Deciphering the Influence of Socioeconomic Status on Brain Structure: Insights from Mendelian Randomization

Socioeconomic status (SES) influences physical and mental health, however its relation with brain structure is less well documented. Here, we examine the role of SES on brain structure using Mendelian randomisation. First, we conduct a multivariate genome-wide association study of SES using individual, household, and area-based measures of SES, with an effective sample size of n=893,604. We identify 469 loci associated with SES and distil these loci into those that are common across measures of SES and those specific to each indicator. Second, using an independent sample of ∼35,000 we provide evidence to suggest that total brain volume is a causal factor in higher SES, and that SES is protective against white matter hyperintensities as a proportion of intracranial volume (WMHicv). Third, we find evidence that whilst differences in cognitive ability explain some of the causal effect of SES on WMHicv, differences in SES still afford a protective effect against WMHicv, independent of that made by cognitive ability.


Introduction
Socioeconomic status (SES) is a multi-dimensional construct influencing, and influenced by, multiple physical, socio-cultural, and environmental factors.Differences in SES are a determining factor of health where those from more advantaged backgrounds have a higher level of physical health, mental health and psychiatric conditions, are less likely to receive a dementia diagnosis, and live longer lives [1][2][3][4] .These inequalities in physical health, and mental health are present across different indicators of SES and have been found for occupation, income, educational attainment, and measures of social deprivation 1,[5][6][7] .The communality of such findings highlights the need to examine the influence of SES using a multifactorial approach to examine the causes and consequences of differences in SES.
As with any other quantitative trait, such as height or weight, differences in SES have a heritable component 8 meaning that genetic differences within a population will covary with phenotypic differences.However, and unlike traits such as height or weight, such genetic differences associated with SES are unlikely to form part of a biological pathway from gene to phenotype directly, but are more likely the result of a phenotypic pathway, known as vertical pleiotropy 9 , where a number of traits (which are themselves heritable) contribute towards differences in SES [10][11][12] .As such, the heritability of SES is not static, and differences between societies can result in differences in the heritable traits that give rise to the observed differences in SES 13,14 .
Despite the genetically heterogeneous nature of SES, genome-wide association studies (GWAS) examining indicators of SES such as measures of income 11 , educational attainment 15 , and social deprivation 8 have identified hundreds of associated genetic loci.These genetic indicators of SES are also linked to physical health outcomes, indicative of a common genetic aetiology between SES and physical health 8,11,15 .Furthermore, psychiatric traits including schizophrenia, major depressive disorder, and attention deficit hyperactivity disorder, as well as neurological disorders such as Alzheimer's disease, early-onset stroke, and intra-cerebral haemorrhage also share genetic effects with measures of SES 16 .As with genetic influences that act on SES, these links between SES and brain-related health outcomes may themselves include other phenotypes such as neuroanatomy 11 .
Genetic links between SES and brain morphology have been identified previously where genes highly expressed in the brain and both neuronal and glial cells are enriched for their associations with both income 11 and educational attainment 17 .Furthermore, strong genetic correlations are found between indicators of SES and brain morphology where a genetic correlation of rg = 0.34, SE = 0.07, P =1.2×10 -6 has been identified between intracranial volume and educational attainment 18 , and loci associated with cognitive ability 19 are found to be overrepresented in the associated loci from a GWAS of income 11 .These genetic links between SES and brain-based phenotypes have been explored using Mendelian randomisation (MR) to examine the direction of causality between them.
For example, evidence of bidirectional causal effects was found between poverty (n = 668,288) and mental illness 20 using MR.
However, the following are some fundamental gaps in our understanding of the relationship between SES and brain structure.First, do different indicators of SES confer the different levels of risk or is SES best captured using a single factor?Second, is there evidence for causality in the relationship between SES and brain morphology?Third, to what extend does differences in cognitive ability explain the relationship between SES and brain morphology?Importantly, the use of brain morphology as an outcome in MR can allow for the risk factors of late-life cognitive function that act on cognitive decline in adulthood to be distinguished from those that differentiate the trajectory of cognitive growth through childhood.The importance of which is underscored in the context of dementia which, whilst typically diagnosed using cognitive tests such as the Mini-Mental State Examination 21 , is distinguished from other neurodevelopmental disorders (such as intellectual disability) by a progressive later-life loss of cognitive ability that affects daily life 22 .As such, risk of dementia can be seen to be composed of two components: cognitive development influencing the level of cognitive function prior to the onset of cognitive decline and, the rate at which decline occurs.Whilst large GWAS of cognitive decline are currently lacking, MR combined with GWAS conducted on frank indictors of brain ageing, such as white matter hyperintensities 23 , can be used to identify potentially modifiable risk factors causal in brain ageing.
In the current study, we combine multivariate analysis with MR to examine the bidirectional effects between SES and brain morphology and to examine likely heritable traits that are captured by measures of SES, and to identify potentially modifiable risk factors of age-related brain change associated with cognitive development and cognitive decline.First, we perform a common-factor model multi-variate GWAS of four indicators of SES: occupational prestige (OP, n = 279,644), household income (HI, n = 488,233), educational attainment (EA, n = 753,152), and social deprivation (SD, n = 440,350) for an effective size of 893,604 participants.The use of these four measures in a multivariate framework allows for the assessment of heterogeneous effects across indicators of SES in conjunction with an investigation of common genetic effects that act on the individual, as well as the household, and geographical area in which one resides.Thus, genetic effects can be categorised as common across measures of SES or unique to specific indicators.Second, to examine the bidirectional causal effects of SES on brain structure we use two-sample MR on 13 brain imaging phenotypes sourced from an independent sample of ~36,000 UKB participants.Finally, we examine the role of cognitive ability on the links between SES and brain morphology as one of the heritable traits that is captured by GWAS conducted on the general factor of SES and these four indicators.

