Intrauterine Growth and Offspring Neurodevelopmental Traits

Key Points Question Is the association between lower birth weight and offspring neurodevelopmental difficulties causal? Findings In this conventional epidemiological cohort study of 46 970 offspring, lower birth weight was associated with neurodevelopmental difficulties across various offspring ages. However, mendelian randomization causal analyses of 44 134 mother-child dyads did not find evidence for a causal association between intrauterine growth (with maternal genetic factors influencing fetal growth as a proxy) and offspring neurodevelopmental difficulties. Meaning This study found that maternal factors influencing intrauterine growth do not appear to drive the observational association between lower birth weight and offspring neurodevelopmental difficulties.


eAppendix 4. Additional information on conventional epidemiological analyses
Conventional epidemiological analyses were conducted using the GCTA software tool v 1.93.2 beta 48,49 .This software implements a genetic linear mixed model where covariates and tests for association are fit in the fixed-effects part of the model, whereas cryptic relatedness and residual population stratification are modelled in the random-effects part of the model using a genetic relationship matrix (GRM), generated from all genotyped and imputed autosomal loci.The fixedeffects part of the model included terms for offspring sex, offspring birth year, maternal age at birth, paternal age at birth, gestational duration, and offspring genotyping batch, while the random-effects part of the model included a GRM of the offspring.Sex-stratified conventional epidemiological analyses were also conducted (eFigure 4 and eFigure 5).
To inform on which covariates should be included in the analyses described above, univariate linear regression analyses,  Individuals included in this analysis are offspring with birthweight and at least one neurodevelopmental trait outcome available, as well as genotype data available for themselves and one or more parents.Estimates reflect standardised regression coefficients and 95% confidence intervals.

eAppendix 5. Proxy SNP identification
The LDmatrix tool (with the Utah Residents from North and West Europe (CEU) reference population) was used to identify proxy SNPs for missing variants 50 .Three SNPs in high linkage disequilibrium (LD) (r 2 > 0.8) were selected as proxies for missing variants (eTable 2).We were unable to identify proxies for some of the variants missing in the MoBa cohort after QC.We also used the LDmatrix tool and the same reference population to explore the LD between all variants used in the MR analyses and confirmed that the SNPs were independently associated with birthweight (all pairwise r 2 < 0.01).For individuals who were missing a birthweight SNP, the mean dosage (from the founders, i.e., parents) was imputed across the entire triad/dyad/.Mean dosage imputation of missing genotype data would have added uncertainty to the measure of SNP dosage, and can lead to regression dilution bias, shifting the effect estimate obtained in the MR analyses towards the null.However, we believe the extent of this bias to be small, since only 0.5% of allele dosages were missing across all individuals.In addition, the missingness was not limited to particular imputation or genotyping batches, meaning that the imputation was non-systematic.While it is possible to apply a more complex approach and impute SNPs at a one-by-one basis (i.e., using allele frequencies and information from relatives), this would be computationally intensive.

