Educational attainment, structural brain reserve and Alzheimer’s disease: a Mendelian randomization analysis

Abstract Higher educational attainment is observationally associated with lower risk of Alzheimer’s disease. However, the biological mechanisms underpinning this association remain unclear. The protective effect of education on Alzheimer’s disease may be mediated via increased brain reserve. We used two-sample Mendelian randomization to explore putative causal relationships between educational attainment, structural brain reserve as proxied by MRI phenotypes and Alzheimer’s disease. Summary statistics were obtained from genome-wide association studies of educational attainment (n = 1 131 881), late-onset Alzheimer’s disease (35 274 cases, 59 163 controls) and 15 measures of grey or white matter macro- or micro-structure derived from structural or diffusion MRI (nmax = 33 211). We conducted univariable Mendelian randomization analyses to investigate bidirectional associations between (i) educational attainment and Alzheimer’s disease; (ii) educational attainment and imaging-derived phenotypes; and (iii) imaging-derived phenotypes and Alzheimer’s disease. Multivariable Mendelian randomization was used to assess whether brain structure phenotypes mediated the effect of education on Alzheimer’s disease risk. Genetically proxied educational attainment was inversely associated with Alzheimer’s disease (odds ratio per standard deviation increase in genetically predicted years of schooling = 0.70, 95% confidence interval 0.60, 0.80). There were positive associations between genetically predicted educational attainment and four cortical metrics (standard deviation units change in imaging phenotype per one standard deviation increase in genetically predicted years of schooling): surface area 0.30 (95% confidence interval 0.20, 0.40); volume 0.29 (95% confidence interval 0.20, 0.37); intrinsic curvature 0.18 (95% confidence interval 0.11, 0.25); local gyrification index 0.21 (95% confidence interval 0.11, 0.31)]; and inverse associations with cortical intracellular volume fraction [−0.09 (95% confidence interval −0.15, −0.03)] and white matter hyperintensities volume [−0.14 (95% confidence interval −0.23, −0.05)]. Genetically proxied levels of surface area, cortical volume and intrinsic curvature were positively associated with educational attainment [standard deviation units change in years of schooling per one standard deviation increase in respective genetically predicted imaging phenotype: 0.13 (95% confidence interval 0.10, 0.16); 0.15 (95% confidence interval 0.11, 0.19) and 0.12 (95% confidence interval 0.04, 0.19)]. We found no evidence of associations between genetically predicted imaging-derived phenotypes and Alzheimer’s disease. The inverse association of genetically predicted educational attainment with Alzheimer’s disease did not attenuate after adjusting for imaging-derived phenotypes in multivariable analyses. Our results provide support for a protective causal effect of educational attainment on Alzheimer’s disease risk, as well as potential bidirectional causal relationships between education and brain macro- and micro-structure. However, we did not find evidence that these structural markers affect risk of Alzheimer’s disease. The protective effect of education on Alzheimer’s disease may be mediated via other measures of brain reserve not included in the present study, or by alternative mechanisms.


