2 Study design and results

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2.1 What did you do in this paper? How was the study designed? Why was the study designed in this way?

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We conducted a GWAS (see FAQ 1.3) of educational attainment (see FAQ 1.2) in a sample of over 3 million people. The sample size we used in the current study is much larger than that used in previous GWAS of educational attainment (see FAQ 1.8). By constructing a sample of over 3 million, we expected to estimate genetic effects with much greater accuracy than previous studies (with smaller samples). As a result, we expected to identify many more specific SNPs that are associated with educational attainment and to build a more accurate polygenic index.

To construct such a large sample, we started with the data analyzed in our most recent paper (Lee et al., 2018): a GWAS of roughly 300,000 research participants from 69 datasets; a GWAS of roughly 440,000 research participants from the UK Biobank, a large-scale biomedical database and research resource; and a GWAS of roughly 365,000 research participants from the personal genomics company 23andMe. We then replaced the earlier 23andMe sample with an updated GWAS based on roughly 2.3 million 23andMe research participants. This new data increased the combined sample size from about 1.1 million participants to about 3 million participants. All of these datasets have surveyed and genotyped their research participants.

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Our study was limited to only the most common type of genetic difference: SNPs (see FAQ 1.3). Like our most recent previous study (Lee et al., 2018) but unlike most other studies, which have analyzed only the autosomes (the non-sex chromosomes), our study also included SNPs on the X chromosome (see FAQ 2.9). Also unlike most other studies (including our own previous work), which have studied only the additive (i.e., linear) effects of SNPs, our study also studied their dominance (i.e., non-linear) effects (see FAQ 2.10). In total, our analyses included approximately 10 million SNPs.

As in other GWASs, our analyses included only individuals of primarily European genetic ancestries. (We say geneticancestries because we are not talking about who someone identifies as their ancestors but, rather, the similarity between someone’s genome and the genome of a “reference sample” for a population from prior genetic studies. And throughout these FAQs we refer to European and African genetic ancestries, plural, because there is tremendous genetic diversity within each continent, especially Africa.) Such individuals are identified in different ways in different cohorts that participated in our study (depending on, for example, the demographic composition of the country where the individuals live). In all cohorts, though, statistical summaries of the allele frequencies and allele correlation patterns in people’s genomes (see FAQ 2.2), called principal components, are used as part of the procedure. In particular, individuals are only identified as having European genetic ancestries if their principal components are sufficiently similar to those of reference individuals recruited in prior genetic studies, whose ancestors over several generations were all born in a European country. The restriction to European genetic ancestries is needed in order to reduce statistical confounds that otherwise arise from studying populations that include people with different genetic ancestries (see the discussion of population stratification bias in FAQ 2.2; see also FAQs 1.4, 2.7 & 3.5).

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In the remainder of the paper, we used the findings from the GWAS for a range of additional analyses that explored (among other things):

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• the predictive power of the polygenic index for educational attainment (FAQ 2.4), as well as cognitive performance and high school academic achievement;

• why the polygenic index is less predictive in individuals of African genetic ancestries than in individuals of European genetic ancestries (FAQ 2.5);

• the predictive power of the polygenic index for the risk of various diseases (FAQ 2.6);

• the extent to which the polygenic index’s predictive power for educational attainment and other outcomes is due to its correlation with environmental factors rather than to genes, per se (see FAQ 2.7); 

• assortative mating based on educational attainment (see FAQ 2.8);

• the effects of SNPs on the X chromosome on educational attainment (FAQ 2.9); and

• the magnitude of “dominance effects” for the effects of SNPs on educational attainment (see FAQ 2.10). 

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2.2       What are common pitfalls in GWASs? What precautions did you take against them?

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There are many potential pitfalls that can lead to spurious results in genome-wide association studies (GWASs). We took many precautions to guard against these pitfalls.

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One potential source of spurious results is incomplete “quality control” (QC) of the genetic data. To avoid this problem, we use QC protocols from medical genetics research (Winkler et al., 2014). We supplement these protocols by developing and applying additional, more stringent QC filters.