Study design and implementation.
Genome-wide association study (GWAS) data sets were used to identify instrumental variables for five exposures.These were four measures of SES (occupational prestige, household income, educational attainment, and social deprivation), and one cognitive exposure (cognitive ability).GWASs were also performed in an independent sample on thirteen MRI phenotypes (total brain volume, TBV; grey matter volume, GM; normal appearing white matter, NAWM; white matter hyperintensity volume, WMH; TBV as a proportion of intracranial volume, TBVicv; GM as a proportion of intracranial volume, GMicv; white matter volume as a proportion of intracranial volume, WMicv; WMH as a proportion of intracranial volume, WMHicv; a general factor of brain white matter tract fractional anisotropy, gFA; a general factor of brain white matter tract mean diffusivity, gMD; a general factor of brain white matter tract intracellular volume fraction, gIVCF; a general factor of brain white matter tract isotropic volume fraction, gISOVF; a general factor of brain white matter tract orientation dispersion, gOD) capturing different aspects of brain morphology.
Using LDSC 24 on each of the GWASs conducted on the indices of SES (occupational prestige, household income, educational attainment, and social deprivation), a significant heritable component was captured explaining between 3.5% -13% of trait variation (Supplementary Table 2).
LDSC intercepts were consistently close to 1 for each SES measure indicating that polygenicity, rather than population stratification or other factors, explained the inflation in GWAS association test statistics (Supplementary Table 2).
Strong genetic correlations between indicators of SES (mean rg = 0.761, range rg = 0.563 -0.963, SE range = 0.011 -0.026) were observed (Supplementary Table 3).The moderate phenotypic correlations but large genetic correlations indicate that whilst each measure of SES captures a different environmental component, they each draw upon similar heritable traits.This was confirmed by extracting a general genetic factor of SES using genomic structural equation modelling (Genomic SEM 25 , Figure 1 B & Table 1) where, in contrast to the phenotypic data, a single factor explained the covariance across the genetic data sets well (χ2(2) = 184.737,p = 7.67×10 ˗41 ; SRMR=0.051;CFI=0.988).The general genetic factor of SES captured on average 76.30% of the genetic variance in each indicator of SES with the proportion being consistent across occupational prestige, household income, and educational attainment (>75%), with the lowest being social deprivation where the general factor captured 49.08% (Supplementary Table 4).This general factor of SES was then regressed onto 7,462,726 SNPs to derive genome wide associations with SES.Furthermore, to differentiate between SNPs whose loci are relevant to a general factor of SES from those whose patterns of association are inconsistent with a general factor, we derive genome-wide heterogeneity statistics using Genomic SEM 25 .The general genetic factor of SES had a h 2 = 9.40% (SE = 0.20%), and showed little evidence of inflation in test statistics due to population stratification (LDSC intercept = 1.06,SE = 0.02).In order to attain independent groups to perform Two-sample MR a general factor of SES was also derived by omitting participants and their relatives who contributed MRI data.This resulted in an effective sample size of 665,662 participants.This general factor had a highly similar factor structure as the full data set (Supplementary Table 4) and a similar heritability (h 2 = 11.3%,SE = 0.30%).