eAppendix 7. SNP and allele score benchmarking
Various benchmarking checks were performed to investigate the validity of the allele scores used in the MR analysis (i.e., MR relevancy assumption).Firstly, we attempted to replicate the association between each SNP included in the allele scores and both own birthweight and offspring birthweight in MoBa, using linear regression analyses while adjusting for gestational duration, sex, birth year, genotyping batch and the first 10 genetic principal components (PCs) that were generated during the MoBaPsychGen QC process 36 .Most SNPs significant in the SEM analyses replicated in the conditional analysis (p < 0.05) (eTable 6).
Next, genetic linear mixed model analyses were conducted, to examine the association between birthweight allele scores and birthweight, whilst adjusting for offspring sex, offspring birth year, maternal and paternal age at birth, gestational duration and genotyping batches.A GRM, excluding birthweight SNPs and surroundings, was also included in the model.
We demonstrate that offspring and maternal allele scores are associated with birthweight in the expected patterns (eTable 3).For example, maternal allele scores conditional on offspring/paternal allele scores (M1, M2, M3) are all significantly and positively associated with birthweight, while offspring allele scores conditional on maternal/paternal allele scores (F1, F2, F3) are also significantly and positively associated with birthweight.Paternal allele scores were not significantly associated with birthweight after conditioning on maternal and offspring allele scores (except for M1).In addition, for all the scores reflecting maternal genetic effects (M1, M2, M3), the maternal allele scores are more strongly associated with birthweight than offspring and paternal scores, whereas for the allele scores reflecting offspring genetic effects (F1, F2, F3), offspring scores are more strongly associated with birthweight than maternal allele scores.
Instrument strength was assessed using a conditional F-statistic, calculated from the same genetic linear mixed models described above (eTable 3).Two-sided P-values from the conditional effect of each allele score on offspring birthweight were converted to F-statistics involving 1 and N -k -1 degrees of freedom, where k is the number of fixed-effects estimated in the model.For all allele scores of interest, the F-statistics were much larger than the recommended threshold of 10.
The variance in birthweight explained by the allele scores conditional on other covariates in the model (eTable 3) suggests that the offspring scores (F1, F2, F3) are better powered than the maternal scores (M1, M2, M3) to detect association, in line with past investigations into variance explained by maternal and fetal birthweight variants (see Discussion) 27 .
eTable 3. Association between offspring, maternal and paternal birthweight alleles scores and Z-transformed birthweight.Genetic linear mixed models were used to examine the association between birthweight allele scores and birthweight, whilst adjusting for offspring sex, offspring birth year, maternal and paternal age at birth, gestational duration and genotyping batches.A GRM was also included in the model.CI = 95% confidence intervals outcomes would be overly conservative.Instead, we performed a PCA in 15,719 offspring with measures available for all 20 neurodevelopmental traits to determine the number of PCs that explained more than 80% of the covariance between the offspring neurodevelopmental traits 55 .We determined that 10 PCs accounted for 80% of the covariance and applied a Bonferroni correction based on this number instead.This resulted in a multiple-testing corrected p-value threshold of p < 0.005 for statistical significance (eTable 4).Analyses were performed in R using the prcomp function.The relationship between maternal genetic effect, which is the proportion of variance in the trait explained by maternal genetic effects at the loci, offspring genetic effects, sample size and statistical power is presented in eFigure 7, eFigure 8 and eFigure 9.The power calculations found that the mother-offspring dyad analyses (N = 40,000) were better powered than trio analyses (N = 30,000) to detect both maternal genetic effects and offspring genetic effects (eFigure 7 and eFigure 8).However, trio analyses were still conducted to enable unbiased comparison between maternal genetic effect and paternal genetic effect estimates to understand the role of the postnatal environment on offspring NDDs.Furthermore, power to detect a maternal (or offspring genetic effect) does not differ in the presence of an offspring genetic effect (or maternal genetic effect).Under a multiple-testing correction for 10 tests (i.e., 10 independent offspring NDDs in the PCA), we had 80% power to detect a maternal (or fetal) genetic effect of 0.044% in 40,000 mother-offspring dyads (eFigure 9).
The power calculations suggest that we have ≥ 80% power to detect a maternal genetic effect that explained as little as 0.026% of the variance in offspring outcome (N = 40,000 dyads; offspring genetic effect = 0; two tailed alpha = 0.05; eFigure 7).For the trio analyses, we had ≥ 80% power to detect a maternal genetic effect that explained 0.039% of the variance in offspring outcome (N = 30,000 trios; offspring genetic effect = 0; two tailed alpha = 0.05; eFigure 7).We had 80% power to detect an offspring genetic effect that explained 0.026% and 0.052% of the variance in offspring outcome for maternal-dyad and trio analyses respectively (N = 40,000 dyads or 30,000 trios; maternal genetic effect = 0; two tailed alpha = 0.05; eFigure 8).eFigure 7. Maternal genetic effect power calculations for mother-child dyad (N = 40,000) and parent-offspring trio (N = 30,000) analyses.We used adjusted and unadjusted linear regression analyses to assess whether father's presence in MoBa (i.e., the father was genotyped, and offspring was part of a parent-child trio or father-child dyad) was associated with the offspring NDDs.
The adjusted model included offspring sex, health region of mother's place of residence, and maternal-age as covariates.
The linear regression analyses found that paternal presence was associated with lower offspring neurodevelopmental outcome scores (eTable 6 adjusted analyses; p < 0.005; all SCQ scales, subscales and timepoints, CBCL-ADHD-18m, CBCL-ADHD-3yr, RSDBD-ADHD-8yr, ASQ-LANG-3yr and 5yr, and CCC-S-8yr).These analyses showed evidence to support this hypothesis; i.e., father's presence in MoBa (i.e., father is genotyped and offspring is part of a parent-offspring trio or father-offspring dyad) was associated with lower offspring neurodevelopmental outcomes in the expected direction (across all domains except for motor difficulties).eTable 6.The relationship between paternal presence in MoBa and offspring neurodevelopmental trait outcomes.Linear regression analyses were used to test for an association between father's presence and the neurodevelopmental outcomes.The adjusted model included offspring sex, health region of mother's place of residence, and maternal age as covariates.Offspring who were part of a parent-offspring trio, mother-child dyad and father-child dyad were included in these analyses.Bolded p-values < 0.005.
were used to investigate the relationship between possible confounders (i.e., maternal and paternal age at birth, offspring birth year, gestational duration, trio membership, mother-child dyad membership and father-child dyad membership) and birthweight (conducted in R version 3.6.0).The relationship between birthweight and potential confounders are shown in eFigure 6.