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Another potential source of spurious results is a confound known as “population stratification bias.” (We discuss a well-known illustration of this confound—a hypothetical GWAS of chopstick use—in FAQ 1.3.) In our study we correct for population stratification bias as much as possible. At the outset, we restrict the study to individuals of European genetic ancestries. As is standard in GWASs, we also control for “principal components” of the genetic data in the analysis; these principal components capture the small genetic differences across genetic ancestry groups within European populations, so controlling for them largely removes the spurious associations arising solely from these small differences.

After taking these steps to minimize bias stemming from population stratification, we conduct a standard analysis to assess how much population stratification bias still remains in our data after our efforts to minimize it, called LD Score regression (Bulik-Sullivan et al., 2015). The results of this analysis indicate that the biases in our results due to population stratification are small.

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The “direct effect” of the polygenic index from our within-family analysis, described in FAQ 2.7, is immune to any remaining population stratification bias. Population stratification bias can only arise when individuals are from different families with different genetic ancestries. By controlling for the polygenic indexes of an individual’s parents, we are also controlling for any differences in genetic ancestry across individuals.

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2.3       What did you find in the main GWAS of educational attainment?

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In our sample of roughly 3 million people, we found 3,952 SNPs that were associated with educational attainment (using the standard statistical threshold in GWAS, which adjusts for multiple hypothesis testing). This is a substantial increase from the 1,271 SNPs identified in our last GWAS of around 1 million individuals (Lee et al., 2018), further confirming the importance of large sample size for identifying SNPs associated with socio-behavioral outcomes. 

The current study further confirmed the finding from our earlier work that the effects of individual SNPs on educational attainment are each extremely small. The median effect size across the 3,952 SNPs was just 1.4 weeks of schooling per allele; even the SNPs with the strongest associations only predicted around 3.5 weeks of additional schooling per allele. Taken together, these 3,952 SNPs accounted for roughly 8% of the variation across individuals in years of education completed.

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Here is another way to think about this result. We could use the results for these 3,952 SNPs (not the ~1 million SNPs across entire genome that we discuss in FAQ 2.4) to predict the educational attainment for a new group of people (separate from our discovery sample) whose educational attainment is unknown to us. We could then compare each individual’s predictededucational attainment to their actual educational attainment. If we did so, our results would show that if someone were predicted to complete an above average number of years of schooling (i.e., to be in the top half of educational attainment), that person would have about a 59% chance of actually being in the top half of educational attainment. 59% is better than the 50% odds of making a correct prediction that you would have if you used a coin flip to predict whether someone is in the top or bottom half of educational attainment—but only a bit better. By contrast, a prediction based on a polygenic index that combines the complete set of ~1 million SNPs that we studied (see FAQs 1.6 & 2.4) has more predictive power: about 13% of the variation across individuals. (Even this amount of predictive power still corresponds to having only a 62% chance of correctly guessing whether someone is in the top or bottom half of educational attainment.)

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The contrast between the 8% of the variation predicted by the 3,952 SNPs and the 20% estimated to be explained by common SNPs (see FAQ 1.8) implies that there are many other SNPs that have not yet been identified. Even larger sample sizes will be needed to identify them. 

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It is also important to keep in mind that educational attainment is a complex outcome, and our study focuses on only a tiny piece of the bigger picture. In this paper, we only examine one type of genetic difference (SNPs). Other genetic effects, environmental effects, and their interactions are important topics of active research and of future work by the SSGAC. Such work includes studies of associations between educational attainment and epigenetic marks, i.e., other molecules that attach to a person’s DNA over the course of their lifetime and tell their genes to switch “on” or “off” (Linnér et al., 2017).

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2.4       How predictive is the polygenic index developed in this study?

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As discussed in FAQ 1.6, we can create a polygenic index using the GWAS results from around ~1 million SNPs. The polygenic index we construct “predicts” (see FAQ 1.5) around 13% of the variation in education across individuals of European genetic ancestries (when tested in independent data that was not included in the GWAS). This ~1 million SNP polygenic index predicts much more of the variation than does the genetic predictor described in FAQ 2.2, which was based on only 3,952 SNPs. Including all ~1 million SNPs tends to add predictive power because the threshold for significance/inclusion that is used to identify the 3,952 SNPs is very conservative (i.e., many of the other ~1 million SNPs are also associated with educational attainment but are not identified by our study, and on net, it turns out empirically that more signal than noise is added by including them). This study’s polygenic index has much more predictive power than polygenic indexes constructed from our earlier three GWASs of educational attainment, because all of those studies had much smaller sample sizes (~100,000, ~300,000, and ~1.1 million individuals, respectively, compared with ~3 million individuals in the current study).

