation in children’s BMI than the adult BMI PGS did, consis-
tent with other studies (Richardson et al., 2020; Brandkvist et al., 2021), while the adult BMI PGS
explained more variation in maternal and paternal BMI. Genetic analyses which used the childhood
body size SNPs provided little evidence that the child’s BMI affected their depressive or ADHD symp-
toms outcomes. This suggests that genetic variation associated with adult BMI has a greater impact
on these outcomes than genetic variation associated with recalled childhood body size. This is consis-
tent with the moderate correlation observed between the two polygenic scores, indicating that they
capture both overlapping and unique variation. Our results may therefore reflect differences in how
each set of SNPs relate to traits other than childhood BMI which are relevant to a child’s depressive
and ADHD symptoms. Nevertheless, within-­family MR estimates using the childhood body size PGS
were still consistent with small effects of the child’s BMI on all outcomes, with upper confidence limits
around a 0.2 standard-­deviation increase in each outcome per 5 kg/m2 increase in BMI. There was
little evidence that maternal or paternal BMI affected a child’s ADHD or anxiety symptoms. In within-­
family MR models using the adult BMI PGS, but not the childhood body size PGS, maternal BMI was
positively associated with children’s depressive symptoms. This is consistent with a causal impact of
the mother’s recent BMI but not their BMI in childhood, but it may also reflect family-­level biases from
previous generations.

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The positive association between BMI and depressive symptoms in non-­genetic models accords
with previous observational studies (Lindberg et al., 2020; Patalay and Hardman, 2019; Quek
et al., 2017; Geoffroy et al., 2014). The inverse association between BMI and anxiety symptoms
in non-­genetic models contrasts with the results of a recent study, in which Swedish 6–17 year olds
receiving treatment for obesity had a greater likelihood of a diagnosis or prescription for anxiety
disorder compared to controls (Lindberg et al., 2020). The discrepancy may reflect confounding (we
adjusted for more factors, including parental BMI), age of the participants (children in our study were
younger) or differences in the outcome or exposure, since we considered anxiety symptoms rather
than diagnosis, and a continuous BMI measure rather than obesity. However, anxiety symptoms in our
sample were not raised in the top BMI quintile. Another difference concerns the population: children
receiving obesity treatment may be more likely than other children with obesity to experience anxiety
symptoms or to receive a diagnosis. The inverse association between BMI and ADHD symptoms
in non-­genetic models contrasts with previous reports of positive or null associations with obesity,
which typically adjusted for fewer confounders (Cortese and Tessari, 2017; Nigg et al., 2016). Since
previous studies have found more evidence of an association in adults than children, and often consid-
ered ADHD diagnoses rather than symptoms, the discrepancy may also point to age-­varying associ-
ations, or to different influences on likelihood of diagnosis compared to parent-­reported symptoms
(Nigg et al., 2016; Cortese and Tessari, 2017).
For depressive symptoms and ADHD, classic and within-­family MR estimates using the adult BMI
PGS were larger than estimates from non-­genetic models. Horizontal pleiotropy, which we could not
rule out, could have inflated MR estimates. It could also help explain the discrepancy in results using
the adult BMI and childhood body size polygenic scores, if SNPs in the adult BMI polygenic score have
a greater impact on depressive or ADHD symptoms via pathways independent of childhood BMI. We
found little evidence of pleiotropy using MR-­Egger estimators, but the power to detect pleiotropy
with this method is low. Additionally, classic MR estimates may be inflated by demographic and familial
factors, but within-­family MR estimates for effects of a child’s own BMI are robust to these factors.
For depressive symptoms, the within-­family MR estimate was closer to the non-­genetic estimate than
the classic MR estimate, which may reflect bias in the classic MR estimate due to demographic and
familial factors. At the same time, the within-­family MR estimate was imprecise, and confidence limits
consistent with a substantial effect of children’s BMI on depressive symptoms. For ADHD, point esti-
mates from the classic MR and within-­family MR models using the adult BMI PGS were very similar,
and both statistically distinguishable from the null. These results therefore accord with a recent study
which accounted for family-­level biases by using dizygotic twin pairs, obtaining between-­family and
within-­family estimates for the effect of BMI on ADHD symptoms (Liu et al., 2021). Using a PGS of
SNPs associated with adult BMI, within-­family analysis found a 0.07 S.D. increase in ADHD symptoms
at age 8 per S.D. increase in BMI PGS, which was consistent with the between-­family estimate. The
between-­family estimate was attenuated by adjustment for parental education, suggesting an influ-
ence of family-­level processes. In our study, classic MR estimates for depressive and ADHD symptoms
which adjusted for parental education were consistent with the main results, with largely overlap-
ping confidence intervals, although point estimates were closer to the null. Thus, our results are also
consistent with an influence of demographic or family-­level effects, and with earlier evidence that such
processes impact the relationship between BMI and ADHD (Chen et al., 2014; Geuijen et al., 2019).
Several sources of genetic familial bias may have influenced classic MR estimates of the impact of
the child’s own BMI. Firstly, frequencies of BMI-­associated variants may differ between sub-­populations
in a similar manner to environmental influences on emotional or behavioural functioning (popula-
tion stratification). Such gene-­environment correlation can inflate estimates from classic MR models,
but are unlikely to affect within-­family MR models, where ancestry is fully controlled for via parental
genotypes. Although we included principal components of ancestry in all models, residual population
stratification may nevertheless have influenced the classic MR results. Secondly, there may be indirect
effects of parental BMI via the family environment (dynastic effects, or genetic nurture). This could
explain the association of maternal BMI with children’s depressive symptoms in the within-­family MR
model using the adult BMI PGS. In observational studies, maternal pre-­pregnancy obesity is linked
with children’s risk of emotional disorders and ADHD (Sanchez et al., 2018). Although mechanisms
are not well understood, an in utero effect on children’s neurodevelopment of metabolic correlates
of obesity has been proposed (Edlow, 2017). Our within-­family MR results suggest that previously

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 Research article Epidemiology and Global Health | Genetics and Genomics

reported associations of maternal BMI with a child’s ADHD are not causal, but are consistent with an
effect on the child’s depressive symptoms. This could reflect an impact of maternal BMI later in the
child’s life. A well-­documented ‘wage penalty’ exists for high BMI (Howe et al., 2020), especially for
women (Bozoyan and Wolbring, 2018) reflecting social consequences of obesity being a stigma-
tized condition (Giel et al., 2010). High BMI in adulthood is also linked to worse mental health, with
stronger associations for women again pointing to gendered social processes (Rubino et al., 2020).
Maternal BMI may therefore influence children’s emotional and behavioural problems via economic
consequences, or via maternal mental health, throughout childhood. However, while our results are
consistent with an influence of maternal BMI on child’s depressive symptoms, these results should
be interpreted with caution. In contrast to estimated effects for the child’s BMI, where controlling
for parental genotype is likely to eliminate familial biases, estimated maternal and paternal effects
from within-­family MR models may have been impacted by familial biases in previous generations.
Adjustment for grandparental genotype would be required to obtain similarly unbiased estimates for
the parents. Thirdly, people with high BMI may be more likely to partner with people with emotional
or behavioural conditions (cross-­trait assortative mating). Over generations, this would induce an
association of not only the phenotypes but of associated genetic variants. We found some genomic
evidence of assortative mating for BMI, and cross-­trait assortative mating between BMI and ADHD,
but not between other traits. However, associations between polygenic scores, which only capture
some of the genetic variation associated with these phenotypes, may not capture the full extent of
genetic assortment on these traits.
Despite a high participation rate, MoBa is not perfectly representative, and selection biases linked
to participation could have affected our results. The current analyses were restricted to families with
complete genetic data and at least some relevant questionnaire data. These families were found
to have slightly more years of education than the wider MoBa sample, and the children to score
slightly lower for depressive, anxiety, and ADHD symptoms. Reflecting the requirement of genetic
data for fathers, single mothers were under-­represented. Analyses were restricted to individuals of
European ancestry, with polygenic scores based on results of GWAS which were also restricted to
individuals of European ancestry. Consequently, our results may not be generalisable to other popu-
lations. Outcomes were based on mother-­reported symptoms of depression, anxiety disorders and
ADHD, and estimates based on diagnoses may have differed. However, a child’s sociodemographic
characteristics can influence their likelihood of diagnosis independently of symptoms (Thompson
et al., 2021), indicating that such an approach is not always preferable. BMI measurements were
based on reported height and weight, so reporting bias may have influenced relationships. In many
families, fathers’ BMI was based on height and weight reported by the mothers. However, these
measures were very highly correlated with father’s self-­reports, so additional measurement error is
unlikely to have greatly affected our results for father’s BMI. Due to attrition, a substantial proportion
of values for the child’s BMI and outcomes were imputed, and we cannot be sure that observations
were missing at random conditional on variables included in imputation models. Effects of parental
BMI may be time-­varying, for example a parent’s own BMI during childhood could influence their
child independent of the parent’s later BMI. We could not explore these effects because information
on parent’s childhood BMI was not available. Within-­family MR may still be affected by horizontal
pleiotropy, and recent genetic work points to genetic overlap between BMI and psychiatric disorders
including major depression (Bahrami et al., 2020). While robustness checks found little evidence of
pleiotropy, these methods rely on assumptions. Moreover, MR-­Egger is known to give imprecise esti-
mates (Burgess and Thompson, 2017), and confidence intervals from MR-­Egger models were wide.
Thus, pleiotropy cannot be ruled out. The Mendelian randomization methods employed here assume
any causal impact of BMI is linear – that a kg/m2 increase in BMI will have the same impact regardless
of the child’s initial BMI. There is substantial evidence for a ‘J-­shaped’ phenotypic association of BMI
with common mental disorders, consistent with an impact of both high and low BMI on risk of depres-
sion or anxiety (McCrea et al., 2012; Gaysina et al., 2011; Geoffroy et al., 2014). Genetic methods
exist for exposures with nonlinear effects but require much larger samples (Sun et al., 2019). If there
exist nonlinear effects of BMI on mental health, rather than vice versa, our results may underestimate
the effects of high BMI. Finally, the effects of BMI on emotional and behavioural functioning likely
differ by age, and relationships may be substantially different for older children or adolescents. In
particular, depressive symptoms do not tend to occur until the teenage years (Kwong et al., 2019)