Table 1.
Table 1.Showing the standardised factor loadings for each of the four indicators of SES in the total sample.The direction of social deprivation was reversed so that all scores indicate a greater level of SES across the four indicators used.The upper portion shows the phenotypic structure of SES where the bottom portion shows the genetic structure of SES.Common and specific, by definition sum to 100%, but for the genetic structure this indicates the proportion from common and specific sources that contribute to the total heritability.The total heritability was derived using LDSC implemented in genomic SEM.

Estimating bi-directional causal effects of SES on brain structure.
Using Steiger filtering 26 followed by two-sample Mendelian randomisation (MR) 27 a higher SES was found to be a protective factor against WMHicv (β = -0.218,SE = 0.056, P = 8.63×10 ˗5 , Table 2, Supplementary Table 5, Supplementary Figures 1 & 2).The use of both MR-Egger and MR-PRESSO did not identify any horizontal pleiotropy and no significant heterogeneity was found (Supplementary Table 5 & Supplementary Table 6).There was very little evidence of any other causal effects.
In the reverse direction a greater total brain volume was associated with higher SES (β = No horizontal pleiotropy was detected using MR-Egger or MR-PRESSO but significant heterogeneity was found (Supplementary Table 5 & Supplementary Table 6).None of the other structural brain measures showed evidence of being a causal factor in differences in SES.

Estimating causal effects of specific indices of SES on brain structure.
Following Steiger filtering, WMHicv's were found to be a consequence of differences in household income, occupational prestige, and educational attainment.The direction of effect was the same across these indicators where a lower SES was found to be a causal factor in the increase of WMHicv.
The causal effect of education on WMHicv was replicated using an independent sample from the SSGAC.The education replication data set yielded a protective effect against WMHicv of β = -0.186,SE = 0.083, P = 0.026, with no evidence of horizontal pleiotropy, nor was there evidence of heterogeneous effects (Q = 36.138,Q df = 49, Q P = 0.914, Supplementary Table 9 & Supplementary Table 10).
Despite the lower power of the social deprivation data set both a greater TBV (β = 23273, SE = 11127, P = 0.036) and gMD (β = 0.202, SE = 0.097, P = 0.038) were identified as being a consequence of a greater level of social deprivation (

Estimating causal effects of brain structure on indices of SES.
In contrast with the causal effects of greater SES on brain imaging traits which showed evidence of causal effects on lower white matter and white matter hyperintensity traits, the causal effects of brain structure on measures of SES provided evidence of total brain volume causally contributing to each indicator of SES: occupational prestige (β = 2.15×10 ˗5 , P = 4.57×10 ˗13 ), household income (β = 1.67×10 ˗6 , P = 1.02×10 ˗22 ), and educational attainment (β = 6.50×10 ˗7 , P = 1.62×10 ˗13 ), and social deprivation (β = -1.84×10˗7 , P = 3.41×10 ˗8 , Table 4 & Supplementary Table 7).MR-Egger regression indicated little evidence of horizontal pleiotropy as the MR-Egger intercept was indistinguishable from zero in each comparison (Supplementary Table 7) and MR-PRESSO did not detect any outliers influencing the causal estimate through horizontal pleiotropy (Supplementary Table 8 & Supplementary Figure 12-14).
In addition to total brain volume both WMicv and GMicv showed evidence of causal effects on income, and occupational prestige respectively.However, MR-PRESSO identified four SNPs distorting the causal estimate of WMicv on household income (Supplementary Table 8) and following their removal, little evidence of a causal effect was found.Furthermore, no effect of WMicv on household income was identified using the IVW method performed in our replication sample (Supplementary

The role of cognitive ability in the link between SES and brain structure
Genetic associations with SES variables are unlikely to be due to the identified variant exerting a biological effect that contributes directly to the observed differences in SES 11 .Rather, the observed SNP-trait association is more likely due to the effects of vertical pleiotropy where genetic variation contributes towards heritable traits that are themselves responsible for the differences in SES 11,12 .Due to the strong genetic 19 and phenotypic correlations between measures of SES and cognitive ability, as well as the finding that cognitive ability is one of the likely heritable, causal, traits on the phenotypic pathway between genetic inheritance and income differences 11,30,31 , we examine if the heritable traits captured by GWAS conducted on the four indices of SES show causal effects on brain structure that can be explained by cognitive ability.