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Individuals with high polygenic indexes have, on average, higher levels of education than those with lower polygenic indexes. In the present study, we found that among the individuals of European genetic ancestries from a U.S. sample of young adults (the National Longitudinal Study of Adolescent to Adult Health), 7% of those with the lowest 10% of polygenic indexes graduated from college, compared with 71% of those with the highest 10% of polygenic indexes. These results show both that polygenic indexes have some predictive power but also that polygenic indexes do not at all pin down individual outcomes: even when polygenic indexes are based on a GWAS of many more people and therefore have even greater predictive power than ours, there will always be many people whose polygenic indexes “predict” lower educational attainment who in fact attain relatively high amounts of education and vice-versa.

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As we discuss further in FAQ 3.4, an individual’s polygenic index for education (even a polygenic index based on ~1 million SNPs) is still not a very accurate prediction of that individual’s actual level of education attained. We emphasize that point using Figure 2c in the paper, reproduced here:

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In the figure on the left, each point is an individual of European genetic ancestries from the U.S. sample of younger adults mentioned above (the National Longitudinal Study of Adolescent to Adult Health). In the figure on the right, each point is an individual of European genetic ancestries from a U.S. sample of older adults (the Health and Retirement Study). In both figures, the x-axis is the individual’s polygenic index, and the y-axis is the individual’s actual number of years of formal schooling (after converting the level of education to an internationally standardized scale and adjusting for age and sex). The points are jittered slightly from their actual values in order to ensure that points do not lie directly on top of each other. While the figures show that there is a relationship between the polygenic index and the actual amount of an individual’s education, they also show that people with the same polygenic index value—points with the same x-axis value—vary a great deal in how much education they have. For instance, in both samples, among those with a polygenic index that is one standard deviation below average, individuals range in their actual educational attainment from about 7 years of formal education to about 22 years.

Despite the fact that polygenic indexes are not useful for predicting a particular individual’s educational attainment, they are useful for scientific studies (including social science, health research, etc.). Such studies are concerned with aggregate population trends and averages rather than with individual outcomes. In particular, because the polygenic index predicts about 13% of the variation across individuals, studies of its association with other variables can be well powered in sample sizes as small as 61 individuals (but not as small as 1 individual!).

Through this lens, the fact that the current study’s polygenic index for educational attainment predicts 13% of the variation across individuals in education attained is quite meaningful and rivals the predictive power of other variables commonly used in research—none of which, taken alone, predicts a large amount of variation in a socio-behavioral outcome. For example, in our prior work (Lee et al., 2018) we estimated that household income predicts ~7% of variation in educational attainment and mother’s education predicts ~15%. Thus, our index has approached the predictive power of important demographic variables and can be used in similar ways (e.g., to control for genetics as an additional confound when evaluating the effects of environmental differences or interventions). 

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​With a relatively high level of population-level predictive power, the polygenic index we constructed enables other research that is of value to social scientists and health researchers. Such studies are already being conducted with the (less powerful) polygenic indexes from our earlier GWASs of educational attainment (see FAQ 1.7). Our new results will enable many additional applications, such as studies that use the polygenic index in relatively small samples that contain rich health and socio-behavioral data that is expensive to collect (e.g., a randomized controlled trial that studies the effects of subsidizing higher education and uses the polygenic index as a control variable).

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A major caveat to all of this is that polygenic indexes developed from GWASs of particular genetic ancestry populations are known to be less predictive when applied to people of any other genetic ancestry (for reasons we discuss in FAQ 2.5). (As noted above in FAQ 2.1, we say genetic ancestries because we are not talking about who someone identifies as their ancestors but, rather, the similarity between someone’s genome and the genome of a “reference sample” for a population from prior genetic studies. And throughout these FAQs we refer to European and African genetic ancestries, plural, because there is tremendous genetic diversity within each continent, especially Africa.) For example, studying polygenic indexes for various health outcomes derived from GWAS participants of European genetic ancestries, Martin et al., (2017) and Duncan et al.(2019) found that, on average across the polygenic indexes, the predictive power for the outcomes was roughly 20-30% as large in samples of African genetic ancestries as it was in samples of European genetic ancestries.