Introduction
Despite a large body of observational epidemiological evidence supporting education as a protective factor for Alzheimer's disease, [1][2][3][4][5][6][7][8] the biological mechanisms underpinning this association are not wellestablished. A potential mechanism by which higher educational attainment (EA) protects against risk of Alzheimer's is through increasing or maintaining the underlying 'brain reserve' of the individual. 5 Brain reserve refers to individual differences in the anatomical and structural characteristics of the brain that enable some individuals to preserve their cognitive and functional status despite neuropathology. [9][10][11] The progression of amyloid-β and tau pathology in Alzheimer's disease is associated with several structural alterations in the brain, including progressive cortical thinning, [12][13][14][15] widespread grey matter atrophy in cortical and subcortical regions 16,17 and damage to the integrity and organization of white matter tracts. [18][19][20][21] Many of these structural characteristics can be measured in vivo using structural or diffusion MRI, and thus their pre-morbid levels may serve as a useful proxy for the structural basis of brain reserve capacity. 22,23 Consistent with the brain reserve hypothesis, observational neuroimaging studies of cognitively intact older adults have provided evidence for an association of education with several MRI measures of brain macro-and micro-structure that are implicated in Alzheimer's disease. For instance, higher education levels have been associated with increased whole-brain and regional grey matter volume, [24][25][26] cortical thickness [27][28][29][30][31] and increased surface areas of sub-regions of the hippocampus and amygdala that are vulnerable to Alzheimer's disease pathology. 32 Similar findings have been reported for the association between education levels and white matter micro-structure in cognitively intact elderly, with more highly educated individuals showing increased white matter tract integrity in several brain regions that are characteristic sites of Alzheimer's pathology. 28,33 Given the observed associations between education and structural markers of brain reserve, it is plausible to hypothesize that changes in brain structure may mediate the protective effect of education on Alzheimer's disease risk, through determining the underlying brain reserve of the individual. However, interpreting these observational associations as evidence of causal relationships between education, brain structure and Alzheimer's risk relies on several untestable and potentially implausible assumptions, including the absence of residual and/or unmeasured confounding and reverse causation. 34 For instance, the association of education with brain structural metrics may be confounded by early-life factors that are common predictors of both EA and brain structure, such as childhood socioeconomic status, 35,36 birthweight, [37][38][39][40][41] childhood cognitive ability 42 and maternal smoking during pregnancy. 37,43 Confounding may also affect the relationship between MRI markers of structural brain reserve and Alzheimer's risk. Several of the established risk factors for Alzheimer's disease and other dementias (e.g. smoking, hypertension, diabetes, excessive alcohol consumption and physical inactivity) have been shown to be associated with various aspects of brain macro-and micro-structure in community-dwelling populations. [44][45][46][47][48][49][50][51][52][53][54][55] Therefore, it may be that these factors, rather than poor pre-morbid structural brain health, underlie the increase in Alzheimer's disease risk. In addition, even if the observed associations reflect causal relationships, the direction of causality (i.e. from the exposure to the outcome or vice versa) cannot be definitively established using observational methods. 34 For instance, the observational association between education and brain structure could arise as a result of longer duration of education causing a change in brain structural metrics, or alternatively, individuals with better structural brain health (e.g. larger brain volumes or cortical thickness) seeking longer durations of education (or a combination of both). Reverse causation could also affect the association between MRI markers of brain reserve and Alzheimer's disease. Specifically, while greater structural brain reserve (as proxied by MRI metrics) may confer protection against advancing neuropathology and risk of an Alzheimer's diagnosis, it is also possible that changes in these structural markers occur in response to pre-clinical Alzheimer's disease (e.g. loss of brain volume or cortical thickness prior to clinical manifestations of dementia).
Mendelian randomization (MR) 34,[56][57][58] can be a useful approach for assessing putative causal relationships between education, brain structure and Alzheimer's disease, as it addresses some of the common limitations of classical epidemiological studies (e.g. confounding and reverse causation). By using genetic variants that are specifically associated with a putative exposure as instrumental variables, MR can be used to make inferences about the causal effect of an exposure on an outcome. 59,60 Due to the random assortment of alleles at conception, the distribution of genetic variants that are associated with a particular exposure is largely independent of factors that confound exposure-outcome associations in conventional observational analyses. 61-63 Therefore, estimates from MR are less affected by environmental confounders, and can provide more reliable insights into causal relationships between risk factors and disease outcomes than classical epidemiological studies. In addition, given that the genotype of an individual is determined at conception and cannot be modified by subsequent disease outcomes, the direction of causation will always be from the genetic variant to the trait of interest, eliminating the potential for reverse causation. 34 Therefore, MR can be particularly useful for obtaining reliable causal inferences in retrospective settings (e.g. in case-control studies) where genetic variants are measured after the occurrence of the disease outcome. 64 For instance, while MRI markers of structural brain reserve cannot be reliably measured in individuals with Alzheimer's disease (as the disease is likely to distort their measurement in cases), genetic variants associated with brain structure cannot be modified by the disease event and can therefore be used as a reliable proxy for pre-morbid brain structure in individuals with Alzheimer's disease.
In recent years, a growing number of MR investigations have found evidence for an inverse association of genetically predicted EA with Alzheimer's disease risk. [65][66][67][68][69] However, the mechanisms underlying the protective effect of education remain relatively unexplored. Recent advances in genotyping and multi-modal neuroimaging technologies have facilitated the collection of these data in large-scale prospective cohort studies, 70 enabling the discovery of genetic variants associated with brain structure using considerably larger sample sizes than was previously possible. [71][72][73][74] The present study aimed to expand on previous work by using MR to investigate putative causal relationships between EA, brain structure as measured by MRI and risk of Alzheimer's disease. In addition, we aimed to explore whether there was any evidence for the hypothesis that brain structural alterations lie on the causal pathway from education to Alzheimer's disease (i.e. the brain reserve hypothesis). We proxied structural brain reserve using imaging markers of grey and white matter macro-and micro-structure derived from structural or diffusion MRI (see Methods for the description and choice of these imaging-derived phenotypes). Our primary objectives were: (i) to replicate, using the latest genome-wide association study (GWAS) data, the previous MR findings supporting a protective causal effect of EA on Alzheimer's disease risk; (ii) to assess whether EA has a causal effect on brain macro-and/or micro-structure; (iii) to assess whether brain macro-and/or micro-structure phenotypes causally affect risk of Alzheimer's disease; and (iv) to assess whether the protective effect of EA on Alzheimer's disease risk is mediated via changes to brain macro-and/or micro-structure, using multivariable MR (an extension to univariable MR which can be used to investigate mediating relationships). 75,76 A directed acyclic graph illustrating the putative causal effects explored in this study is presented in Fig. 1. Although our primary hypotheses were in the directions stated before and shown in Fig. 1, we tested for a causal effect between each pair of variables in both directions (i.e. bidirectional or reciprocal MR), since this is a useful method for orientating the direction of causal effect (if any) between two variables. 77

Data sources
The present study is based on a two-sample MR analysis strategy, an extension of MR in which the effects of the genetic instruments on the exposure and the outcome are obtained from two separate datasets. 78,79 To minimize the possibility of confounding due to population stratification, all data sources were restricted to individuals of European ancestry. The GWAS used to obtain the summary statistics for each phenotype are listed in Table 1. Detailed description of the data sources is available in Supplementary material. Summary-level genetic association estimates with EA were obtained from a GWAS meta-analysis of ∼1.1 million individuals by Lee et al. 80 EA was defined as the number of years of schooling (YOS) completed, measured at an age of at least 30 years. Genetic variant association estimates with Alzheimer's disease were taken from the largest available GWAS meta-analysis of clinically diagnosed late-onset Alzheimer's disease (onset age > 65 years), as conducted by the International Genomics of Alzheimer's Project. 81 Summary statistics for the imaging-derived phenotypes were obtained from three separate data sources based on the early-2020 release of combined genetic and multi-modal brain imaging data from the UK Biobank. 83 Although several thousand imaging-derived phenotypes can be generated from UK Biobank MRI data, many are highly inter-correlated, and analysis of all imaging-derived phenotypes could lead to spurious results or challenges in controlling for multiple comparisons. Our strategy was to focus on 15 imaging-derived phenotypes ( Fig. 2 and Supplementary material), most of which reflect global brain measures previously shown to be associated phenotypically with EA and/or Alzheimer's disease. 12,14,[16][17][18][19][24][25][26][27][28][31][32][33] We also chose to study the total volume of white matter hyperintensities as a metric closely linked to age-related cognitive decline and thus a putative marker of structural brain health. [84][85][86][87] A more detailed explanation of the rationale for selection of imaging-derived phenotypes is provided in the Supplementary material. To generate genetic variant association estimates with the whole-brain cortical macro-structure (surface area, volume, cortical thickness, intrinsic curvature, mean curvature, local gyrification index) and micro-structure phenotypes (mean diffusivity, fractional anisotropy, intracellular volume fraction and orientation dispersion index), we conducted an in-house GWAS 82 using the latest UK Biobank data release (Supplementary material). Genetic variant association estimates with the white matter micro-structure phenotypes were obtained from a recently published GWAS of diffusion MRI data by Zhao et al. 74 For this study, we used summary statistics for the global fractional anisotropy and mean diffusivity phenotypes, which were averaged across 21 predefined cerebral white matter tracts. For hippocampal volume and the total volume of white matter hyperintensities, we obtained Imaging-derived measures of brain structure are explored as potential mediators of the effect of EA (exposure) on Alzheimer's disease (outcome). G X represents the set of instrumental variables for EA. G M represents the set of instrumental variables for brain imaging-derived phenotype 1, …, N . Parameter a represents the direct causal effect of EA on imaging-derived phenotype 1, …, N . Parameter b represents the direct causal effect of imaging-derived phenotype 1, …, N on Alzheimer's disease. Parameter c' represents the direct causal effect of EA on Alzheimer's disease. Parameters a and c' are estimated using the set of variants G X , and parameter b is estimated using the set of variants G M . Confounding variables are omitted from the diagram. genetic variant association estimates from a recently published GWAS of 3913 imaging-derived phenotypes by Smith et al. 73 The cortical macro-/micro-structure and white matter micro-structure phenotypes were not corrected for intracranial volume (ICV) or total brain volume, as these were all global measures and would be highly correlated with whole-brain volume. However, for the localized phenotypes (hippocampal volume and the total volume of white matter hyperintensities), we used genetic association estimates that were corrected for ICV. All genetic association estimates were taken from GWAS conducted on the combined discovery and replication cohorts.