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 Research article Epidemiology and Global Health | Genetics and Genomics

and observational associations of BMI and ADHD become clearer with age (Nigg et al., 2016). Work
in larger samples of related individuals will be needed to precisely estimate the influence of a child’s
BMI on their emotional and behavioural outcomes. In response to a reviewer’s request, we conducted
post-­hoc power calculations to estimate the minimum effect on the outcomes of the child’s BMI which
could be detected with 80% power in a dataset of this size (40,949 trios). Simulations indicated that,
using the adult BMI PGS, an effect on each outcome of 0.15 S.D. per 5 kg/m2 could be detected using
classic MR, and an effect on each outcome of 0.22 S.D. per 5 kg/m2 using within-­family MR. Using the
childhood body size PGS, equivalent detectable effects were 0.12 S.D. and 0.16 S.D. per 5 kg/m2.
MoBa is currently the largest individual study in which this approach can be applied, but new data are
becoming available which will allow analyses of this kind within and across studies, such as through
the Within Family Consortium https://www.withinfamilyconsortium.com/home/. Meanwhile, studies
with extensive intergenerational information will be needed to fully explore mechanisms linking child
outcomes to maternal BMI.

Conclusion
Our results suggest that genetic variation associated with BMI in adulthood affects a child’s depressive
and ADHD symptoms, but genetic variation associated with recalled childhood body size does not
substantially affect these outcomes. There was little evidence that BMI affects anxiety. However, our esti-
mates were imprecise, and these differences may be due to estimation error. There was little evidence
that parental BMI affects a child’s ADHD or anxiety symptoms, but factors associated with maternal BMI
may independently influence a child’s depressive symptoms. Genetic studies using unrelated individuals,
or polygenic scores for adult BMI, may have overestimated the causal effects of a child’s own BMI.

Acknowledgements
The Norwegian Mother, Father and Child Cohort Study is supported by the Norwegian Ministry of
Health and Care Services and the Ministry of Education and Research. We are grateful to all the partic-
ipating families in Norway who take part in this on-­going cohort study. We thank the Norwegian Insti-
tute of Public Health (NIPH) for generating high-­quality genomic data. This work was performed on
the TSD (Tjeneste for Sensitive Data) facilities, owned by the University of Oslo, operated and devel-
oped by the TSD service group at the University of Oslo, IT-­Department (USIT). (​tsd-­​drift@​usit.​uio.​no).
The analyses were performed on resources provided by Sigma2 - the National Infrastructure for High
Performance Computing and Data Storage in Norway. This research is part of the HARVEST collabo-
ration, supported by the Research Council of Norway (#229624). We also thank the NORMENT Centre
for providing genotype data, funded by the Research Council of Norway (#223273) and deCODE
Genetics, South East Norway Health Authority and KG Jebsen Stiftelsen. We further thank the Center
for Diabetes Research, the University of Bergen for providing genotype data and performing quality
control and imputation of the data funded by the ERC AdG project SELECTionPREDISPOSED, Stif-
telsen Kristian Gerhard Jebsen, Trond Mohn Foundation, the Research Council of Norway, the Novo
Nordisk Foundation, the University of Bergen, and the Western Norway Health Authorities (Helse Vest).
Funding: This research was funded by a project entitled ‘social and economic consequences of health:
causal inference methods and longitudinal, intergenerational data’, which is part of the Health Foun-
dation’s Social and Economic Value of Health Programme (Grant ID: 807293). The Health Foundation
is an independent charity committed to bringing about better health and health care for people in the
UK. This research is part of the HARVEST collaboration, supported by the Research Council of Norway
(#229624). Individual co-­authors area also supported by specific sources of funding. ZA is supported
by a Marie Skłodowska-­Curie Fellowship from the European Union (894675) and the South-­Eastern
Norway Regional Health Authority (2019097). TR is supported by the Research Council of Norway
(274611 PI: Reichborn-­Kjennerud). OAA is funded by the Research Council of Norway (223273) and
EU H2020 RIA (847776 CoMorMent). ØH is supported by the University of Bergen, Norway. SJ was
supported by Helse Vest’s Open Research Grant (grants #912250 and F-­12144), the Novo Nordisk
Foundation (grant NNF19OC0057445) and the Research Council of Norway (grant #315599). PN is
supported by the European Research Council (AdG SELECTionPREDISPOSED #293574), the Trond
Mohn Foundation (Mohn Center for Diabetes Precision Medicine), the Research Council of Norway
(FRIPRO grant #240413), the Western Norway Regional Health Authority (Strategic Fund “Person-
alized Medicine for Children and Adults”), the Novo Nordisk Foundation (grant #54741), and the

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 Research article Epidemiology and Global Health | Genetics and Genomics

Norwegian Diabetes Association. AH was supported by the South-­Eastern Norway Regional Health
Authority (2018059, 2020022) and the Research Council of Norway (288083). LDH is supported by
a Career Development Award from the UK Medical Research Council (MR/M020894/1). NMD was
supported via a Research Council of Norway grant (295989). The Medical Research Council (MRC) and
the University of Bristol support the MRC Integrative Epidemiology Unit [MC_UU_00011/1] (AMH, ES,
LDH, NMD, GDS, TM). The funders had no role in the design or execution of this analysis, interpreta-
tion of results, or the decision to publish.

Additional information

Competing interests
Ole A Andreassen: has received speaker’s honorarium from Sunovion and Lundbeck and is a consul-
tant for HealthLytix. The other authors declare that no competing interests exist.

Funding
Funder Grant reference number Author

Medical Research Council MC_UU_00011/1 Amanda M Hughes

Eleanor Sanderson
Tim Morris
George Davey Smith
Laura D Howe
Neil M Davies

University of Bristol Amanda M Hughes

Eleanor Sanderson
Tim Morris
George Davey Smith
Laura D Howe
Neil M Davies

European Research Council 894675 Ziada Ayorech

South-Eastern Norway 2019097 Ziada Ayorech

Regional Health Authority

Research Council of Norway 295989 Neil M Davies

Research Council of Norway 288083 Alexandra Havdahl

South-Eastern Norway 2018059 Alexandra Havdahl

Regional Health Authority

Research Council of Norway 274611 Ted Reichborn-Kjennerud

Research Council of Norway 223273 Ole A Andreassen

European Research Council 847776 CoMorMent Ole A Andreassen

University of Bergen Øyvind Helgeland

South-Eastern Norway 2020022 Alexandra Havdahl

Regional Health Authority

Helse Vest 912250 Stefan Johansson

Helse Vest F-12144 Stefan Johansson

Novo Nordisk NNF19OC0057445 Stefan Johansson

Research Council of Norway 315599 Stefan Johansson

Medical Research Council MR/M020894/1 Laura D Howe

European Research Council 293574 Pål Njølstad

Trond Mohn stiftelse Pål Njølstad

Research Council of Norway 240413 Pål Njølstad

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 Research article Epidemiology and Global Health | Genetics and Genomics

Funder Grant reference number Author

Western Norway Regional Pål Njølstad

Health Authority

Novo Nordisk 54741 Pål Njølstad

Norwegian Diabetes Pål Njølstad

Association

The funders had no role in study design, data collection and interpretation, or the
decision to submit the work for publication.