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Our educational attainment polygenic index, like most other polygenic indexes, was developed with participants of European genetic ancestries (because currently most genotyped people are of European genetic ancestries, and very large numbers of people are needed to create meaningful polygenic indexes). We illustrate and quantify the attenuation in predictive power for individuals of African genetic ancestries, populations for which previous work has found that the attenuation is especially large. Specifically, we examined the predictive power of our educational attainment polygenic index in the samples of African genetic ancestries of our two prediction datasets, HRS and Add Health. The polygenic score explained 12.0% and 15.8% of the variance among the participants of European genetic ancestries in the HRS and in Add Health, respectively. By contrast, the polygenic index explained far less in the participants of African genetic ancestries: 1.3% and 2.3%, respectively. Thus, when applied to those of African genetic ancestries, the polygenic index has only 10-15% of the predictive power in has with those of European genetic ancestries. (In our previous GWAS of educational attainment, we also tested the predictive power of the polygenic index in a sample of HRS participants with African genetic ancestries (who may or may not have additional genetic ancestries). We similarly found that the earlier polygenic index had predictive power only 11% as large as the predictive power in the European genetic ancestries sample.) Thus, our results suggest that the drop-off in predictive power for the polygenic index for educational attainment is especially large, relative to polygenic indexes for other outcomes.

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Unfortunately, this attenuation of predictive power means that for most populations, many of the benefits of a polygenic index will be postponed until large GWAS studies are conducted using samples from these populations. Currently, most large, genotyped samples are of European genetic ancestries. We prioritize GWASs of samples of other genetic ancestries, but cannot implement this analysis until large enough samples of these populations have been genotyped and are made available to the research community.

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2.5       Why is the polygenic index less predictive in samples of African genetic ancestries than in samples of European genetic ancestries?

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As noted above in FAQ 2.4, we expect attenuated predictive power when applying a polygenic index developed with participants from any particular genetic ancestry populations to people of any other genetic ancestry, and we illustrated this attenuation in samples of participants of African genetic ancestries. We conducted additional analysis in order to shed some light on why the polygenic index is less predictive in participants of African genetic ancestries than in samples of European genetic ancestries. We study the main potential reasons, which fall into two categories.

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The first category is primarily about environmental factors. In this category, there are two main explanations of the reduced predictive power in samples of African genetic ancestries. First, genetic factors as a whole might simply matter relatively less for predicting educational attainment in samples of African genetic ancestries because environmental factors matter relatively more. In that case, the polygenic index—which captures some of these genetic factors—would similarly predict less well in the samples of African genetic ancestries. Second, there are gene-environment interactions (see FAQ 3.2). Since the samples of African genetic ancestries face different environments on average than do the samples of European genetic ancestries—for instance, racist expectations for classroom performance, poorer access to educational resources, and other average socio-economic circumstances that can affect the ability to succeed or remain in school—the associations between SNPs and educational attainment could be different in those of African genetic ancestries than in those of European genetic ancestries. If so, the SNP weights that produce a predictive polygenic index in populations of European genetic ancestries will turn out to be suboptimal weights for prediction in African-genetic-ancestry populations.

The second category can be thought of as purely genetic reasons. In this category, there are also two main explanations of the reduced predictive power in samples of African genetic ancestries (to use our example). First, purely by chance, particular alleles are more or less common in populations with different genetic ancestries. Much of the predictive power of the polygenic index comes from the (positive or negative) weights it puts on alleles that are relatively common in populations of European genetic ancestries. Because many of these alleles are not as common in populations of African genetic ancestries, the polygenic index will have less predictive power in those populations. Second, populations also differ from each other in their linkage disequilibrium (LD) patterns, i.e., their correlation structure across SNPs (see FAQs 2.2 & 3.5). A given SNP may be associated with educational attainment because the SNP is in LD (i.e., correlated) with a SNP elsewhere in the genome that causally affects education (see FAQ 1.6). If the strength of the correlation is greater in one genetic ancestry group than in another, then the size of the association will be larger in that genetic ancestry group. The fact that there are differences across genetic ancestry groups in the set of associated SNPs and their effect sizes means that the weights for constructing polygenic indexes in individuals of European genetic ancestries (FAQ 1.4) would be the “wrong” weights for individuals of other genetic ancestries.