Selection of genetic instruments and data harmonization
For each MR analysis, we selected all single nucleotide polymorphisms (SNPs) associated with the exposure of interest at a genome-wide significance threshold (P < 5 × 10 −8 ) as instrumental variables. The resulting instruments were pruned to nearindependence using a linkage disequilibrium (LD) threshold of r 2 < 0.001 over 10 000 kilobase pairs. We used the LD reference panel for the European super-population in the 1000 Genomes Project reference dataset, which was restricted to bi-allelic SNPs with minor allele frequency >0.01. We extracted the following summary-level data from each exposure and outcome GWAS: SNP rs number, effect and other alleles, effect allele frequency, sample size, number of cases/controls (if applicable), standardized β-coefficients, standard errors and P-values. Where an instrument SNP was not available in the outcome dataset, we used LDlink 88 to identify a proxy SNP in LD with the target SNP (r 2 > 0.8). The exposure and outcome GWAS datasets were then harmonized to ensure that the genetic variant association estimates corresponded to the effect of the same allele. We used allele frequency information to infer the orientation of alleles in the exposure and outcome GWAS. Palindromic SNPs with minor allele frequency >0.42 were dropped from the analysis. 89 Details of the SNPs used as instruments in each MR analysis (including proxies for SNPs not available in the outcome datasets) are available in the Supplementary material. For each analysis, we used the online power calculator by Burgess 90 (https://sb452.shinyapps.io/power/) to estimate the minimum causal effect that we had 80% power to detect at a multiple-testing-corrected significance threshold (see the 'Correction for multiple testing' section later). Power calculations are presented in Supplementary Table 1.

Statistical analyses Bidirectional univariable Mendelian randomization
We performed univariable MR analyses to estimate each of the following total causal effects: (i) EA on Alzheimer's disease; (ii) EA on each of the 15 imaging-derived phenotypes; and (iii) imaging-derived phenotypes on Alzheimer's disease. To examine the direction of association and investigate the possibility of reverse causation, we additionally estimated each of these causal effects in the direction opposite to that initially hypothesized (i.e. bidirectional MR). 77 As recommended by Burgess et al., 91 we used inverse-variance weighted (IVW) MR 92 with multiplicative random-effects as the primary analysis method, as it provides the most efficient combination of the variant-specific ratio estimates [91][92][93] and accounts for heterogeneity in the causal estimates obtained from individual variants. 91,94  All genetic association estimates were taken from GWAS conducted on combined discovery and replication cohorts. Note that for some phenotypes there is a difference in sample size between the exposure and outcome datasets. This was either because the summary statistics for the full set of variants were not publicly available for one or more of the meta-analysed cohorts (e.g. 23andMe), or the full replication analysis on which the final list of genome-wide significant variants was based was only conducted on a subset of the variants meeting pre-specified significance thresholds at earlier discovery stages. Where this was the case, all analyses of the phenotype as an exposure were based on genome-wide significant variants from the largest analysed sample (to maximize power for selecting instruments). In the analyses of the phenotype as an outcome, summary statistics were obtained from the dataset for which association estimates were provided for the full set of variants.

Correction for multiple testing
To account for the number of MR analyses performed to test for bidirectional effects of education on brain structure and brain structure on Alzheimer's disease, we applied the multiple-testing correction approach described by Lord et al. 68 Given the correlation structure between the various MRI metrics considered, applying a simple Bonferroni correction could be overly conservative. We therefore used a principal component analysis approach (https:// github.com/hagax8/independent_tests) to estimate the number of independent hypotheses tested from the matrix of squared phenotypic correlations between the imaging-derived phenotypes (Supplementary material and Supplementary Fig. 1). We first calculated the number of principal components that explained 99.5% of the variance in the matrix as n = 13. The number of individual tests within the squared correlation matrix was then calculated as T = (n × n − n)/2 (=78), and the square root of T (=8.83) was used to establish the final number of individual imaging-derived phenotypes to correct for. Bidirectional associations between EA and imaging-derived phenotypes and between imaging-derived phenotypes and Alzheimer's disease were therefore considered significant at a multiple-testing corrected threshold of P < 0.006 (=0.05/ 8.83). For testing bidirectional causal relationships between EA and Alzheimer's disease, we set statistical significance at P < 0.05. Note that the purpose of the multiple-testing correction was to control the family-wise error rate within each objective (i)-(iv), rather than across the total number of univariable MR analyses performed (i.e. 62). Controlling the family-wise error rate across all 62 tests would be appropriate if we were interested in the global null hypothesis (i.e. the intersection hypothesis of all null hypotheses of interest). 95 Given that each of the objectives of interest were distinct (i.e. we were interested in detecting putative causal relationships between education and Alzheimer's disease, education and brain structure, and brain structure and Alzheimer's disease), we applied the multiple-testing correction to the number of hypotheses within each objective.