Author contributions
Amanda M Hughes, Conceptualization, Formal analysis, Investigation, Visualization, Writing – original
draft, Writing – review and editing; Eleanor Sanderson, Formal analysis, Methodology, Writing – review
and editing; Tim Morris, Ziada Ayorech, Martin Tesli, Helga Ask, Øyvind Helgeland, Stefan Johansson,
George Davey Smith, Investigation, Writing – review and editing; Ted Reichborn-­Kjennerud, Data
curation, Investigation, Writing – review and editing, Funding acquisition; Ole A Andreassen, Per
Magnus, Pål Njølstad, Data curation, Investigation, Writing – review and editing; Alexandra Havdahl,
Conceptualization, Data curation, Funding acquisition, Investigation, Writing – review and editing;
Laura D Howe, Funding acquisition, Writing – review and editing, Conceptualization; Neil M Davies,
Conceptualization, Funding acquisition, Investigation, Writing – review and editing

Author ORCIDs
Amanda M Hughes ‍ ‍http://orcid.org/0000-0001-5896-7650
Tim Morris ‍ ‍http://orcid.org/0000-0001-8178-6815
Helga Ask ‍ ‍http://orcid.org/0000-0003-0149-5319
George Davey Smith ‍ ‍http://orcid.org/0000-0002-1407-8314
Neil M Davies ‍ ‍http://orcid.org/0000-0002-2460-0508

Ethics
The establishment of MoBa and initial data collection was based on a license from the Norwegian
Data Protection Agency and The Regional Committees (REC) for Medical and Health Research Ethics.
The REC South East Norway, one of four in Norway, was the ethical committee that evaluated the
ethics of this study. Approval from the REC was granted (2016/1702). Informed consent was obtained
from each MoBa participant upon recruitment, which included consent to link to the Medical Birth
Registry of Norway (MBRN). The MoBa cohort is now based on regulations related to the Norwegian
Health Registry Act.

Decision letter and Author response

Decision letter https://doi.org/10.7554/eLife.74320.sa1
Author response https://doi.org/10.7554/eLife.74320.sa2

Additional files
Supplementary files
• Supplementary file 1. (a) SNPs used in the polygenic score for adult BMI. (b) SNPs used in the
polygenic score for childhood body size BMI. (c) SNPs used in the polygenic score for depression. (d)
SNPs used in the polygenic score for ADHD.
• Transparent reporting form
• Reporting standard 1. Strobe checklist.

Data availability
The consent given by the participants does not open for storage of data on an individual level in repos-
itories or journals. Researchers who want access to data sets for replication should submit an applica-
tion to ​datatilgang@​fhi.​no. Access to data sets requires approval from The Regional Committee for
Medical and Health Research Ethics in Norway and an agreement with MoBa.

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 Research article Epidemiology and Global Health | Genetics and Genomics

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Appendix 1
Additional methods
1. MoBa study details
This study is based on the Norwegian Mother, Father and Child Cohort Study (MoBa) and uses
data from the Medical Birth Registry of Norway (MBRN). The Medical Birth Registry (MBRN) is a
national health registry containing information about all births in Norway. The current analysis is
based on version 12 of the quality-­assured data files released for research in January 2019. The
establishment of MoBa and initial data collection was based on a license from the Norwegian Data
Protection Agency and approval from The Regional Committees for Medical and Health Research
Ethics. The MoBa cohort is now based on regulations related to the Norwegian Health Registry Act.
The current study was approved by The Regional Committees for Medical and Health Research
Ethics (2016/1702).
The Norwegian Mother, Father and Child Cohort Study is supported by the Norwegian Ministry
of Health and Care Services and the Ministry of Education and Research. We are grateful to all the
participating families in Norway who take part in this on-­going cohort study.

2. Genotyping
Genotyping of MoBa has been conducted through multiple research projects, spanning several
years. The research projects (HARVEST, SELECTIONpreDISPOSED, and NORMENT) provided
genotype data to MoBa Genetics. In total, 238,001 MoBa samples were sent to be genotyped in
24 genotyping batches. This was carried out at 3 centres (1. Genomics Core Facility, Trondheim,
Norway, 2. ERASMUS MC, Rotterdam, Netherlands, and 3. deCODE Genetics, Reykjavik, Iceland)
using six genotyping arrays. The 24 batches had varying selection criteria; this included a batch of
ADHD child cases and their parents, and another of matched control children and their parents.
Detailed information on batch selection and the genotyping process are described elsewhere
(Corfield et al., 2022).

3. Genetic quality control

Pre-­imputation QC, phasing, imputation, and post-­imputation QC were carried out according to
the MoBaPsychGen pipeline, which includes QC on both single nucleotide polymorphism (SNP) and
individual level, and whose full details are provided elsewhere (Corfield et al., 2022). Output of the
pipeline included 207,569 unique individuals and 6,981,748 SNPs after post-­imputation QC; unique
individuals comprised 76,577 children, 53,358 fathers, and 77,634 mothers. Phasing and imputation
were performed using the publicly available Haplotype Reference Consortium release 1.1 panel
as a reference. Information from the Medical Birth Registry of Norway and MoBa questionnaires
were used to identify biological sex, year of birth, reported parent-­offspring (PO) relationships, and,
in the offspring generation, multiple births. Ancestry outliers were identified based on principal
component analysis with the 1000 Genomes phase 1 unrelated data (1,083 individuals) (Auton et al.,
2015). Approximately 95% of the participants were identified as having European ancestry. Ancestry
outliers were removed based on visual inspection, using pairwise plots for the first seven principal
components. Similarly, principal component analysis was used to identify substructure within each
subpopulation of all MoBa batches. PCs were first estimated in founders only, and non-­founders
projected into the PC space of the founders. Outliers were removed based on visual inspection,
using pairwise plots for the first ten principal components.
Relatedness was inferred using KING version 2.2.5 (Manichaikul et al., 2010). In the presence
of admixture, KING accurately infers MZ twin or duplicate pairs (kinship coefficient >0.3540), first-­
degree (PO, FS, DZ twin pairs; kinship coefficient range 0.1770–0.3540), second-­degree (HS, GO,
AUNN; kinship coefficient range 0.0884–0.1770), and third-­degree (first cousins; kinship coefficient
range 0.0442–0.0884) relationships. After within-­ family and between-­ family relationships were
confirmed by genetic data, a check for Mendelian errors (ME) was performed in PLINK. The ME
check included families with one or two parents present in the data. Families with >5% errors and
SNPs with >1% errors were removed. The remaining ME were set to missing.

4. Multiple imputation
Multiple imputation by chained equations was performed in STATAv16 to estimate missing
phenotypic information for the 40,949 trios with complete genetic data. 100 imputed datasets were

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 Research article Epidemiology and Global Health | Genetics and Genomics

produced and analysis across these datasets conducted with STATA’s mi estimate commands. The
imputation model included all BMI variables used in the main analyses (child’s BMI at age 8, mother’s
pre-­pregnancy BMI and father’s BMI as reported at 17 weeks gestation), the child’s sex and year of
birth, and other phenotypic covariates used in non-­genetic models, including mother’s and father’s
smoking status reported at 17 weeks gestation, mother’s and father’s depressive/anxiety symptoms
[using selected items from the 25-­item Hopkins Checklist (Hesbacher et al., 1980)], and ADHD
symptoms [from the 6-­item adult ADHD self-­report scale (Kessler et al., 2005)], maternal parity at the
child’s birth, and family socioeconomic characteristics, including parental educational qualifications
and categorical variables of income and subjective financial strain. Variables from the birth registry
file were also included as auxiliary variables: the mother’s marital status, the age of the mother
and father, and the child’s birthweight and length. Approximately normally-­distributed continuous
variables including BMI were imputed using truncated regression, specifying as upper and lower
limits the smallest and largest values observed in the full MoBa sample. Ordered categorical variables
were imputed with ordered logistic regression. There was no missingness in genetic information
within the analytic sample. Polygenic scores for adult BMI, childhood body size, depression, ADHD,
and educational attainment were included on the right-­hand side of the imputation equations, along
with indicators for genotyping centre and chip and the 20 principal components of ancestry for all
individuals. Continuous variables which were not normally-­distributed were imputed with predictive
mean matching, specifying knn(10). This included child’s depressive and anxiety symptoms at age
8 (SMFQ and SCARED summary scores), mother’s and father’s depressive/anxiety symptoms at
17 weeks gestation (summary scores based on items from the 25-­item Hopkins Checklist (Hesbacher
et al., 1980), and mother’s and father’s ADHD symptoms from the 6-­item adult ADHD self-­report
scale (Kessler et al., 2005). To facilitate analysis of ADHD inattention and hyperactivity subscales,
the two subscales were imputed, again with predictive mean matching, and the full scale calculated
post-­imputation with mi passive. An earlier measure of the child’s ADHD symptoms at 5 yrs, based
on questions from the Short-­Form Conners Parent Rating Scale (Kumar and Steer, 2003), was
included as an auxiliary variable. The percentage of imputed data in the analytic sample for each
variable was: mother’s education 3.4%, father’s education 2.2%, mother’s smoking 2.0%, father’s
smoking 0.7%, mother’s depressive symptoms 3.2%, father’s depressive symptoms 7.1%, mother’s
ADHD symptoms 40.9%, father’s ADHD symptoms 60.1%, mother’s BMI: 4.0%, father’s BMI: 3.8%,
child’s BMI at age 8: 60.6%, child’s depressive symptoms at age 8: 54.2%, child’s anxiety symptoms
at age 8: 54.1%, child’s ADHD symptoms (inattention and hyperactivity) both 54.1%.