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The first category of explanations is difficult for us to directly assess given the data we have, but in our paper, we directly evaluated the second category of explanations and used those results to indirectly assess the first category. Geneticists have conducted in-depth studies of the genetic differences across genetic ancestry groups in allele frequencies and LD. This makes it possible for us to assess how much the polygenic index’s predictive power would be expected to be reduced in samples of African genetic ancestries based on these factors alone. The paper that developed the methodology for this analysis applied it in the UK Biobank dataset and studied height, BMI, HDL and LDL cholesterol, triglycerides, asthma, type 2 diabetes, and hypertension (Wang et al., 2020). We also used the UK Biobank in order to enable us to compare educational attainment to these other phenotypes.

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We find that, based on the second category of explanations, we would expect the predictive power for educational attainment to be 35% as large in samples of African genetic ancestries than in samples of European genetic ancestries. This is much larger than the 10-15% we actually find in our U.S.-based samples (see FAQ 2.4). We conclude that the first category of explanations—the environmental factors—is therefore likely to be important. Moreover, the discrepancy between the actual predictive power in samples of African genetic ancestries and the predictive power expected based on the second category of explanations is larger for educational attainment than for the phenotypes studied by Wang et al. (2020), suggesting that the environmental factors are more important for educational attainment.

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For a number of reasons, this analysis of ours is only suggestive. One reason is that the UK Biobank sample of African genetic ancestries likely includes a higher fraction of immigrants to the UK than does the sample of European genetic ancestries, and individuals who completed some or all of their schooling outside the UK education system are less comparable. However, we believe our analysis points toward one direction for future work to understand why the polygenic index is less predictive in people of different genetic ancestries.

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2.6       What did you find in the analysis of disease risk?

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In addition to studying how accurately the polygenic index predicts educational attainment, we also examined how accurately it could predict some common diseases. Prior work, including our own, has found that the SNPs that predict educational attainment overlap with those that predict health outcomes, including Alzheimer’s disease, bipolar disorder, ADHD, schizophrenia, coronary artery disease, and longevity (Okbay, Beauchamp, et al., 2016; Pickrell et al., 2016; Riccardo E Marioni et al., 2016; Warrier et al., 2016; Anderson et al., 2017; Tillmann et al., 2017). However, the polygenic index for educational attainment has not been used as a predictor of such outcomes.

We studied ten common diseases, including asthma, arthritis, migraine, depression, and several related to heart disease (such as Type 2 diabetes and heart attack). We chose diseases that themselves have been the focus of large-scale GWASs. Thus, we could compare the predictive accuracy of our polygenic index for educational attainment with disease-specific polygenic indexes from those GWASs. For these analyses, we used a sample of roughly 440,000 individuals from the UK Biobank (the number of individuals with each disease varied depending on the disease).

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The main result from these analyses is that, on average across the diseases, predicting disease risk using both the polygenic index for educational attainment and the disease-specific polygenic index increases predictive accuracy by roughly 50%, relative to using only the disease-specific polygenic index. On average, a disease-specific polygenic index predicts roughly 1.2% of the variation across individuals, whereas a disease-specific polygenic index together with the polygenic index for educational attainment jointly predict roughly 1.8% of the variation. This finding points to the potential value of the polygenic index for educational attainment for medical and epidemiological research. However, we highlight that the actual amounts of predictive power are small, much smaller than the roughly 13% for predicting educational attainment itself (see FAQ 2.4). We also note that genes are estimated to have a stronger influence (relative to environmental influences) on many complex diseases than they do on educational attainment; the primary reason that the educational attainment polygenic index has much greater predictive power than these disease polygenic indexes is that the GWASs that created the disease polygenic indexes are to date much smaller than our educational attainment GWAS.