Sensitivity analyses
For each univariable MR analysis where a causal effect was detected using the IVW method, we used the following four methods to assess the robustness of that finding to potential violations of MR assumptions: the Contamination Mixture method, 96 Weighted Median MR, 97 MR-Egger 98 and the MR pleiotropy residual sum and outlier (MR-PRESSO) method. 99 These four robust methods were selected since they each produce a valid estimate of the causal effect of the exposure on the outcome under different assumptions (see Supplementary material for a description of the assumptions of each method). 100 In addition to robust MR methods, we performed a range of other sensitivity analyses where a causal effect was detected using the IVW method. First, we assessed the presence of heterogeneity amongst the variant-specific causal estimates using Cochran's Q statistic. 101,102 Second, we generated funnel plots of the precision Figure 2 Overview of the brain imaging-derived phenotypes investigated in this study. Structural brain reserve was proxied by 15 brain imaging-derived phenotypes. These included 10 global cortical phenotypes (six macro-structural metrics derived from T 1 -weighted structural MRI and four micro-structural metrics derived from diffusion MRI), two white matter micro-structural phenotypes (measured at 21 major white matter tracts across the whole brain), bilateral hippocampal volumes and the total volume of white matter hyperintensities in the brain (derived from T 2 -weighted MRI).
of the variant-specific causal estimates against the estimates themselves. The funnel plot is expected to be symmetrical about the IVW estimate, with more precise estimates having less variability. 103 The presence of asymmetry in the funnel plot is suggestive of directional pleiotropy and bias in the overall causal estimate. 98,103 Third, we carried out leave-one-out sensitivity analyses to identify influential data points amongst the instruments for each exposure, and to assess the reliance of the causal effect estimate on individual genetic variants. 104 Finally, to orient the direction of causality between the exposure and the outcome, we used the Steiger directionality test, 105 an extension to two-sample MR, which detects variants that have a stronger association with the outcome than with the exposure. Where there was evidence from the Steiger test that some genetic instruments had a stronger association with the outcome, we repeated the analysis excluding those variants. 91 During the review process, we conducted additional sensitivity analyses using summary statistics from a recently published GWAS 106 of longitudinal changes in brain structure across the lifespan (see Supplementary material and Supplementary Table 7 for details).

Multivariable Mendelian randomization to test for mediation
We performed multivariable MR analyses 75,76,107 to investigate the potential mediating role of brain structure in the relationship between EA and Alzheimer's disease. Multivariable MR allows the genetic variants associated with both the primary exposure and the secondary exposure (mediator) to be included as instruments in the analysis, and can be used to dissect the total causal effect of the exposure on the outcome into an indirect effect via the mediator, and a direct effect of the exposure on the outcome not via the mediator (i.e. via other causal pathways or other mediators; Supplementary material and Supplementary Fig. 2). 76,108 While univariable MR estimates the total causal effect of the exposure on the outcome, multivariable MR estimates the direct effect of the exposure on the outcome, while adjusting for the mediator. The indirect (mediated) effect of the exposure on the outcome can then be estimated by subtracting the direct effect from the total effect. 76,108 This broadly mirrors the difference-in-coefficients method used in traditional noninstrumental variable regression-based approaches to mediation. 109 Using this approach, we estimated the direct causal effect of EA on Alzheimer's disease risk, while adjusting for each of the 15 imaging-derived phenotypes in turn. A difference between the estimate of the total causal effect of EA on Alzheimer's disease (from univariable MR) and the direct causal effect estimate (from the multivariable MR model including an imaging-derived phenotype) would indicate a mediating role of that brain structure phenotype on the causal pathway from education to Alzheimer's disease. 107,108 For each multivariable MR analysis, we selected all SNPs associated with the primary exposure (EA) or the mediator (imaging-derived phenotype of interest) as instrumental variables. The pooled set of SNPs were clumped to pairwise LD (r 2 < 0.001) over 10 000 kilobase pairs, on the basis of the lowest P-value for association with any of the two traits. The extraction of summary-level data from the Alzheimer's disease GWAS, harmonization of the exposure and outcome datasets, and identification of proxies for missing SNPs, followed the same procedure as univariable MR, as described before.

Ethical approval
The present study is a secondary analysis of publicly available data. Ethical approval was granted for each of the original GWAS studies, the details of which can be found in the respective publications.

Data and code availability
Summary statistics from the in-house GWAS of cortical macro-and micro-structure are available at https://portal.ide-cam.org.uk. Individual-level imaging and genetic data used for the in-house GWAS analyses may be requested through the UK Biobank (https://www.ukbiobank.ac.uk/), and the code used in generating the imaging phenotypes is available on GitHub (https://github. com/ucam-department-of-psychiatry/UKB). Summary-level genetic association estimates with all other phenotypes were obtained from publicly available published GWAS, and can be accessed from the respective publications. R code for reproducing all MR analyses can be found on https://github.com/as2970/EA_brain_AD_MR.

Inverse association of genetically predicted educational attainment with Alzheimer's disease risk
There was strong evidence for an inverse association between genetically proxied EA and Alzheimer's disease across all MR methods ( Fig. 3 and Supplementary Fig. 3). The results of the main IVW analysis suggested that each SD increase in genetically predicted YOS (∼4.2 years) was associated with a 30% reduction in odds of Alzheimer's disease (OR = 0.70, 95% CI 0.60, 0.80). The weighted median and MR-PRESSO methods provided similar estimates to the IVW analysis, while larger inverse estimates were observed in the contamination mixture and MR-Egger analyses (Fig. 3).
Cochran's Q statistic provided no evidence that there was more heterogeneity in the variant-specific causal estimates than expected due to chance (Supplementary Table 2). There was no evidence of directional pleiotropy using the MR-Egger intercept test (Supplementary Table 3), no evidence of departure from symmetry in the funnel plot ( Supplementary Fig. 4) and no distortion in the leave-one-out plot ( Supplementary Fig. 5). The Steiger directionality test indicated that 24 (7%) of the 332 education-associated SNPs explained more variance in Alzheimer's disease than in EA. When these variants were excluded from the analysis, there was still strong evidence for an inverse association of genetically proxied education with Alzheimer's disease (OR IVW = 0.72, 95% CI 0.62, 0.83; Supplementary Table 4).
In the opposite direction, as expected, there was no association between genetically predicted Alzheimer's disease and years of education. The IVW estimate (representing the SD change in YOS per doubling the odds of Alzheimer's disease) was 0.00 (95% CI 0.00, 0.01, P = 0.145).