5. Polygenic score construction

Beginning with the full GWAS results for each phenotype (Yengo et al., 2018; Richardson et al.,
2020; Wray et al., 2018; Demontis et al., 2019), R was used to subset SNPs included in full
GWAS results to SNPs also available in the quality controlled MoBa data. From SNPs available in
both, independent genome-­wide significant associations were identified by clumping in MRBase,
specifying r=0.01 and p<5.0 × 10–8 (Hemani et al., 2018b). First subsetting to SNPs available in
MoBa and then clumping within these avoids the need for an additional step identifying proxy SNPs.
This left 954 SNPs associated with adult BMI, and 321 associated with childhood body size.
Dosage data for MoBa participants for the genetic variants relevant to each polygenic score were
extracted from the final quality controlled -bfiles using PLINK, a
​ nd.​raw files imported to STATA. SNPs
were harmonized by comparing effect alleles in the GWAS and reference alleles in MoBa.
Polygenic scores were calculated as the sum of the number of effect alleles (0, 1, or 2) multiplied
in each case by the harmonized SNP-­coefficient from the GWAS. There was a very small amount of
missingness in individual SNPs due to quality control measures. Among SNPs included in the adult
BMI PGS, the median proportion of individuals missing the SNP was 0.001 and the maximum 0.04.
For SNPs included in the childhood body size PGS, equivalent values were 0.002 and 0.04, for SNPs
included in the depression and the ADHD PGS these were 0.003 and 0.01. Where individual SNP
information was missing for an individual, the sample mean for the number of effect alleles (between
0 and 2) was added for that SNP.

6. Model equations
In within-­family MR models, we used polygenic scores for all members of a child-­mother-­child trio to
instrument the BMI of all three individuals. Within-­families MR models were adjusted for child’s sex,
the first 20 principal components of ancestry for the child and both parents, and the genotyping chip
and centre of the child and both parents.

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In Stata, this was specified in the form: ivregress 2sls outcome (c_bmi m_bmi f_bmi = c_pgs m_
pgs f_pgs) sex c_PC* m_PC* f_PC* c_genotyping_centre* m_ genotyping_centre* f_ genotyping_
centre* c_genotyping_chip* m_ genotyping_chip* f_ genotyping_chip*
This can be represented with the following equations:
The outcomes (depressive, anxiety, and ADHD symptoms) can be expressed as:
yi = β0 + β1 Xic + β2Xim + β3Xif + βcC +ei
The three exposures are offspring’s, mother’s, and father’s BMI:
Xic = γoc + γ1cZic + γ2cZim + γ3cZif + γ4cC+ vic
Xim=γom + γ1mZic + γ2mZim + γ3mZif + γ4mC + vim
Xif=γoc + γ1fZic + γ2fZim + γ3fZif + γ4fC + vif where: yi = outcome
Xic = child’s BMI
Xim = mother’s BMI
Xif = father’s BMI
Zic = child’s polygenic score
Zim = mother’s polygenic score
Zif = father’s polygenic score
C=covariates including principal components for offspring, mother and father and genotyping
centre and chip ei = error term for the outcome equation vic = error term for the child exposure
(BMI) equation vim = error term for the mother exposure (BMI) equation vif = error term for the
father exposure (BMI) equation

Additional Results
1. Comparison of analytic sample and excluded participants
To assess if participants included in the analytic sample (N=40,949) differed from others in the birth
registry file (N=72,742) (Appendix 1—figure 1), we conducted t-­tests and chi-­squared tests for
key characteristics at birth, BMI, and outcomes using unimputed data. Reflecting the large size of
the sample population, several differences reached statistical significance. Children in the analytic
sample did not differ from those excluded on sex but were slightly older (mean year of birth: 2005.4
vs 2004.5). They had slightly higher birthweight (mean = 3.6 kg vs 3.4 kg) and slightly younger
fathers (mean paternal 32.6 vs 32.8 years). Mothers and fathers included in the analytic sample had
slightly higher educational qualifications (e.g., 24.1% and 24.3% of mothers and fathers respectively
had 4 years of college education, against 21.0% and 21.5% for those not included). At the time of
the child’s birth, mothers in the analytic sample had fewer existing children (e.g., 46.8% vs 42.4% had
none), were more likely to be married or cohabiting (97.4% vs 94.4%), and less likely to have smoked
in pregnancy (e.g., daily smoking: 4.5% vs 6.3%). Fathers in the analytic sample were also more likely
to have stopped smoking during the pregnancy (20.9% vs 15.8%). There was little of a difference in
BMI for mothers, fathers, or children. Children in the analytic sample had slightly lower depressive
symptoms (mean SMFQ = 1.81 vs 1.91),anxiety symptoms (mean SCARED: 1.04 vs 1.00),and ADHD
symptoms (mean RS-­DBD ADHD: 8.4 vs 8.7). Descriptive characteristics of the full MoBa sample are
in Appendix 1—table 1.

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Appendix 1—figure 1. Flow chart of inclusion and exclusion of MoBa participants into the study sample.

Appendix 1—figure 2. Associations of child’s BMI polygenic scores with ancestry. Associations of the child’s
polygenic scores for BMI and the child’s principal components of ancestry, adjusted for the child’s genotyping
centre and chip.

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Appendix 1—figure 3. Associations of child’s BMI polygenic scores with ancestry, adjusted for parental polygenic
scores. Associations of the child’s polygenic scores for BMI and the child’s principal components of ancestry,
adjusted for the child’s genotyping centre and chip and the parents’ polygenic scores.

Appendix 1—table 1. Descriptive statistics of full MoBa sample (N=113,691)*.

Continuous variables mean SD N obs

Maternal age at birth 30.1 4.6 113,691

Paternal age at birth 32.7 5.5 113,172

Maternal depressive/anxiety symptoms, 1.3 2.0 100,570

based on 5 items from the
Hopkins Symptoms Checklist-­25 (SCL-­25)†

Paternal depressive/anxiety symptoms, 1.2 2.1 77,018

based on 8 items from the
Hopkins Symptoms Checklist-­25 (SCL-­25)‡

Maternal ADHD symptoms: adult ADHD 6.6 3.5 56,255

self-­report scale§

Paternal ADHD symptoms: adult ADHD 8.2 3.2 34,425

self-­report scale¶

Maternal pre-­pregnancy BMI (kg/m2) 24.0 4.1 100,060

2
Paternal BMI (kg/m ) 25.9 3.3 79,536
2
Child’s BMI at age 8 (kg/m ) 16.2 2.0 36,894

Child depressive symptoms age 8: Short 1.9 2.4 43,065

Mood and Feelings Questionnaire
(SMFQ)**

Child anxiety symptoms age 8: Screen for 1.0 1.2 43,298

Child Anxiety Related Disorders (SCARED)††

Child ADHD symptoms age 8: Parent/ 8.5 7.2 43,238

Teacher Rating Scale for Disruptive
Behaviour Disorders (RS-­DBD)‡ ‡
Appendix 1—table 1 Continued on next page

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 Research article Epidemiology and Global Health | Genetics and Genomics

Appendix 1—table 1 Continued

Continuous variables mean SD N obs

Child ADHD symptoms (inattention) age 8: 5.0 4.1 43,194

Parent/Teacher Rating Scale for Disruptive
Behaviour Disorders (RS-­DBD)§ §

Child ADHD symptoms (hyperactivity) 3.6 3.9 43,177

age 8: Parent/Teacher Rating Scale for
Disruptive Behaviour Disorders (RS-­DBD)§ §

Categorical variables Category % N obs

Child’s sex male 51.3 113,477

female 48.7

maternal educational 9 year elementary education 2.8 101,020

qualifications
Up to 2 years further education 5.2

Further education: vocational 12.8

Further education: general 15.7

studies, sixth form

Higher education: college/ 40.9

university, up to 4 years

Higher education: college/ 22.6

university, over 4 years

paternal educational 9 year elementary education 4.8 100,891

qualifications
Up to 2 years further education 6.6

Further education: vocational 26.2

Further education: general 13.2

studies, sixth form

Higher education: college/ 26.5

university, up to 4 years

Higher education: college/ 22.7

university, over 4 years

maternal parity at child’s birth 0 44.0 113,691

1 35.9

2 15.6

3 3.4

4+ 1.1

Mother’s marital status at birth Married/registered partner 95.5 113,691

single 4.5

Mother’s smoked during never 49.9 101,373

pregnancy
Stopped before week 17 41.7

Currently, sometimes 2.8

Currently, daily 5.6

*All participants in the birth registry file who had not withdrawn consent.
†
Possible range: 0–15.
‡
Possible range: 0–24.
§
Possible range: 0–24.
¶
Possible range: 0–24.
**Possible range: 0-­26.
††
Possible range: 0-­10.
‡‡
Possible range: 0–54.
§§
Possible range: 0–27.