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2.7       What did you find in the family-based analyses?

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Our family-based analyses involve looking at how predictive the polygenic index for educational attainment is once we control for the educational attainment polygenic indexes of the individual’s parents. Doing this allows us to better understand some of the sources of the predictive power of the polygenic index. There are three categories of sources of predictive power, listed here along with conventional names for these sources used in the literature:

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• Direct genetic effects: Some SNPs (that are either included in the polygenic index or correlated with SNPs that are included) may have an effect on characteristics of an individual, such as cognitive skills and personality, that in turn may influence educational attainment. These effects may be mediated by environmental factors (e.g., a child who likes reading will be more likely to pursue that interest in school if the child lives in a society where reading is valued in school).

• Gene-environment correlation: The polygenic index is correlated with environmental factors that affect educational attainment. For example, a person’s polygenic index is correlated with the polygenic indexes of that person’s biological parents. Rearing parents’ polygenic indexes affect the environment in which the person grows up. For example, if the parents are more educated, they are likely to earn higher incomes and live in a neighborhood with well-funded schools (where local funding matters), which may provide educational advantages to their child. (Another source of gene-environment correlation is “population stratification,” in which certain genetic variants are more common in certain genetic ancestries, e.g., English versus Scottish. This can generate “population stratification bias” if having those genetic ancestries is also associated with cultural influences that affect educational attainment. However, population stratification bias should be largely reduced by the “quality control” procedures of our GWAS; see FAQ 2.2.)

• Assortative mating: Having a higher polygenic index is correlated with having other SNPs that are also associated with greater educational attainment. Assortative mating on educational attainment refers to the fact that, on average, there is a tendency for people to marry and have children with other people who have a similar amount of education (see FAQ 2.8). Consequently, people who inherit SNPs associated with higher educational attainment from one of their parents are also more likely than average to inherit SNPs associated with higher educational attainment from their other parent. Thus, the SNPs included in the polygenic index are correlated with SNPs not included in the polygenic index in such a way that magnifies the index’s predictive power.

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The key idea of the family-based analyses is to study the predictive power of the polygenic index controlling for the polygenic indexes of an individuals’ parents. This allows us to control the second and third sources of a polygenic index’s predictive power from the bullet list above and isolate the first, which are commonly referred to as the “direct genetic effects.” (This terminology is used to distinguish effects of SNPs on one’s own outcome—the “direct effects” of a SNP—from effects on someone else’s outcome, which are called “indirect effects.” An example of indirect effects is in the second bullet list above: parents’ SNPs affecting someone else’s—the child’s—educational attainment.) When controlling for the polygenic indexes of a person’s parents, the association between the person’s polygenic index and that person’s outcomes captures only direct genetic effects. We therefore call it the “direct effect” of the polygenic index.

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While we have noted that the predictive power of the polygenic index as a whole does not necessarily reflect causal effects (see FAQ 1.6)—and indeed, the second and third categories above generate predictive power that is correlational but not causal—the component of the polygenic index’s predictive power that is due to “direct effects” does reflect the causal effects of some SNPs. Because of that, when we identify how much of the predictive power is due to direct effects, we interpret it as telling us how much is due to causal effects. However, we cannot infer that it is the SNPs included in the polygenic index that have those causal effects; the “direct effects” might be due to correlation between measured non-causal SNPs and unmeasured causal SNPs.  

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Controlling for the polygenic indexes of a person’s parents requires having genetic information on the person’s parents. Such data is not available in most of the samples available to us, but we have it or can construct it in some of the samples. The Generation Scotland sample contains data on ~3,500 trios: individuals and both their parents. Two other samples—the UK Biobank and the Swedish Twin Registry (where we use only the fraternal twins)—contain large numbers of siblings, ~53,000 individuals in total. From the sibling data, we use a recently developed method (Young et al., 2020) to impute (i.e., statistically partially reconstruct) parental genetic data. These are the samples we use for our family-based analyses.