Measures of SES capture a set of heritable traits common to each indicator
First, we use the heterogeneity (Q) statistics derived using our common factor model of socioeconomic status and the GWAS results of each individual indicator of SES to examine if SNP effects on the indicators are better explained as SNP effects that act on a latent factor common to each indicator of SES (Table 5).Such evidence would be consistent with the idea that a GWAS conducted on each indicator of SES will capture similar heritable traits.FUMA 32 was used to derive independent genomic loci in the general factor of SES and in each of the four indictors.A total of 469 independent genomic loci were identified for the general factor of SES, and of these 98 loci showed no overlap with any indicator of SES indicating these loci act on the genetic architecture that is shared between each indicator.Occupational prestige, household income, educational attainment, and social deprivation were found to have 68, 73, 491, and 10 independent loci, respectively.However, only eight loci for occupational prestige, 13 for household income and 143 associated with educational attainment, and four for social deprivation were independent from the general factor of SES indicating that the bulk of the genetic effects for each of these SES traits act on the same underlying heritable trait/s.Table 5.
Table 5. Showing a summary of the general factor of SES multivariate GWAS and the univariate GWAS on each indicator of SES.

Overlap of causal loci for cognitive ability and SES
Using MiXeR 33 , we examined the degree of polygenic overlap between cognitive ability with the general factor of SES, as well as with each indicator of SES.We found that most of the loci associated with each index of SES overlap heavily with loci associated with cognitive ability (Figure 2).The genetic relationship between cognitive ability and SES changed, modestly, depending on the measure of SES used, and was not predicted by the genetic correlations.For example, both education and occupational prestige showed a genetic correlation with cognitive ability of ~ rg = 0.75, however where education had a large number of education specific causal variants (~1,500, SE = 700), occupational prestige did not (Figure 2A).Furthermore, occupational prestige, which had a genetic correlation with cognitive ability of a similar magnitude as educational attainment (rg = 0.60), similarly showed no evidence of causal loci that were not also associated with differences on cognitive ability test scores.However, the comparison between occupational prestige and cognitive ability did tentatively indicate that there were loci causal in cognitive ability test score differences that were unrelated to differences in occupational prestige (Figure 2A & Supplementary Figure 15).
There was little evidence of cognitive ability loci that were not also associated with SES.

Estimating the bidirectional effects between cognitive ability and socioeconomic status.
Previous work has indicated a bi-directional causal relationship between educational attainment with cognitive ability 30,31 and that cognitive ability is one of the causal factors in income differences 11 .Here we show a bi-directional causal relationship between the general factor of SES with cognitive ability, and a bi-directional causal relationship between each indicator of SES with cognitive ability (Table 6 & Supplementary Table 11).Following Steiger filtering, we find evidence that higher cognitive ability was causally linked to having a higher level of SES using the general factor of SES (β =0.192, SE = 0.012, P = 1.24×10 ˗53 ).Cognitive ability was also a causal factor in each specific indicator of SES and was linked with a higher level of occupational prestige (β = 2.67, SE = 0.15, P = 2.21×10 ˗69 ), a greater level of household income (β = 0.131, SE = 0.011, P = 2.66×10 ˗31 ), a greater chance of attaining a university level education (β = 0.077, SE = 0.004, P = 5.75×10 ˗67 ), and decrease in level of deprivation in which one lives (β = -0.84,SE = 0.025, P = 0.001, Table 6 & Supplementary Table 11).There was evidence of heterogeneity in each estimate of the causal effects of cognitive ability on SES as indicated by significant Cochran's Q statistics 28 (Supplementary Table 11).This heterogeneity statistic provides an indication of the variability of the estimated effect between SNPs and can arise if the SNPs have horizontal pleiotropic effects.
However, there was little evidence that horizontal pleiotropy biased the causal estimates of cognitive ability on SES; the MR Egger regression intercepts were close to zero and MR PRESSO indicated no significant distortion in the causal estimate due to SNPs with a horizontal pleiotropic effect (Supplementary Table 12, & Supplementary Figures 16-18).
Using the GWASs conducted on each SES variable, instrumental variables were identified to examine if they captured heritable traits that were causal factors in differences in cognitive ability.We find evidence that in addition to the causal effect on the general factor of SES (β = 1.159,SE = 0.045, P = 1.19×10 ˗143 ), increases in cognitive ability were a consequence of increases in education (β = 2.433, SE = 0.129, P = 7.54×10 ˗90 ), income (β = 1.103,SE = 0. 116, P = 2.17×10 ˗21 ), and occupational prestige (β = 0.071, SE = 0.007, P = 7.93×10 ˗27 ), whereas there was weak evidence that the heritable traits linked to increases in social deprivation acted to reduce cognitive ability (β = -0.415,SE = 0.121, P = 0.001, Supplementary Table 11).As with the causal effects of cognitive ability on SES there was significant heterogeneity in the estimates (Supplementary Table 11) but little evidence of bias arising due to horizontal pleiotropy indicated by the MR Egger intercepts not being significantly different from zero and no distortion detected using MR-PRESSO (Supplementary Table 12 & Supplementary Figures 19-21).Table 6.
Table 6.Showing the bi-directional total causal effects of cognitive ability on the general factor of SES and each of the four indicators of SES.Beta weights are unstandardized and reflect the original unit of measure.