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Appendix 1—table 2. Descriptive statistics of analytic sample (N=40,949)*, unimputed data.

Continuous variables mean SD N obs

Maternal age at birth 30.2 4.4 40,949

Paternal age at birth 32.6 5.1 40,945

Maternal depressive/anxiety symptoms, based on 5 items 1.2 1.9 39,647

from the
Hopkins Symptoms Checklist-­25 (SCL-­25)†

Paternal depressive/anxiety symptoms, based on 8 items 1.1 2.1 38,050

from the
Hopkins Symptoms Checklist-­25 (SCL-­25)‡

Maternal ADHD symptoms: adult ADHD self-­report scale§ 6.5 3.4 24,192

Paternal ADHD symptoms: adult ADHD self-­report scale¶ 8.2 3.1 16,348

Maternal pre-­pregnancy BMI (kg/m2) 24.0 4.1 39,323

Paternal BMI (kg/m2) 25.9 3.2 39,405

Child’s BMI at age 8 (kg/m2) 16.2 2.0 16,144

Child depressive symptoms age 8: Short Mood and 1.8 2.4 18,747
Feelings Questionnaire (SMFQ)**

Child anxiety symptoms age 8: Screen for Child Anxiety 1.0 1.2 18,834
Related Disorders (SCARED)††

Child ADHD symptoms age 8: Parent/Teacher Rating 8.4 7.1 18,813

Scale for Disruptive Behaviour Disorders (RS-­DBD)‡ ‡

Child ADHD symptoms (inattention) age 8: Parent/ 4.9 4.0 18,794

Teacher Rating Scale for Disruptive Behaviour Disorders
(RS-­DBD)§ §

Child ADHD symptoms (hyperactivity) age 8: Parent/ 3.5 3.8 18,787

Teacher Rating Scale for Disruptive Behaviour Disorders
(RS-­DBD)§ §

Categorical variables Category % N obs

Child’s sex male 51.0 40,949

female 48.9

maternal educational 9 year elementary education 2.0 39,569

qualifications
Up to 2 years further education 4.1

Further education: vocational 12.1

Further education: general studies, sixth form 14.9

Higher education: college/university, up to 42.8

4 years

Higher education: college/university, over 24.8

4 years

paternal educational 9 year elementary education 3.4 40,062

qualifications
Up to 2 years further education 5.6

Further education: vocational 25.1

Further education: general studies, sixth form 12.9

Higher education: college/university, up to 28.5

4 years

Higher education: college/university, over 24.4

4 years
Appendix 1—table 2 Continued on next page

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Appendix 1—table 2 Continued

Continuous variables mean SD N obs

maternal parity at child’s birth 0 46.8 40,949

1 35.7

2 14.0

3 2.7

4+ 0.7

Mother’s marital status at birth Married/registered partner 97.4 40,949

single 2.6

Mother’s smoked during never 51.1 40,118

pregnancy
Stopped before week 17 42.0

Currently, sometimes 2.4

Currently, daily 4.5

*The reasons for exclusions and numbers in each case are shown in Appendix 1—figure 1.
†
Possible range: 0–15.
‡
Possible range: 0–24.
§
Possible range: 0–24.
¶
Possible range: 0–24.
**Possible range: 0-­26.
††
Possible range: 0–10.
‡‡
Possible range: 0–54.
§§
Possible range: 0–27.

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Appendix 1—table 3. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa, adult BMI PGS (N=40,949)*.
Non-­genetic estimate† MR estimate ‡ Within-­families MR estimate ‡

Beta (per 5 Beta (per 5 Beta (per 5

Outcome kg/m2) CI p kg/m2) CI p kg/m2) CI p

Child BMI 0.05 0.01,0.09 0.02 0.45 0.26,0.64 <0.001 0.26 –0.01,0.52 0.06

Mother’s BMI 0.05 0.03,0.07 <0.001 0.11 0.02,0.19 0.01

Depressive symptoms:
standardized SMFQ§ score Father’s BMI 0.01 –0.02,0.03 0.67 0.02 –0.09,0.13 0.71

Child BMI –0.07 −0.11,–0.03 0.001 –0.06 –0.25,0.12 0.51 0.01 –0.25,0.26 0.96
Anxiety symptoms: Mother’s BMI 0.01 –0.01,0.03 0.47 –0.03 –0.11,0.05 0.49

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standardized SCARED¶
score Father’s BMI –0.00 –0.02,0.02 0.89 –0.02 –0.13,0.09 0.72

Child BMI –0.07 −0.11,–0.03 0.001 0.35 0.17,0.53 <0.001 0.36 0.09,0.63 0.009
ADHD symptoms: Mother’s BMI 0.04 0.02,0.06 <0.001 0.00 –0.08,0.09 0.97
standardized RS-­DBD**
score, ADHD items Father’s BMI 0.02 –0.00,0.04 0.10 –0.01 –0.12,0.09 0.80

Child BMI –0.06 −0.10,–0.02 0.006 0.32 0.14,0.49 <0.001 0.38 0.12,0.65 0.005
ADHD-­inattention
symptoms: standardized Mother’s BMI 0.05 0.03,0.07 <0.001 0.01 –0.08,0.09 0.86
RS-­DBD** score, inattention
items Father’s BMI 0.02 –0.00,0.05 0.06 –0.06 –0.17,0.04 0.24

Child BMI –0.06 −0.10,–0.02 0.002 0.31 0.13,0.49 0.001 0.27 –0.00,0.54 0.05
ADHD-­hyperactivity
symptoms: standardized RS-­ Mother’s BMI 0.03 0.01,0.05 0.005 –0.00 –0.09,0.08 0.92
DBD** score, hyperactivity
items Father’s BMI 0.01 –0.01,0.04 0.32 0.04 –0.07,0.15 0.47

*Coefficients represent S.D. change in symptoms per 5 kg/m2 increase in BMI.


†
Phenotypic models adjust for the child’s sex and birth year, the mother’s parity at the child’s birth, and the mother’s and father’s: educational qualifications, depressive/anxiety and ADHD
symptoms, and smoking status during pregnancy. They also adjust for the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
‡
Genetic models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
§
Short Mood and Feelings Questionnaire.
¶
Screen for Child Anxiety Related Disorders.
**Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 4. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa, childhood body size PGS (N=40,949)*.
Non-­genetic estimate† MR estimate ‡ Within-­families MR estimate ‡

Beta (per 5 Beta (per 5 Beta (per 5

Outcome kg/m2) CI p kg/m2) CI p kg/m2) CI p

Child BMI 0.05 0.01,0.09 0.02 0.08 –0.07,0.22 0.29 0.02 –0.20,0.23 0.88

Mother’s BMI 0.05 0.03,0.07 <0.001 0.02 –0.09,0.14 0.67

Depressive symptoms:
§
standardized SMFQ score Father’s BMI 0.01 –0.02,0.03 0.67 0.05 –0.10,0.19 0.51

Child BMI –0.07 −0.11,–0.03 0.001 –0.04 –0.18,0.11 0.62 0.02 –0.18,0.23 0.83
Anxiety symptoms: Mother’s BMI 0.01 –0.01,0.03 0.47 –0.02 –0.12,0.09 0.78

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standardized SCARED¶
score Father’s BMI –0.00 –0.02,0.02 0.89 –0.06 –0.19,0.08 0.42

Child BMI –0.07 −0.11,–0.03 0.001 –0.07 –0.21,0.07 0.35 –0.03 –0.22,0.17 0.80
ADHD symptoms: Mother’s BMI 0.04 0.02,0.06 <0.001 –0.03 –0.12,0.07 0.62
standardized RS-­DBD**
score, ADHD items Father’s BMI 0.02 –0.00,0.04 0.10 –0.02 –0.15,0.11 0.77

Child BMI –0.06 −0.10,–0.02 0.006 –0.04 –0.18,0.11 0.63 –0.05 –0.25,0.14 0.59
ADHD-­inattention
symptoms: standardized Mother’s BMI 0.05 0.03,0.07 <0.001 0.03 –0.07,0.13 0.61
RS-­DBD** score,
inattention items Father’s BMI 0.02 –0.00,0.05 0.06 –0.01 –0.14,0.12 0.86

Child BMI –0.06 −0.10,–0.02 0.002 –0.08 –0.22,0.05 0.24 0.01 –0.20,0.22 0.95
ADHD-­hyperactivity
symptoms: standardized Mother’s BMI 0.03 0.01,0.05 0.005 –0.07 –0.18,0.03 0.18
RS-­DBD** score,
hyperactivity items Father’s BMI 0.01 –0.01,0.04 0.32 –0.02 –0.16,0.11 0.74

*Coefficients represent S.D. change in symptoms per 5 kg/m2 increase in BMI.