Association of genetically predicted educational attainment with brain structure
After correction for multiple testing, genetically proxied EA was positively associated with four measures of cortical macro-structure ( Fig. 4 and Supplementary Fig. 6). In IVW analyses, each SD increase in genetically predicted YOS was associated with a 0.30 SD increase in surface area (95% CI 0.20, 0.40), 0.29 SD increase in cortical volume (95% CI 0.20, 0.37), 0.18 SD increase in intrinsic curvature (95% CI 0.11, 0.25) and 0.21 SD increase in local gyrification index (95% CI 0.11, 0.31). In addition, inverse associations were observed with intracellular volume fraction (β IVW = −0.09, 95% CI −0.15, −0.03) and the total volume of white matter hyperintensities (β IVW = −0.14, 95% CI −0.23, −0.05). The results of the pleiotropy robust methods were broadly consistent with the IVW analyses ( Supplementary Fig. 6). For local gyrification index, intracellular volume fraction and white matter hyperintensities volume, confidence intervals around the MR-Egger estimate included the null. However, the point estimates were still in the same direction, and all other robust methods were in line with the IVW analysis.
All analyses demonstrated significant evidence of heterogeneity in the variant-specific causal estimates (Supplementary Table 2). The funnel plot for cortical surface area demonstrated a slight departure from symmetry, but all other funnel plots were symmetrical about the IVW estimate ( Supplementary Figs 7-12). The MR-Egger intercept test did not show evidence of directional pleiotropy in any of the analyses (Supplementary Table 3), and there was no distortion in any of the leave-one-out plots ( Supplementary Figs 13-18). The proportion of education-associated SNPs that explained more variance in the imaging phenotype than in EA ranged from 14% for intracellular volume fraction to 30% for white matter hyperintensities volume (Supplementary Table 4). In sensitivity analyses excluding the invalid variants from each analysis, all estimates were attenuated towards the null, and the associations with local gyrification index and white matter hyperintensities volume were no longer statistically significant (Supplementary Table 4).

Association of genetically predicted brain structure with educational attainment
After correction for multiple testing, genetically predicted levels of three cortical macro-structure phenotypes (surface area, volume and intrinsic curvature) were positively associated with EA ( Fig. 4 and Supplementary Fig. 19). The IVW estimates, representing the change in YOS (SD units) per 1 SD increase in genetically predicted levels of imaging-derived phenotypes were 0.13 (95% CI 0.10, 0.16) for surface area, 0.15 (95% CI 0.11, 0.19) for volume and 0.12 (95% CI 0.04, 0.19) for intrinsic curvature. For cortical surface area and volume, all robust methods provided similar estimates to the IVW analysis, but confidence intervals around the MR-Egger estimates were considerably wider than the other methods and included the null (Supplementary Fig. 19). The MR-Egger estimate of the association between genetically predicted intrinsic curvature and EA was negative, whereas all other estimates of this association were positive. However, the confidence interval for the MR-Egger estimate still overlapped with all other point estimates ( Supplementary Fig. 19).
Using Cochran's Q statistic, we found evidence of heterogeneity in all three analyses (Supplementary Table 2). However, the funnel plots showed little evidence of departure from symmetry ( Supplementary Figs 20-22), and the MR-Egger intercept term did not significantly differ from zero in any analysis (Supplementary Table 3). In leave-one-out sensitivity analyses, the overall IVW estimates did not change on exclusion of any variant ( Supplementary  Figs 23-25). The Steiger directionality test did not identify any SNPs that explained more variance in EA than in the imaging phenotype for any analysis (Supplementary Table 4).

Association of genetically predicted Alzheimer's disease with brain structure
Using the primary IVW analysis method, we did not find evidence for an association between genetically predicted levels of any imaging-derived phenotype and Alzheimer's disease (Fig. 5). However, genetically predicted Alzheimer's disease was associated with four measures of brain structure ( Fig. 5 and Supplementary  Fig. 26 Fig. 26). For orientation dispersion index, the 95% CI for the contamination mixture estimate included the null, but the point estimate was identical to the other methods ( Supplementary Fig. 26). The contamination mixture and MR-PRESSO methods both suggested a null association of genetically predicted Alzheimer's disease with white matter mean diffusivity (Supplementary Fig. 26).
We found evidence of heterogeneity in the variant-specific causal estimates for the association of genetically proxied Alzheimer's disease with white matter mean diffusivity (Supplementary Table 2). In addition, there was evidence of potential horizontal pleiotropy in this analysis using the MR-Egger intercept test (Supplementary  Table 3). There was little evidence of departure from symmetry in the funnel plots ( Supplementary Figs 27-30). In leave-one-out sensitivity analyses, the association of genetically predicted Alzheimer's disease with all four imaging-derived phenotypes appeared to be driven entirely by one genetic variant (rs12721046). In each case, exclusion of this variant from the analysis attenuated the IVW estimate towards the null (Supplementary Fig. 31). To further investigate the

Figure 4 MR estimates of bidirectional associations between EA and brain imaging-derived phenotypes. Left:
Estimates from IVW MR of the association between genetically proxied EA and imaging-derived brain structure phenotypes. Estimates represent the SD change in the imaging phenotype per 1 SD increase in genetically predicted YOS (∼4.2 years). Right: Estimates from IVW MR of the association between genetically proxied brain structure phenotypes and EA. Estimates represent the SD change in YOS per 1 SD increase in genetically predicted levels of each imaging-derived phenotype. Estimates marked with an asterisk were significant after correction for multiple testing. The SNPs column represents the number of SNPs remaining after clumping for independence and data harmonization. There were no significant clumps for the FA (cortex) phenotype after LD pruning. CT = cortical thickness; FA = fractional anisotropy; HC = hippocampus; IC = intrinsic curvature; ICVF = intracellular volume fraction; LGI = local gyrification index; MC = mean curvature; MD = mean diffusivity; ODI = orientation dispersion index; SA = surface area; Vol = volume; WM = white matter; WMH = white matter hyperintensities.