The bidirectional causal effect of cognitive ability on brain structure
Consistent with the idea that GWASs of SES capture variance in cognitive ability, we find evidence that cognitive ability has a protective causal effect on WHMicv (β = -0.080,SE = 0.026, P = 0.002).Furthermore, and again consistent with what was identified for measures of SES, there was evidence to suggest a greater total brain volume resulted in a higher level of cognitive ability (β = 3.97×10 -6 , 4.96×10 -7 , 1.28×10 -15 ).No evidence of horizontal pleiotropy was identified using MR Egger (Eggerintercept P = 0.492) and MR-PRESSO found no evidence of distortion in the causal estimate following the removal of five SNPs with evidence of horizontal pleiotropy (MR-PRESSO distortion P-value = 0.516).There was however, significant heterogeneity in the causal estimate of TBV on cognitive ability (Q P-value = 1.85×10 -10 , Supplementary Tables 13-14 & Supplementary Figures 22-24).

Direct effects of SES on brain structure
Using Multivariable MR (MVMR) 34 to control for the effects of cognitive ability on each of the SES variables we examine if the causal effects of each SES variable on brain structures were independent of cognitive ability.
When both cognitive ability and the general factor of SES were included in a single multivariate model there was evidence that SES effects on WMHicv that were independent of cognitive ability (total effect β = -0.218,SE = 0.056, P = 8.63×10 ˗5 , direct effect β = -0.182,SE = 0.079, P = 0.022).