eFigure 4 .eFigure 5 .eFigure 6 .
Sex-stratified conventional epidemiological associations between birthweight and neurodevelopmental trait outcomes whilst adjusting for covariates in male offspring.The model was adjusted for birth year, maternal and paternal age at birth, gestational duration, and offspring genotyping batch and included an offspring genetic relationship matrix.Estimates reflect standardised regression coefficients and 95% confidence intervals.Sex-stratified conventional epidemiological associations between birthweight and neurodevelopmental trait outcomes whilst adjusting for covariates in female offspring.The model was adjusted for birth year, maternal and paternal age at birth, gestational duration, and offspring genotyping batch, and included an offspring genetic relationship matrix.Estimates reflect standardised regression coefficients and 95% confidence intervals.Conventional epidemiological associations between potential confounders and birthweight.

eAppendix 10 .
Investigation into potential paternal selection biasAn additional post-hoc analysis into potential paternal selection bias into MoBa was conducted to help explain the positive findings in the negative control parental exposure analyses.We hypothesise that if allele scores for birthweight are pleiotropically associated with neurodevelopmental traits, and if fathers' participation in MoBa is influenced by these same neurodevelopmental traits, then selection may act as a collider and induce a positive association between paternal allele scores for birthweight and offspring neurodevelopmental outcomes (eFigure 10).eFigure 10.Diagram illustrating the effect of selection bias on the parent-offspring trio study design for investigating the effect of an intrauterine exposure (proxied by birthweight; BW) on offspring neurodevelopmental (ND) outcomes.If there is a relationship between paternal ND traits and participation in the cohort, a collider path (red dotted line) may open up and induce an association between paternal BW allele scores and offspring ND outcomes, even when conditioning on both offspring and maternal BW allele scores.Conditioned upon variables are outlined, whereas positive and negative associations are represented by + and -symbols, respectively.

eAppendix 6. Missing genotype handling
. Bolded p-values < 0.05.Var(BW) is the variance explained in birthweight by the allele scores conditional on other covariates in the model.* denotes F-statistics and Var(BW) of interest Due to the high correlation between the offspring neurodevelopmental outcomes, Bonferroni correction for all 20

eTable 4 .
54incipal components analysis to determine the number of independent traits assessed in the present study.We investigated the power to detect genetic effects in a MR study consisting of complete parent-offspring trios and maternal-dyads, under various scenarios, using the Power Calculator for Parent Offspring Trios With Complete Genotype Information53and the Maternal and Offspring Genetic Effects Power Calculator54.
Phenotypic and genetic characteristics of the genotyped MoBa offspring, mothers and fathers after QC.