†
Phenotypic models adjust for the child’s sex and birth year, the mother’s parity at the child’s birth, and the mother’s and father’s: educational qualifications, depressive/anxiety and ADHD
symptoms, and smoking status during pregnancy. They also adjust for the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
‡
Genetic models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
§
Short Mood and Feelings Questionnaire.
¶
Screen for Child Anxiety Related Disorders.
**Parent/Teacher Rating Scale for Disruptive Behaviour Disorders

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Appendix 1—table 5. Associations of phenotypes and polygenic scores within parental pairs*.
Phenotypes: regression of father’s BMI, depressive symptoms, and ADHD symptoms on mother’s phenotypes

Father’s: BMI Father’s: Depressive symptoms Father’s: ADHD symptoms

Beta (95% CI), p Beta (95% CI), p Beta (95% CI), p

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Mother’s: BMI 0.23 (0.22,0.25) p<0.001 0.01 (-­0.00,0.02) p=0.09 0.03 (0.02,0.05) p<0.001

Mother’s: Depressive symptoms 0.00 (-­0.01,0.01), p=0.85 0.18 (0.16,0.20) p<0.001 0.10 (0.09,0.12), P<0.001

Mother’s: ADHD symptoms 0.01 (-­0.02,0.01) p=0.32 0.05 (0.05,0.06) p<0.001 0.11 (0.09,0.13) p<0.001

Polygenic scores: regression of father’s PGS for BMI, depression, and ADHD: regression of father’s PGS on mother’s PGS

Father’s: Adult BMI PGS Father’s: Childhood body size PGS Father’s: Depression PGS Father’s: ADHD PGS

Beta (95% CI), p Beta (95% CI), p Beta (95% CI), p Beta (95% CI)

Mother’s: Adult BMI PGS 0.01 (0.00,0.02), p=0.02 0.01 (0.00,0.02), p=0.008 –0.00 (-­0.01,0.01), p=0.62 –0.00 (-­0.01,0.01), p=0.49

Mother’s: Childhood body size PGS 0.01 (-­0.00,0.02), p=0.10 0.01 (-­0.00,0.02), p=0.15 0.00 (-­0.00,0.01), p=0.33 0.01 (0.00,0.02), p=0.03

Mother’s: Depression PGS –0.01 (−0.02–0.00), p=0.11 –0.00 (-­0.01,0.01), p=0.76 –0.00 (-­0.01,0.01), p=0.44 –0.00 (-­0.01,0.01), p=0.47

Mother’s: ADHD PGS –0.00 (-­0.01,0.01), p=0.58 0.01 (-­0.00,0.02), p=0.24 –0.00 (-­0.01,0.01), p=0.42 –0.00 (-­0.01,0.01), p=0.93

*All models adjusted for the first 20 principal components of ancestry, genotyping centre and genotyping chip of the mother and father.


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Appendix 1—table 6. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa, adult BMI PGS, log-­transformed outcomes (N=40,949)*.
Non-­genetic estimate† MR estimate ‡ Within-­families MR estimate ‡

Outcome Beta (per 5 CI p Beta (per 5 CI p Beta (per 5 CI p

kg/m2) kg/m2) kg/m2)

Depressive symptoms: log-­ Child BMI 0.03 0.01,0.06 0.02 0.31 0.18,0.45 <0.001 0.16 –0.04,0.35 0.12
transformed SMFQ§ score
Mother’s BMI 0.04 0.03,0.05 <0.001 0.08 0.02,0.14 0.01

Father’s BMI 0.01 –0.01,0.02 0.56 0.03 –0.05,0.10 0.52

Anxiety symptoms: log-­ Child BMI –0.03 −0.05,–0.01 0.001 –0.04 –0.14,0.05 0.38 –0.00 –0.14,0.13 0.97
transformed SCARED¶ score
Mother’s BMI 0.00 –0.01,0.01 0.60 –0.02 –0.06,0.02 0.35

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

Father’s BMI –0.00 –0.01,0.01 1.00 –0.01 –0.06,0.05 0.79

ADHD symptoms: log-­ Child BMI –0.05 −0.08,–0.02 0.002 0.27 0.13,0.40 <0.001 0.28 0.08,0.49 0.006
transformed RS-­DBD**
score Mother’s BMI 0.03 0.02,0.05 <0.001 0.00 –0.06,0.07 0.90

Father’s BMI 0.02 –0.00,0.03 0.07 –0.02 –0.10,0.06 0.66

ADHD-­inattention Child BMI –0.04 −0.07,–0.01 0.007 0.22 0.09,0.34 0.001 0.29 0.10,0.47 0.003
symptoms: log-­transformed
RS-­DBD** score, inattention Mother’s BMI 0.03 0.02,0.05 <0.001 0.00 –0.06,0.07 0.92
items
Father’s BMI 0.02 0.00,0.03 0.05 –0.06 –0.14,0.02 0.13

ADHD-­hyperactivity Child BMI –0.05 −0.08,–0.01 0.004 0.24 0.10,0.39 0.001 0.18 –0.04,0.40 0.10
symptoms: log-­transformed
RS-­DBD** score, Mother’s BMI 0.02 0.00,0.04 0.01 0.00 –0.07,0.07 1.00
hyperactivity items
Father’s BMI 0.01 –0.01,0.03 0.25 0.05 –0.04,0.14 0.29

*Coefficients represent change in symptoms, log-­transformed after adding 1, per 5 kg/m2 increase in BMI.


†
Phenotypic models adjust for the child’s sex and birth year, the mother’s parity at the child’s birth, and the mother’s and father’s: educational qualifications, depressive/anxiety and ADHD
symptoms, and smoking status during pregnancy. They also adjust for the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
‡
Genetic models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
§
Short Mood and Feelings Questionnaire.
¶
Screen for Child Anxiety Related Disorders.
**Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 7. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa, childhood body size PGS, log-­transformed outcomes (N=40,949)*.
Non-­genetic estimate† MR estimate ‡ Within-­families MR estimate ‡

Outcome Beta (per 5 CI p Beta (per 5 CI p Beta (per 5 CI p

kg/m2) kg/m2) kg/m2)

Depressive symptoms: log-­ Child BMI 0.03 0.01,0.06 0.02 0.07 –0.04,0.17 0.20 0.02 –0.14,0.17 0.84
transformed SMFQ§ score
Mother’s BMI 0.04 0.03,0.05 <0.001 0.02 –0.06,0.10 0.67

Father’s BMI 0.01 –0.01,0.02 0.56 0.05 –0.06,0.15 0.39

Anxiety symptoms: log-­ Child BMI –0.03 −0.05,–0.01 0.001 –0.03 –0.10,0.05 0.49 0.01 –0.10,0.12 0.89
transformed SCARED¶ score
Mother’s BMI 0.00 –0.01,0.01 0.60 –0.01 –0.07,0.04 0.69

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

Father’s BMI –0.00 –0.01,0.01 1.00 –0.03 –0.10,0.04 0.43

ADHD symptoms: log-­ Child BMI –0.05 −0.08,–0.02 0.002 –0.06 –0.17,0.05 0.30 –0.03 –0.19,0.13 0.70
transformed RS-­DBD**
score Mother’s BMI 0.03 0.02,0.05 <0.001 –0.02 –0.10,0.06 0.68

Father’s BMI 0.02 –0.00,0.03 0.07 –0.01 –0.11,0.09 0.79

ADHD-­inattention Child BMI –0.04 −0.07,–0.01 0.007 –0.03 –0.14,0.07 0.52 –0.05 –0.19,0.10 0.52
symptoms: log-­transformed
RS-­DBD** score, inattention Mother’s BMI 0.03 0.02,0.05 <0.001 0.02 –0.06,0.09 0.64
items
Father’s BMI 0.02 0.00,0.03 0.05 –0.01 –0.10,0.09 0.87

ADHD-­hyperactivity Child BMI –0.05 −0.08,–0.01 0.004 –0.07 –0.19,0.04 0.21 –0.00 –0.18,0.17 0.98
symptoms: log-­transformed
RS-­DBD** score, Mother’s BMI 0.02 0.00,0.04 0.01 –0.06 –0.15,0.03 0.22
hyperactivity items
Father’s BMI 0.01 –0.01,0.03 0.25 –0.02 –0.13,0.09 0.73

*Coefficients represent change in symptoms, log-­transformed after adding 1, per 5 kg/m2 increase in BMI.