Discussion
Those individuals from more advantaged socioeconomic backgrounds will typically have fewer instances of poor physical and mental health compared to those from more deprived backgrounds 1,[5][6][7] .Understanding the causes of such differences has the potential to decrease health disparities and improve our understanding of the intricate working of societal risk factors of illnesses.
In the current study we examine the role that SES plays on brain structure by performing a multivariate GWAS to capture sources of SES differences that effect the individual, the household, and the area in which one lives.Our GWAS on SES was then used to derive instrumental variables to examine the causal effect differences in SES has on brain morphology and health.The current study contributes to our understanding of the genetic contributions to SES in at least five ways.
First, we show that whilst a common phenotypic factor explains only 31.2% of phenotypic variation across each indicator of SES, our multivariate general genetic factor of SES accounted for on average 76% (range =49%-93%) of the genetic variation found across occupational prestige, household income, educational attainment, and social deprivation.Furthermore, our common factor model showed that the same heritable traits underlie the bulk of the heritable variation in SES across each of the indicators where, of the 469 independent genomic loci identified, only two showed evidence of a heterogenous effect indicated by a significant Q value.This asymmetry in the variance captured by a common phenotypic factor of SES compared with the variance captured by a common genetic factor of SES, and the finding that the majority of loci associated with the general factor acted on each of the four indicators of SES, implies that although each indicator captures a different environmental component of SES, the heritable traits that give rise to these phenotypic differences are largely the same.
The identification of this common genetic factor of SES allows for the recontextualisation of the results of previous GWAS that have been conducted on individual indicators of SES.
Specifically, many of the loci identified in univariate GWAS of a single indicator of SES are generalisable to SES more broadly, as they are associated with all indicators that load on the general genetic factor of SES.For example, previous GWAS examining educational attainment 17 and income 11 have reported 3,952 and 149 loci respectively as showing an association with a specific indicator of SES.Here, we find that 78.8% of the genetic variance of educational attainment and 84.2% of the genetic variance of income is through this general factor of SES indicating that only a minority of the loci captured by those GWAS on specific indicators of SES will be trait specific.
Second, we find evidence that cognitive ability is one of the likely causal traits captured by GWAS on SES.By using MiXeR 33 we show that of the estimated 11,000 causal variants for cognitive ability, 10,800 are shared with the general factor of SES with only 1,800 causal variants for SES not shared with cognitive ability.Whilst MiXeR cannot differentiate between vertical and horizontal pleiotropy 33 , across each indicator of SES there was little evidence of loci associated with cognitive ability that were not also associated with differences in SES, consistent with the hypothesis that differences in cognitive ability are one of multiple heritable traits that influence differences in SES.
By using Two-sample MR we were able to confirm that vertical pleiotropy, and not horizontal pleiotropy, best explained the overlapping genetic architecture between cognitive ability and SES identified using MiXeR.Higher cognitive ability was one of the causal elements of having a greater level of the general factor of SES, a higher occupational prestige and educational attainment, a higher household income, and living in a less deprived environment.This effect was replicated using educational attainment and household income data sets that included participants from outside the UK indicating these effects were not specific to the UK or to the participants of UK Biobank.These effects were bidirectional and differences in SES were also shown to influence cognitive ability.
Third, using Two-sample MR we show that higher levels of this common factor of SES is a consequence of a greater total brain volume and a likely causal factor in lower levels of white matter hyperintensities (WMHicv).White matter hyperintensities are white matter lesions that, on fluid attenuated inversion recovery (FLAIR) MRI scans, show a signal intensity that is brighter than surrounding white matter 35 .WMHs are associated with vascular risk and small vessel disease 36 and may indicate permeability in the blood brain barrier as well as axonal and myelin degeneration 37 Furthermore, increases in WMH volume are associated with cognitive decline and higher risk of Alzheimer's disease, as well as with lower levels of cognitive ability 38 .
In the context of non-clinical community-dwelling adults, WMH volume is also a frank marker of neurodegeneration, being of extremely low prevalence in young adulthood 39 .However, lower levels of cognitive ability at age 11 are associated with greater WMH volume at age 73 40 indicating that they may influence the trajectory of cognitive decline in adulthood and older age.Our finding that SES was a likely causal factor for WMHicv indicates that lower levels of SES act as a risk factor for the development of WMH across the adult lifespan and may, through the accumulation of damage caused by WMH, increase the rate of cognitive decline and the likelihood of a dementia diagnosis in older age.In contrast, our finding that TBV was a causal factor for SES and cognitive ability may indicate that TBV (which reaches its peak in early adulthood 41 ) is a risk factor that influences the rate of cognitive development in childhood.
Fourth, we show using MVMR, that there are causal effects of SES on WMHicv independent of cognitive ability.In the same way a polygenic score captures the aggregate effect of the SNPs used in its construction 42 , so each SNP in a GWAS conducted on SES will capture the aggregate effect of each heritable trait linked to differences in SES 12 .Using MVMR we were able to remove the effect of one of these traits, cognitive ability, in order to gauge the effect of the remaining traits captured by SES on brain morphology.In doing so we show that the direct effects of SES are protective against WMHicv.This is consistent with the idea that the general factor of SES captures a constellation of risk from multiple genetically influenced traits and higher levels of SES are not protective solely due to them capturing differences in cognitive ability 10,11 .These traits could be social health factors 43 or aspects of personality linked to health, such as conscientiousness, which is phenotypically linked with lower instance of disease 44 and greater longevity 45 and shows genetic correlations with mental health traits such as MDD, ADHD, and schizophrenia 46 .Previous work examining educational attainment, an indicator of SES, identified that differences in wellbeing, health, and personality have been shown to make a contribution to the heritability of educational attainment that is independent from cognitive ability 10 .
Fifth, with the qualified exception of educational attainment, which showed ~15,000 causal loci not also linked to differences in cognitive ability, no evidence was found for loci associated with indicators of SES that were not also loci associated with cognitive ability.However, we find no evidence that these non-cognitive aspects of educational attainment 47 were causally associated with WMHicv.
Our study has limitations that should be considered when interpreting the results.First, all samples used were from western European societies and cultures of the 21 st century.The importance of this caveat is underscored by the observation that the heritable traits that give rise to differences in SES are unlikely to be universal and will be specific to the cultures and samples examined 13,14 .
Without studies aiming to examine the heritable traits that give rise to SES and the role these play in brain structure in other cultures, meaningful comparisons between the present study and other cultures are unwarranted.
Second, genetic variants captured by our measures of SES are likely to have pleiotropic effects 48 .To satisfy the assumptions that the genetic association with the outcome is entirely mediated via the exposure, we performed Steiger filtering to remove variants that are more strongly associated with outcome than the exposure (i.e.reverse causation).Although removing invalid instrumental variables and only keep likely vertical pleotropic instrumental variables can improve the validity of causal effects, such data-driven selection of instrumental variables may yield over precise causal effects, especially when the majority of instrumental variables are affected by heterogeneity.
Furthermore, in order to break the assumptions of MR it is not sufficient for the genetic variants in the instrumental variable to have pleiotropic effects 49 , rather the genetic variants must have horizontally pleiotropic effects that are mediated through mechanisms other than those captured by SES.For example, should genetic variants have vertically pleiotropic effects, e.g.SNP->neuron-> cognitive ability ->education->income->health->brain structure, then our MR derived causal estimates will not be biased.Furthermore, should the SNPs affect other phenotypes, but these phenotypes do not affect the outcomes, then our MR estimates will not be biased.Whilst it is possible that the genetic variants identified in our GWAS conducted on measures of SES do have horizontally pleiotropic effects, it is unclear what mechanisms would mediate such effects (e.g.personality).In the current study we investigate potentially pleiotropic effects using multivariable Mendelian randomization to examine the role of cognitive ability.Future research should use multivariable Mendelian randomization to investigate this the role of other traits that link SES to brain structure.
Third, there is the potential that indirect genetic effects will contribute to the MR estimates 50 .
Indirect genetic effects refer to one individual's genotype influencing the outcome of another individual's phenotype, for example, a parent providing material resources for their offspring which may affect SES or cognitive ability.Detecting the magnitude of potential bias resulting from dynastic effects is challenging outside of using family-based data, and at present no such data exist.
Finally, molecular genetic studies examining traits such as cognitive ability and socioeconomic status are prone to misunderstanding and mischaracterisation.These mischaracterisations can include arguments based around genetic determinism where the role of the environment is disregarded in favour of creating myths about immutable, biological differences underlying trait variation, something incompatible with current knowledge of complex traits.In order to communicate our research findings to a general reader in an ethical and socially responsible way, we have provided an FAQ document in Supplementary Note 1.
Overall, this study offers new insights into the complex interactions between socioeconomic status (SES), brain development and the risk factors underlying cognitive decline.Employing modern analytical methods on extensive datasets, the findings significantly contribute to our comprehension of factors that influence physical and mental health.Ultimately, these results could highlight potential modifiable risk factors for maintaining cognitive ability in older-age.