In our analyses, we compare the direct effect of the polygenic index (i.e., controlling for the polygenic indexes of an individual’s parents) with the “population effect,” which is the term we use for the association between the polygenic index and an outcome when we do not control for the polygenic indexes of an individual’s parents. In contrast to the direct effect of the polygenic index, which captures only the source of predictive power in the first bullet point above, the population effect captures all three sources of predictive power in the bullet list above. Our analyses estimate the ratio of the direct effect of a polygenic index to its population effect. This ratio tells us what fraction of a polygenic index’s association with some outcome is due to direct genetic effects.

When the educational attainment polygenic index is used to predict educational attainment itself, we estimate that this ratio is 0.556. That is, we estimate that 56% of the association between the polygenic index and educational attainment is due to direct genetic effects, and the remainder—44%—is due to the other sources of predictive power representing the second and third bullets above.

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Next, we sought to determine this ratio when using the educational attainment polygenic index to predict other outcomes, such as the diseases we analyzed in the paper, including Alzheimer’s disease, bipolar disorder, ADHD, schizophrenia, coronary artery disease, and longevity (see FAQ 2.6). However, we cannot study this same set of diseases in our family-based analyses because our trio and sibling samples either do not contain data on the diseases or (in the case of the UK Biobank siblings) do not contain a sufficient number of individuals that have one of the diseases. Instead, to estimate the fraction of the educational attainment polygenic index’s association with complex diseases that is due to direct genetic effects, we study a set of 22 health, cognitive, and socioeconomic outcomes. These include several biomarkers related to disease risk, such as BMI, blood pressure, and cholesterol. The set of outcomes also includes height, cognitive performance, smoking, alcohol use, income, and depression. For each of these 22 outcomes, we estimate both the direct effect and the population effect of the polygenic index for educational attainment.

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On average across the 22 outcomes, we estimate that the ratio of direct to population effects is 0.588. This is very similar to the ratio when the outcome is educational attainment, and the conclusion is correspondingly similar: we estimate that 59% of the association between the polygenic index and these other outcomes is due to direct genetic effects, and the remaining roughly 41% is due to the other sources of predictive power.

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In summary, our family-based analyses find that a substantial part of the predictive power of the polygenic index is due to direct effects, and a substantial part is not. This is true both when using the educational attainment polygenic index to predict educational attainment itself, and when using it to predict other outcomes.

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The finding that much of the predictive power is due to direct effects is important for at least three reasons. First, it shows that biases in the GWAS, such as unaccounted-for “population stratification bias” (see FAQs 1.4 & 2.2), are not entirely responsible for the predictive power that we find. This had been shown previously for predicting educational attainment but not for using the educational attainment polygenic index to predict other outcomes. 

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Second, the finding is a preliminary step toward unpacking the reasons why the genetic influences on educational attainment also matter for other outcomes. One possibility is that SNPs influence an outcome that in turn separately influences both education and health. For example, it could be that genetic influences on conscientiousness partially affect both how much education a person gets and also health-promoting behaviors that reduce disease risk. Another possibility is that SNPs influence educational attainment and there is something about formal schooling that, in turn, causes people to engage in more health-promoting behaviors. While our paper does not distinguish between these and other possibilities, our results are informative about the overall strength of the relationship between genetic influences on educational attainment and on certain other outcomes.

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Third, the finding that much of the polygenic index’s predictive power is not due to direct effects—either for educational attainment or for the disease-related biomarkers and outcomes we investigated—is also important. It reinforces the importance of interpreting genetic associations with caution. Our finding implies that a substantial part of the predictive power of the polygenic index is due to some mix of assortative mating and gene-environment correlation. For this and other reasons, we believe it is misleading to use phrases such as “innate ability” or “genetic endowments” to describe what is measured by polygenic indexes based on our GWAS estimates. These phrases incorrectly imply that the polygenic index is entirely capturing direct effects, and they further ignore the potentially important role that environmental factors play in mediating direct effects.  

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2.8       What did you find in the analysis of assortative mating?

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Assortative mating refers to the idea that people tend to have children with people who are similar to themselves in particular ways. Assortative mating is a research topic in the social sciences and also in the field of genomics. 