Figure 5 MR estimates of bidirectional associations between brain imaging-derived phenotypes and Alzheimer's disease. Left:
Estimates from IVW MR of the association between genetically proxied imaging-derived phenotypes and Alzheimer's disease. Estimates represent the odds ratio for late-onset Alzheimer's disease per SD increase in genetically predicted levels of each imaging-derived phenotype. Right: Estimates from IVW MR of the association between genetically proxied Alzheimer's disease and brain structure phenotypes. Estimates represent the average change in each imaging-derived phenotype (SD units) per doubling (2-fold increase) in the odds of genetically predicted late-onset Alzheimer's disease. Estimates marked with an asterisk were significant after correction for multiple testing. The SNPs column represents the number of SNPs remaining after clumping for independence and data harmonization. There were no significant clumps for the FA (cortex) phenotype after LD pruning. CT = cortical thickness; FA = fractional anisotropy; HC = hippocampus; IC = intrinsic curvature; ICVF = intracellular volume fraction; LGI = local gyrification index; MC = mean curvature; MD = mean diffusivity; ODI = orientation dispersion index; SA = surface area; Vol = volume; WM = white matter; WMH = white matter hyperintensities.
reliance of the IVW estimates on this variant, we conducted post hoc single-SNP MR analyses and visualized the results using forest plots ( Supplementary Fig. 32). Although the rs12721046 variant did not have an outlying MR estimate for any imaging-derived phenotype, the precision of its estimates was unusually high, causing this variant to dominate the wider polygenic signal in each case ( Supplementary Fig. 32). In Steiger filtering sensitivity analyses, all instruments explained more variance in Alzheimer's disease than in the imaging phenotypes (Supplementary Table 4).

Mediation analysis
In multivariable MR analyses, there was little change in the association of genetically predicted YOS with Alzheimer's disease after adjusting for genetically predicted levels of each of the 15 imaging-derived phenotypes ( Table 2).