Figure 1 .
Figure 1. A. Showing the phenotypic and genetic correlations between the variables used.The lower diagonal shows the genetic correlations whereas the upper diagonal shows the phenotypic correlations.The diagonal shows the heritability estimates.Colour and size are used to illustrate the magnitude and directions of the correlations.Both heritability and genetic correlations were derived using LDSC implemented in Genomic SEM.Tabulated values are shown in Supplementary Tables1-3.Social deprivation scores were reversed to facilitate a comparison with the other measures of SES.B. Showing the standardised phenotypic (upper) and genetic (lower) factor solutions for the covariance structure across the four indices of SES examined in the total sample.Social deprivation scores were again reversed .C.A miami plot of the general factor of SES.The X axis indicates chromosome and the y axis shows the -log(10) p value of each SNP with the upper section describing its association with the general factor of SES where the lower shows the p value for the heterogeneity Q statistics.TBV, total brain volume; GM, grey matter volume; WMH, white matter hyperintensity volume; TBVicv, TBV as a proportion of intracranial volume; GMicv, GM as a proportion of intracranial volume; WMicv, white matter volume as a proportion of intracranial volume; WMHicv, WMH as a proportion of intracranial volume; gFA, a general factor of brain white matter tract fractional anisotropy; gMD, a general factor of brain white matter tract mean diffusivity; gIVCF, a general factor of brain white matter tract intracellular volume fraction; gISOVF, a general factor of brain white matter tract isotropic volume fraction; NAWM, normal appearing white matter; gOD, a general factor of brain white matter tract orientation dispersion.