†
Phenotypic models adjust for the child’s sex and birth year, the mother’s parity at the child’s birth, and the mother’s and father’s: educational qualifications, depressive/anxiety and ADHD
symptoms, and smoking status during pregnancy. They also adjust for the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
‡
Genetic models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
§
Short Mood and Feelings Questionnaire.
¶
Screen for Child Anxiety Related Disorders.
**Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 8. Robustness checks based on SNP-­specific associations with child’s BMI* and outcomes: SNPs in adult BMI polygenic score.
Inverse-­variance weighted MR-­Egger: slope MR-­Egger: intercept MR-­Median MR-­Modal

For classic MR models Beta p Beta p Beta p Beta p Beta p

Depressive symptoms: 0.12 <0.001 0.09 0.18 0.00 0.56 0.11 <0.001 0.07 0.42
standardized SMFQ† score

Anxiety symptoms: standardized –0.02 0.13 –0.05 0.45 0.00 0.61 –0.01 0.87 0.01 0.92
SCARED‡ score

ADHD symptoms: standardized 0.10 <0.001 0.02 0.77 0.00 0.19 0.09 0.01 0.07 0.40
RS-­DBD§ score

ADHD symptoms (inattention): 0.09 <0.001 –0.02 0.73 0.00 0.07 0.09 0.01 –0.02 0.81
standardized RS-­DBD§ score

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

ADHD symptoms (hyperactivity): 0.08 <0.001 0.05 0.40 0.00 0.61 0.08 0.02 0.05 0.55
standardized RS-­DBD§ score

Inverse-­variance weighted MR-­Egger: slope MR-­Egger: intercept MR-­Median MR-­Modal

For within-­families MR models Beta p Beta p Beta p Beta p Beta p

Depressive symptoms: 0.06 <0.001 0.04 0.67 0.00 0.77 0.07 0.16 0.02 0.83
standardized SMFQ† score

Anxiety symptoms: standardized 0.00 1.00 0.05 0.58 0.00 0.57 0.03 0.57 0.03 0.76
SCARED‡ score

ADHD symptoms: standardized 0.09 <0.001 0.07 0.41 0.00 0.80 0.09 0.07 0.13 0.24
RS-­DBD§ score

ADHD symptoms (inattention): 0.10 <0.001 0.00 0.97 0.00 0.21 0.10 0.03 0.05 0.63
standardized RS-­DBD§ score

ADHD symptoms (hyperactivity): 0.07 <0.001 0.13 0.13 0.00 0.44 0.07 0.14 0.06 0.56


standardized RS-­DBD§ score

*In the main analyses, all coefficients are expressed in terms of S.D. change in symptoms per 5 kg/m2 increase in BMI. In robustness checks, SNP-­exposure associations were taken directly
from the relevant GWAS. Coefficients above for BMI-­outcome associations are therefore on the scale of kg/m2.
†
Short Mood and Feelings Questionnaire.
‡
Screen for Child Anxiety Related Disorders.
§
Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 9. Robustness checks based on SNP-­specific associations with child’s BMI* and outcomes: SNPs in childhood body size polygenic score.
Inverse-­variance weighted MR-­Egger: slope MR-­Egger: intercept MR-­Median MR-­Modal

For classic MR models Beta p Beta p Beta p Beta p Beta p

Depressive symptoms: 0.06 0.03 0.10 0.30 0.00 0.57 0.05 0.52 0.04 0.67
standardized SMFQ† score

Anxiety symptoms: standardized –0.02 0.40 0.01 0.90 0.00 0.66 –0.02 0.74 –0.01 0.95
SCARED‡ score

ADHD symptoms: standardized –0.04 0.14 –0.02 0.85 0.00 0.75 –0.06 0.36 –0.05 0.65
RS-­DBD§ score

ADHD symptoms (inattention): –0.02 0.47 –0.04 0.64 0.00 0.81 –0.08 0.28 –0.08 0.42
standardized RS-­DBD§ score

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

ADHD symptoms (hyperactivity): –0.05 0.05 0.01 0.90 0.00 0.42 –0.05 0.48 –0.04 0.68
standardized RS-­DBD§ score

Inverse-­variance weighted MR-­Egger: slope MR-­Egger: intercept MR-­Median MR-­Modal

For within-­families MR models Beta p Beta p Beta p Beta p Beta p

Depressive symptoms: 0.02 0.59 0.05 0.70 0.00 0.75 0.03 0.76 0.04 0.79
standardized SMFQ† score

Anxiety symptoms: standardized 0.02 0.60 0.07 0.64 0.00 0.69 0.04 0.66 0.05 0.74
SCARED‡ score

ADHD symptoms: standardized –0.02 0.53 0.09 0.49 0.00 0.35 –0.01 0.94 0.03 0.85
RS-­DBD§§ score

ADHD symptoms (inattention): –0.04 0.28 0.06 0.65 0.00 0.41 –0.04 0.68 0.01 0.95
standardized RS-­DBD§ score

ADHD symptoms (hyperactivity): 0.00 0.98 0.11 0.43 0.00 0.39 0.02 0.80 0.06 0.67


standardized RS-­DBD§ score

*In the main analyses, all coefficients are expressed in terms of S.D. change in symptoms per 5 kg/m2 increase in BMI. In robustness checks, SNP-­exposure associations were taken directly
from the relevant GWAS. Coefficients above for BMI-­outcome associations are therefore on the scale of kg/m2.
†
Short Mood and Feelings Questionnaire.
‡
Screen for Child Anxiety Related Disorders.
§
Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 10. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa, adult BMI PGS, complete-­case analysis*.
Non-­genetic estimate† MR estimate ‡ Within-­families MR estimate ‡

Beta (per 5 Beta (per 5 Beta (per 5

Outcome kg/m2) CI p kg/m2) CI p kg/m2) CI p

Child BMI 0.08 0.00,0.15 0.05 0.38 0.00,0.77 0.05 0.16 –0.35,0.66 0.55
Depressive symptoms: Mother’s BMI 0.07 0.03,0.11 <0.001 0.10 –0.06,0.26 0.21
standardized SMFQ § score.
N=5,158 Father’s BMI 0.01 –0.04,0.05 0.79 0.04 –0.15,0.23 0.66

Child BMI –0.04 –0.12,0.03 0.26 –0.15 –0.54,0.24 0.45 –0.07 –0.62,0.48 0.80
Anxiety symptoms:
standardized SCARED¶ Mother’s BMI 0.02 –0.02,0.06 0.26 0.06 –0.11,0.22 0.48
score.

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

N=5,177 Father’s BMI 0.01 –0.04,0.05 0.69 –0.13 –0.34,0.08 0.24

Child BMI –0.03 –0.11,0.04 0.38 0.41 –0.00,0.83 0.05 0.54 0.01,1.08 0.04
ADHD symptoms: Mother’s BMI 0.09 0.05,0.12 <0.001 –0.01 –0.16,0.15 0.93
standardized RS-­DBD**
score, ADHD items. N=5,174 Father’s BMI –0.01 –0.05,0.03 0.60 –0.09 –0.29,0.12 0.41

Child BMI –0.02 –0.10,0.05 0.55 0.44 0.04,0.85 0.03 0.73 0.20,1.25 0.01
ADHD-­inattention
symptoms: standardized Mother’s BMI 0.09 0.05,0.12 <0.001 –0.02 –0.18,0.14 0.84
RS-­DBD** score, inattention
items. N=5,171 Father’s BMI –0.00 –0.05,0.04 0.83 –0.18 –0.39,0.03 0.09

Child BMI –0.04 –0.11,0.03 0.29 0.28 –0.13,0.70 0.18 0.21 –0.32,0.75 0.43
ADHD-­hyperactivity
symptoms: standardized RS-­ Mother’s BMI 0.07 0.03,0.11 0.001 0.01 –0.15,0.17 0.87
DBD** score, hyperactivity
items. N=5,167 Father’s BMI –0.01 –0.06,0.03 0.51 0.03 –0.17,0.24 0.75

*Coefficients represent S.D. change in symptoms per 5 kg/m2 increase in BMI.