Discussion
We conducted bidirectional univariable and multivariable MR analyses using large genome-wide association datasets to examine putative causal relationships between EA, brain macro-and micro-structure as measured by MRI and risk of Alzheimer's disease. We found strong evidence in support of a protective causal effect of EA on Alzheimer's disease risk, with no evidence of a causal effect in the reverse direction. There was also evidence of bidirectional causal relationships between education and several measures of cortical macro-and micro-structure. However, we did not find any evidence in support of a causal effect of the brain structure phenotypes examined in this study on risk of Alzheimer's disease. Additionally, there was no evidence that the protective effect of EA on Alzheimer's disease risk was mediated via changes to these structural markers. In the opposite direction, we found evidence for an association of genetically predicted Alzheimer's disease with hippocampal volume, as well as cortical and white matter micro-structure. However, these effects appeared to be driven entirely by one variant in the APOC1 gene region, and may therefore represent horizontally pleiotropic effects of this variant rather than a causal effect of Alzheimer's disease on brain structure.
Our finding of a protective causal effect of education on Alzheimer's disease risk is consistent with the large body of observational epidemiological literature. [1][2][3][4][5]7 In the current study, the IVW estimate suggested that every additional 4.2 YOS reduced the odds of Alzheimer's disease by ∼30%. This effect size is broadly consistent with the findings of a dose-response meta-analysis, in which every additional year of schooling was associated with a 7% reduction in risk of all-cause dementia. 112 Our results are also consistent with previous MR evidence supporting a causally protective effect of education on Alzheimer's disease risk. [65][66][67][68][69] Evidence from three recent multivariable MR studies suggests that the protective effect of EA on Alzheimer's disease is largely mediated via its effects on later intelligence, rather than an independent protective effect of YOS. 65,68,113 EA and intelligence are phenotypically 114 and genetically 115,116 correlated, and although there is a degree of non-overlap between the genetic predictors of the two traits, 65 we note that the instruments used to proxy EA in our analyses are unlikely to be uniquely associated with years of education. Therefore, the results of the present study may not be informing us narrowly about time spent in formal education in childhood and adolescence, but rather a proxy measure that reflects EA (and to some extent, intelligence) more broadly. We have focused on EA as the exposure of interest as it is a potentially modifiable factor, and has been suggested to be 'the most consistent, robust and durable method yet to be identified for raising intelligence levels'. 117 Indeed, a large meta-analysis of quasi-experimental studies estimated every additional year of education to be associated with an increase of ∼1-5 standardized intelligence quotient points, 117 a result that was consistent across the lifespan and across broad categories of cognitive ability. If, as previous multivariable MR evidence suggests, intelligence lies on the causal pathway from education to Alzheimer's disease, increasing the number of YOS could still be an effective public health strategy for reducing the incidence of Alzheimer's disease, even if the protective effect of higher EA is entirely mediated via increased intelligence levels. Findings from a quasi-experimental study suggest that increasing the school-leaving age in the UK in 1972 has led to improvements in intelligence quotient as well as a range of health and well-being outcomes, including reduced risks of diabetes and all-cause mortality. 37 Our results indicate that education policy reforms that target the length of compulsory schooling are also likely to be effective for the primary prevention of Alzheimer's disease at the population level. 65,69 We found evidence for bidirectional causal relationships between EA and three global macro-structural markers of cortical morphology, namely, volume, surface area and intrinsic curvature. These findings are in agreement with the existing observational neuroimaging literature on the association between EA and brain morphology, 24,26,32 as well as evidence for positive genetic correlations between education and MRI markers of cortical macro-structure. 71,118 To investigate the direction of causation in these associations, we performed sensitivity analyses using Steiger filtering where we excluded any SNPs that explained more variance in the outcome than in the exposure. Although the magnitude of the effect size attenuated in all analyses following the and after adjustment for genetically predicted levels of each brain imaging-derived phenotype in turn (multivariable IVW analyses).
removal of these SNPs, all causal effect estimates remained statistically significant. We note that when a bidirectional MR analysis suggests causal effects in both directions, it is difficult to settle the question of whether these truly represent reciprocal causality or may reflect shared aetiology, whereby the genetic variants used as instrumental variables in both analyses predict a common cause of both traits. Thus, while all our sensitivity analyses suggest distinct causal effects in both directions between EA and these macro-structural markers, the shared aetiology explanation is also possible. We also found evidence for causal effects of EA on local gyrification index and on the total volume of white matter hyperintensities. However, when we removed variants that explained more variance in the outcome than in the exposure, these effects were no longer statistically significant, suggesting that they may be explained by reverse causation or horizontal pleiotropy. As white matter hyperintensities mainly develop in elderly individuals, 87 reverse causation is unlikely in this case and the association with EA probably reflects horizontal pleiotropy.
The observed causal effect of EA on these macro-structural metrics may arise from the beneficial effects of education on neurodevelopment in childhood/adolescence, and/or from its protective effects on neurodegeneration in adulthood/ageing. As we have used GWAS of brain structure measured cross-sectionally in middle to old age, we cannot prioritize either of the two hypotheses in the current study. However, there are several observational studies that have attempted to distinguish between the effects of education on neurodevelopment and neurodegeneration. For instance, a recent study addressed this question by examining the association of EA with total grey matter volume and ICV in both developmental and adult cohorts. 119 Grey matter volume shows marked changes across the lifespan, increasing substantially along with cortical surface expansion in early childhood 120,121 and decreasing through adulthood with reductions in cortical thickness and subcortical volumes. [122][123][124] ICV, on the other hand, increases until mid-to-late adolescence, with little if any changes observed after, 125 and may therefore serve as a proxy for maximal neuroanatomical volume. 119 If education was associated with enhanced brain maturation in childhood/adolescence, we would expect years of education to be strongly related to ICV. If, however, education had a neuroprotective effect in ageing, we would expect a specific association between higher EA and grey matter volume in adulthood/ageing, after controlling for ICV. The study found consistent positive associations between education and ICV in both development and adulthood, but there was no evidence that education was related to ICV-adjusted grey matter volumes in ageing cohorts, 119 indicating a primarily developmental effect of education that is established in early life rather than a protective effect against neurodegeneration in ageing. 119 This finding is also compatible with recent observational evidence on the association between education and rates of cognitive/brain ageing over the course of adulthood and old age. For instance, a longitudinal neuroimaging study of >2000 individuals found no evidence of an association between levels of education and longitudinal rates of volume loss in atrophy-prone cortical regions or in the hippocampus. 29 Similarly, a recent review that examined the effects of EA on cognitive ageing 126 concluded that while there was strong evidence of a positive association between education and level of cognitive functioning, associations between education and the rate of ageing-associated cognitive decline were negligible. Overall, these findings are more consistent with the account that the effects of education on brain structure and cognitive function are established primarily during neurodevelopment in childhood/adolescence, and are largely preserved into old age rather than being grounded in neuroprotective effects on cognitive/brain ageing. 29,119,126 In other words, individuals with higher EA might have an initial advantage in terms of cognitive/brain reserve that persists through their adulthood/ageing. It is this advantage, rather than attenuated longitudinal changes in brain structure and cognition, which reduces the risk of being diagnosed with Alzheimer's disease in more highly educated individuals (i.e. an intercept effect of education across the lifespan rather than an effect on the slope/rate of change). 29,119,126 Across the 15 cross-sectional imaging-derived phenotypes examined, we did not find any evidence of a causal effect of brain structure on Alzheimer's disease risk or for a mediating role of these brain structure phenotypes on the causal pathway from EA to Alzheimer's disease. However, we cannot, on the basis of these findings, rule out the possibility that changes in brain structure mediate the protective effect of education on Alzheimer's risk through determining the underlying brain reserve of the individual. It is possible that capturing the neural basis of brain reserve requires more granular and specific MRI metrics than the ones used in the current study. We reasoned that any putative protective effects of education on Alzheimer's risk would be unlikely to be manifest only in a highly regionally specific manner, and hence decided to primarily study global rather than localized imaging phenotypes. Nevertheless, the use of global imaging metrics in the current study may have masked any significant regionally specific causal effects of brain macro-or micro-structure on Alzheimer's disease risk. 32 We only present analyses in the main paper based on crosssectional brain imaging data, and it is possible that analyses based on longitudinal changes may differ-see Supplementary material p. 13 and Supplementary Table 7 for a preliminary analysis using data on brain structural longitudinal change. It is also plausible that the protective effect of education on Alzheimer's disease is better explained by the related concept of 'cognitive reserve', which refers to the capacity of the brain to cope with pathology through more efficient use of pre-existing cognitive networks or via recruitment of compensatory neural pathways. 9,22,127 Cognitive reserve is a dynamic and active process of adaptation, and is typically measured using behavioural testing or functional neuroimaging modalities (e.g. resting state or task-related networks of brain activation that moderate the effect of Alzheimer's pathology on cognition). 9,128 Although the concepts of cognitive and brain reserve are not mutually exclusive and are hypothesized to operate synergistically in moderating the effect of Alzheimer's pathology on clinical outcome, 9,22 it is possible that the protective effect of education on Alzheimer's disease risk is largely mediated via increased cognitive reserve. 128 Therefore, the use of functional, rather than structural MRI, or cognitive/behavioural phenotypes might be better suited to capturing such mediating effects. Additionally, some of the putative benefits of education on Alzheimer's risk could be mediated primarily through mechanisms minimally related to brain MRI metrics, such as reduced smoking and improved vascular health 5 or via other brain processes (e.g. microscopic or intracellular or vascular) that cannot be captured well by our MRI metrics.