Figure 2 .
Figure 2. A. Venn diagram of cognitive ability and the four indices of SES showing the unique and shared genetic components at the causal level.Grey illustrates the polygenic overlap between trait pairs, orange shows the SES specific components, and blue the unique contributors to cognitive ability.Numbers indicate the estimated quantity of causal variants in thousands with the standard error in brackets.The size of the circle indicates the degree of polygenicity for each trait pair.B. Illustrating the total and direct effects of socioeconomic status, occupational prestige, household income, and educational attainment.Colour represents trait and solid shapes indicate a statistically significant causal estimate.Error bars show ± one standard error

Table 2 .Table 2 .
Showing the inverse variance weighted bi-directional causal effect estimate of socioeconomic status on brain structure.Abbreviations: TBV, total brain volume; GM, grey matter volume; WMH, white matter hyperintensity volume; TBVicv, TBV as a proportion of intracranial volume; GMicv, GM as a proportion of intracranial volume; WMicv, white matter volume as a proportion of intracranial volume; WMHicv, WMH as a proportion of intracranial volume; gFA, a general factor of brain white matter tract fractional anisotropy; gMD, a general factor of brain white matter tract mean diffusivity; gIVCF, a general factor of brain white matter tract intracellular volume fraction; gISOVF, a general factor of brain white matter tract isotropic volume fraction; gOD, a general factor of brain white matter tract orientation dispersion; SES, socio-economic status; SE, standard error; P, p-value; SNP: single nucleotide polymorphism.

Table 3 , Supplementary Table 7 & Supplementary Figure 10-11).
No other causal effects of SES on brain structure were identified.

Table 3 .
Showing the IVW causal effect estimate of each indicator of SES on brain measures.Beta weights are unstandardized and reflect the original unit of measure.Abbreviations: TBV, total brain volume; GM, grey matter volume; WMH, white matter hyperintensity volume; TBVicv, TBV as a proportion of intracranial volume; GMicv, GM as a proportion of intracranial volume; WMicv, white matter volume as a proportion of intracranial volume; WMHicv, WMH as a proportion of intracranial volume; gFA, a general factor of brain white matter tract fractional anisotropy; gMD, a general factor of brain white matter tract mean diffusivity; gIVCF, a general factor of brain white matter tract intracellular volume fraction; gISOVF, a general factor of brain white matter tract isotropic volume fraction; gOD,a general factor of brain white matter tract orientation dispersion.Note in the event that only one SNP was available a Wald ratio was used as an inversevariance weighted model could not be derived.

Table 8
) indicating that this effect was potentially driven by horizontal pleiotropy or a false positive.Similarly the use of MR-PRESSO removed the causal estimate of GMicv on

Table 4 .
Showing the IVW causal effect estimate of each indicator of brain structure on socio-economic status.Beta weights are unstandardized and reflect the original unit of measure.
Abbreviations: TBV, total brain volume; GM, grey matter volume; WMH, white matter hyperintensity volume; TBVicv, TBV as a proportion of intracranial volume; GMicv, GM as a proportion of intracranial volume; WMicv, white matter volume as a proportion of intracranial volume; WMHicv, WMH as a proportion of intracranial volume; gFA, a general factor of brain white matter tract fractional anisotropy; gMD, a general factor of brain white matter tract mean diffusivity; gIVCF, a general factor of brain white matter tract intracellular volume fraction; gISOVF, a general factor of brain white matter tract isotropic volume fraction; gOD, a general factor of brain white matter tract orientation dispersion.