†
Phenotypic models adjust for the child’s sex and birth year, the mother’s parity at the child’s birth, and the mother’s and father’s: educational qualifications, depressive/anxiety and ADHD
symptoms, and smoking status during pregnancy. They also adjust for the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
‡
Genetic models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
§
Short Mood and Feelings Questionnaire
¶
Screen for Child Anxiety Related Disorders
**Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 11. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa, childhood body size PGS, complete-­case analysis*.
Non-­genetic estimate† MR estimate‡ Within-­families MR estimate‡

Outcome Beta (per 5 CI p Beta (per 5 CI p Beta (per 5 CI p

kg/m2) kg/m2) kg/m2)

Depressive symptoms: Child BMIa 0.08 0.00,0.15 0.05 0.13 –0.15,0.42 0.37 0.10 –0.34,0.54 0.65
standardized SMFQ§ score
N=5,158 Mother’s BMI 0.07 0.03,0.11 <0.001 –0.06 –0.26,0.14 0.57

Father’s BMI 0.01 –0.04,0.05 0.79 0.10 –0.20,0.40 0.52

Anxiety symptoms: Child BMI –0.04 –0.12,0.03 0.26 –0.03 –0.32,0.27 0.85 0.06 –0.37,0.48 0.79
standardized SCARED¶ score
N=5,177 Mother’s BMI 0.02 –0.02,0.06 0.26 0.02 –0.19,0.24 0.85

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

Father’s BMI 0.01 –0.04,0.05 0.69 –0.13 –0.43,0.18 0.42

ADHD symptoms: Child BMI –0.03 –0.11,0.04 0.38 0.00 –0.29,0.30 0.98 0.13 –0.31,0.56 0.57
standardized RS-­DBD** score,
ADHD items Mother’s BMI 0.09 0.05,0.12 <0.001 –0.05 –0.25,0.15 0.61
N=5,174
Father’s BMI –0.01 –0.05,0.03 0.60 –0.09 –0.40,0.22 0.56

ADHD-­inattention symptoms: Child BMI –0.02 –0.10,0.05 0.55 –0.00 –0.29,0.29 0.99 0.13 –0.29,0.55 0.55
standardized RS-­DBD** score,
inattention items Mother’s BMI 0.09 0.05,0.12 <0.001 0.04 –0.17,0.24 0.72
N=5,171
Father’s BMI –0.00 –0.05,0.04 0.83 –0.20 –0.51,0.11 0.20

ADHD-­hyperactivity Child BMI –0.04 –0.11,0.03 0.29 0.00 –0.30,0.30 0.99 0.10 –0.35,0.55 0.67
symptoms: standardized RS-­
DBD** score, hyperactivity Mother’s BMI 0.07 0.03,0.11 0.001 –0.14 –0.34,0.06 0.18
items
N=5,167 Father’s BMI –0.01 –0.06,0.03 0.51 0.03 –0.28,0.34 0.84

*Coefficients represent S.D. change in symptoms per 5 kg/m2 increase in BMI.


†
Phenotypic models adjust for the child’s sex and birth year, the mother’s parity at the child’s birth, and the mother’s and father’s: educational qualifications, depressive/anxiety and ADHD
symptoms, and smoking status during pregnancy. They also adjust for the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
‡
Genetic models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
§
Short Mood and Feelings Questionnaire.
¶
Screen for Child Anxiety Related Disorders.
**Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 12. Multivariable-­adjusted associations* of BMI quintiles with symptoms of depression, anxiety, and ADHD at age 8 in MoBa.
ADHD symptoms: ADHD-­inattention symptoms: ADHD-­hyperactivity symptoms:
Depressive symptoms: Anxiety symptoms: standardized RS-­DBD § score, standardized RS-­DBD § score, standardized RS-­DBD § score,
standardized SMFQ† score standardized SCARED ‡ score ADHD items inattention items hyperactivity items

BMI

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

quintile Beta ¶ (95% CI) p Beta ¶ (95% CI) p Beta ¶ (95% CI) p Beta ¶ (95% CI) p Beta ¶ (95% CI) p

1 0.00 (-­0.04,0.04) 0.99 0.04 (0.00,0.09) 0.04 0.05 (0.01,0.09) 0.01 0.05 (0.01,0.09) 0.02 0.04 (-­0.00,0.08) 0.05

2 –0.01 (-­0.05,0.03) 0.70 0.02 (-­0.03,0.06) 0.47 0.02 (-­0.02,0.06) 0.29 0.02 (-­0.02,0.06) 0.38 0.02 (-­0.02,0.06) 0.30

3 (ref) 1 1 1 1 1

4 0.01 (-­0.03,0.05) 0.62 –0.03 (-­0.07,0.01) 0.16 –0.01 (-­0.04,0.03) 0.66 –0.01 (-­0.05,0.02) 0.54 –0.00 (-­0.04,0.03) 0.87

5 0.04 (0.00,0.08) 0.03 –0.03 (-­0.07,0.01) 0.09 –0.02 (-­0.06,0.02) 0.27 –0.01 (-­0.05,0.03) 0.51 –0.03 (-­0.06,0.01) 0.20

*Models adjust for the child’s sex and birth year, the mother’s parity at the child’s birth, and the mother’s and father’s: educational qualifications, depressive/anxiety and ADHD symptoms,
and smoking status during pregnancy. They also adjust for the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
†
Short Mood and Feelings Questionnaire.
‡
Screen for Child Anxiety Related Disorders.
§
Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.
¶
Coefficients represent S.D. difference in symptoms between quintiles of child’s BMI.


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Appendix 1—table 13. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa, adult BMI PGS, genetic models adjusted for parental education
(N=40,949)*.
MR estimate† Within-­families MR estimate†

Outcome Beta (per 5 kg/m2) CI p Beta (per 5 kg/m2) CI p

Depressive symptoms: Child BMI 0.38 0.19,0.58 <0.001 0.26 –0.01,0.53 0.06
standardized SMFQ‡ score
Mother’s BMI 0.09 –0.00,0.17 0.05

Father’s BMI –0.00 –0.11,0.11 0.97

Anxiety symptoms: standardized Child BMI –0.08 –0.26,0.11 0.43 0.01 –0.25,0.27 0.95
SCARED§ score

Hughes et al. eLife 2022;11:e74320. DOI: https://doi.org/10.7554/eLife.74320

Mother’s BMI –0.04 –0.12,0.05 0.40

Father’s BMI –0.03 –0.14,0.08 0.64

ADHD symptoms: standardized Child BMI 0.27 0.09,0.45 0.003 0.37 0.10,0.64 0.007
RS-­DBD ¶ score, ADHD items
Mother’s BMI –0.03 –0.12,0.06 0.52

Father’s BMI –0.05 –0.16,0.06 0.37

ADHD-­inattention symptoms: Child BMI 0.25 0.07,0.42 0.007 0.39 0.13,0.66 0.004
standardized RS-­DBD¶ score,
inattention items Mother’s BMI –0.02 –0.11,0.07 0.64

Father’s BMI –0.10 –0.21,0.01 0.08

ADHD-­hyperactivity symptoms: Child BMI 0.24 0.06,0.42 0.009 0.27 0.00,0.55 0.05
standardized RS-­DBD¶ score,
hyperactivity items Mother’s BMI –0.03 –0.12,0.06 0.49

Father’s BMI 0.01 –0.10,0.12 0.85


*Coefficients represent S.D. change in symptoms per 5 kg/m2 increase in BMI.
†
Models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre, genotyping chip, and first 20 principal components of ancestry.
‡
Short Mood and Feelings Questionnaire.
§
Screen for Child Anxiety Related Disorders.
¶
Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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Appendix 1—table 14. BMI and symptoms of depression, anxiety, and ADHD at age 8 in MoBa,
childhood body size PGS, genetic models adjusted for parental education (N=40,949)*.
MR estimate† Within-­families MR estimate†

Outcome Beta (per CI p Beta (per 5 CI p

5 kg/m2) kg/m2)

Depressive symptoms: Child BMI 0.07 –0.07,0.22 0.33 0.01 –0.20,0.23 0.90
standardized SMFQ‡
score Mother’s BMI 0.02 –0.10,0.13 0.76

Father’s BMI 0.05 –0.09,0.20 0.48

Anxiety symptoms: Child BMI –0.03 –0.18,0.11 0.65 0.03 –0.18,0.23 0.81
standardized SCARED§
score Mother’s BMI –0.02 –0.13,0.09 0.76

Father’s BMI –0.06 –0.19,0.08 0.44

ADHD symptoms: Child BMI –0.08 –0.22,0.06 0.27 –0.03 –0.23,0.16 0.75
standardized RS-­DBD ¶
score, ADHD items Mother’s BMI –0.03 –0.13,0.07 0.50

Father’s BMI –0.02 –0.15,0.11 0.79

ADHD-­inattention Child BMI –0.05 –0.20,0.10 0.52 –0.06 –0.25,0.14 0.57

symptoms: standardized
¶
RS-­DBD score, Mother’s BMI 0.02 –0.08,0.12 0.74
inattention items
Father’s BMI –0.01 –0.14,0.12 0.87

ADHD-­hyperactivity Child BMI –0.10 –0.23,0.04 0.18 –0.00 –0.21,0.21 1.00

symptoms: standardized
¶
RS-­DBD score, Mother’s BMI –0.08 –0.19,0.03 0.15
hyperactivity items
Father’s BMI –0.02 –0.15,0.12 0.77
2
*Coefficients represent S.D. change in symptoms per 5 kg/m increase in BMI.
†
Models adjust for the child’s sex and birth year and the child’s, mother’s, and father’s genotyping centre,
genotyping chip, and first 20 principal components of ancestry.
‡
Short Mood and Feelings Questionnaire.
§
Screen for Child Anxiety Related Disorders.
¶
Parent/Teacher Rating Scale for Disruptive Behaviour Disorders.

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