In the reverse direction, we found evidence for an association of genetically predicted Alzheimer's disease with cortical orientation dispersion index, mean diffusivity in the white matter tracts and bilateral hippocampal volumes. However, these results were entirely driven by a single intron variant in the APOC1 gene region (rs12721046), which has been associated with cerebral amyloid deposition as measured by PET imaging in a recent GWAS. 129 The APOC1 gene encodes a member of the apolipoprotein C1 family, which plays a central role in the regulation of lipid levels and metabolism. 130 It is located in a cluster on chromosome 19, ∼5 kilobase pairs downstream from the APOE gene, 130 where common genetic variation is known to have a relatively large effect on Alzheimer's disease risk. 131,132 A recent fine-mapping study of the APOE and surrounding regions using whole-genome sequencing data identified a cluster of risk variants (including rs12721046) in the APOC1 region as potential causal variants for Alzheimer's disease. 133 This cluster of variants were found to confer increased risk of Alzheimer's independent of the APOE-ϵ4 genotype. 133 In all four analyses, the precision of the variant-specific causal estimate for rs12721046 was substantially higher than the remaining instruments, causing this variant to dominate the IVW estimate. When this variant was removed from the analysis, the overall causal effect estimate was attenuated towards the null and was no longer significant. Since all causal effects were only evidenced by the rs12721046 variant, they may represent horizontally pleiotropic pathways from this variant to brain structure. Therefore, we cannot draw definitive conclusions regarding the effect of genetic liability to Alzheimer's disease on brain structure.
Our findings should be interpreted in the context of some limitations. First, although we have used imaging-derived phenotypes as markers of structural brain reserve, we cannot determine the extent to which these phenotypes capture pre-morbid brain reserve, as opposed to neuropathological changes secondary to disease (e.g. atrophy secondary to Alzheimer's disease). 22 Given the age range of the UK Biobank imaging cohort (45-82 years), 73 the possibility that some individuals in the imaging GWAS harbour pre-clinical Alzheimer's disease cannot be excluded. Using both self-reported diagnoses and International Classification of Diseases 134 codes, we found that only 0.6% of participants in the UK Biobank have a current Alzheimer's diagnosis. Therefore, it is unlikely that a large proportion of the imaging GWAS sample had current or imminent Alzheimer's disease at the time of scanning. Nevertheless, with increasing duration of follow-up, a substantial proportion of these participants may go on to develop Alzheimer's or other dementias.
Second, causal effect estimates in our analyses might be affected by Winner's curse bias, which occurs when the same dataset is used to select the genetic variants as instrumental variables and to estimate their association with the exposure. 135 Although this bias could be avoided by using three non-overlapping datasets from the same underlying population for genetic discovery and the estimation of variant-exposure and variant-outcome associations, restricting our analyses to non-overlapping datasets for the phenotypes examined would have substantially reduced the sample sizes. Therefore, a compromise was necessary to balance the risk of bias against imprecision of the causal estimates. 64 Third, although there were no overlapping samples in the analyses of education and brain structure on Alzheimer's disease, 39% of participants in the EA GWAS and all of those in the brain imaging GWAS were recruited from the UK Biobank. Overlap between the exposure and outcome datasets in two-sample MR can exacerbate bias due to weak instruments, 91 with the magnitude of bias being a linear function of the degree of overlap between the two samples. 136 However, brain imaging is a recent addition to the UK Biobank data collection protocol, and <10% of the UK Biobank cohort contribute to the imaging sample used in the present study. Even if all participants from the UK Biobank imaging sample were included in the EA GWAS, the percentage overlap between the exposure and outcome datasets in the current study would range from 2.8 to 2.9% for the education → brain structure analyses, and from 4.1 to 4.3% for the brain structure → education analyses, suggesting that the extent of sample overlap in the current study is minimal. Therefore, it is unlikely that the use of completely nonoverlapping samples would have changed the direction or magnitude of our results.
Fourth, our findings may have been affected by selection bias in the UK Biobank imaging cohort, which occurs when selection into the study sample depends on a collider. 137 In MR, both the exposure and the outcome are causally downstream of the genetic variants and any confounders of the exposure-outcome association (i.e. they are colliders of the instrumental variable and the confounder). Therefore, if selection into the study sample is a function of the exposure or the outcome, this can introduce an association between the instrumental variable and the confounder 138 leading to a violation of the instrumental variable assumptions. 139 In the analyses assessing the causal effect of EA on imaging-derived phenotypes, selection into the imaging sample is likely to have been a function of the exposure, as participants in the UK Biobank have higher education levels compared to the UK general population. 140,141 Selection bias could have also occurred in the analyses assessing the causal effect of brain structure on Alzheimer's disease, as recruitment into the imaging sample may have been a function of the outcome. Since UK Biobank participants are healthier than the general population, 142 and the imaging cohort is a subset of those participants who have volunteered to undergo extensive additional assessments, 141,143 it is reasonable to assume that those recruited into the imaging cohort were less likely to have Alzheimer's disease at the time of scanning compared to the general population (or develop Alzheimer's disease in the future). However, simulation studies have shown that the impact of selection bias on MR estimates and Type I error rates is only severe when the collider has a particularly large effect on selection, 139 which is unlikely to be the case in the examples discussed previously. Therefore, we believe it is unlikely that our findings can be explained solely by selection bias.
Fifth, genetic association estimates with several phenotypes were taken from GWAS based on the UK Biobank cohort, which is not representative of the general population with regards to several sociodemographic, lifestyle and health-related characteristics. For instance, UK Biobank participants are more likely to be female, older and living in less socioeconomically deprived areas compared with non-participants. 142 They have also been shown to have a lower prevalence of obesity, smoking and daily alcohol consumption compared with the UK general population, as well as lower age-adjusted rates of total cancer incidence and all-cause mortality. 142 These differences are consistent with the well-established 'healthy volunteer effect', 144 which may limit the generalizability of our findings.
Sixth, to minimize the possibility of confounding due to population stratification, we limited our analyses to participants of European ancestry. Therefore, it remains unclear whether our findings will extrapolate to other populations.
Finally, the GWAS data sources used for brain imaging phenotypes had relatively small sample sizes. Although larger GWAS of brain structure are available, 71,145 these are meta-analyses of MRI data from different imaging cohorts. The use of uniform genotyping and neuroimaging protocols in the UK Biobank and the application of consistent genetic and phenotypic quality control pipelines to the data used in the current study is likely to have resulted in lower measurement error and enhanced power, despite the slightly smaller sample size. Nevertheless, statistical power calculations indicated that our analyses may have been underpowered to detect particularly subtle causal effects of brain structure on Alzheimer's risk (Supplementary Table 1). The imaging sample on which the present study is based represents only 40% of the eventual UK Biobank imaging cohort size. 73 As data from more participants become available, replication of these findings using larger and betterpowered GWAS of imaging-derived phenotypes will enable us to draw more definitive conclusions regarding putative causal relationships between education, brain structure and Alzheimer's disease.
In conclusion, our findings add to the extensive body of observational epidemiological literature, as well as evidence from a growing number of MR investigations, providing support for a causally protective role of increased EA on risk of Alzheimer's disease. In addition, our results support potential bidirectional causal associations between education and several aspects of cortical macro-and micro-structure. However, we found no evidence that these structural alterations have downstream effects on risk of Alzheimer's or that they lie on the causal pathway from education to Alzheimer's disease. The observed protective effect of increased EA on risk of Alzheimer's may be mediated via other structural brain changes not captured by these particular MRI phenotypes or by alternative biological mechanisms.