Much prior research has found that there is assortative mating on educational attainment: i.e., the available data reveals a tendency for people to have children with people who have similar educational attainment as themselves (e.g., Mare, 1991). For example, in the UK Biobank, we estimate that the correlation between the educational attainments of mates (i.e., biological mothers and fathers) is roughly 0.4. That is a moderately sized correlation. In recent decades in Western countries, educational attainment is one of the outcomes with the strongest assortative mating. In our analysis of assortative mating, we use height as an outcome to compare with educational attainment because it is another outcome for which assortative mating is relatively strong. In the UK Biobank, we estimate that the correlation between mates’ heights is roughly 0.3.

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In our paper, we study assortative mating using polygenic indexes, which has also been done in some prior research (e.g. Conley et al., 2016; Hugh-Jones et al., 2016; Robinson et al., 2017 and Yengo, Robinson, et al., 2018). In each of the datasets we use, we identify mate pairs based on the genetic data: we find pairs of individuals who share a child in common. We identify 894 mate pairs in the UK Biobank and 2,964 mate pairs in Generation Scotland. Averaging across these data sources, we find that the mate correlation in the polygenic index for educational attainment is roughly 0.17. We again compare with height, this time using a polygenic index for height constructed using the largest published height GWAS that was not based on the datasets we study (Wood et al., 2014). We find that the mate correlation in the polygenic index for height is roughly 0.10.

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What is new in our paper is that we use these correlations to test a model of assortative mating that is often assumed in the genetics literature, called the “phenotypic assortment model.” When applied to educational attainment, this model states that the mate-pair correlation in the polygenic index for educational attainment is entirely due to the mate-pair correlation in educational attainment. Given the predictive power of the polygenic index, which we estimated (see FAQ 2.4), this model makes a precise prediction about how the mate-pair correlation in an outcome should be related to the mate-pair correlation in the polygenic index for that outcome.

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For height, that prediction comes close to what we observe. That is, for height, it does appear that the mate-pair correlation in the polygenic index for height is entirely due to the people tending to marry others with similar height. However, for educational attainment, the prediction of the phenotypic assortment model is far off: the mate-pair correlation in the polygenic index for educational attainment is too high. Thus, for educational attainment, our results provide strong evidence against the phenotypic assortment model. Instead, our results imply that people are marrying other people who are similar to them based on some factor or factors other than educational attainment (perhaps in addition to educational attainment itself) but which is correlated with the polygenic index for educational attainment.

We conduct additional analyses to shed light on what these other factors might be. One possible factor is genetic ancestry, which in our data might reflect, for example, people being more likely to marry others from the same city or region of the UK. Another possible factor is cognitive performance. However, we find that assortative mating on both of these factors, added to the effect of assortative mating on educational attainment itself, are not together sufficient to fully account for the mate-pair correlation in the polygenic index for educational attainment. While our results raise the question of what else explains the high mate-pair correlation in the polygenic index, we cannot fully answer the question with the data we have.

In addition to helping us better understand assortative mating, our results also relate to a common theme across several of our analyses (see FAQs 2.4, 2.6 & 2.7): helping us better understand the sources of the polygenic index’s predictive power. Specifically, we draw two conclusions about the polygenic index’s predictive power from our analysis of assortative mating. First, there are factors besides educational attainment on which people assortatively mate that contribute to the mate-pair correlation in the polygenic index for educational attainment—and these factors in turn likely contribute to the predictive power of the polygenic index for a range of outcomes. Suppose one of these factors is the region where a person grew up. In order to be a factor that contributes to the mate-pair correlation, the region where a person grew up must be associated with the polygenic index. Moreover, the region where a person grew up is likely to be associated with many other things that relate to educational, socioeconomic, and health outcomes, such as quality of local schools, local economic opportunities, air quality, and so on. If the region where a person grew up is correlated with both the polygenic index for educational attainment and these various outcomes, then it is one component of the gene-environment correlation that helps explain the polygenic index’s predictive power (see FAQ 2.4). Thus, the results of our assortative mating analysis provide evidence that there is substantial gene-environment correlation that likely contributes to the polygenic index’s predictive power.

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Second, if people assortatively mate on factors that are correlated with the educational attainment polygenic index—as our results imply that they do—then this increases the variation of the polygenic index in the population and thereby magnifies its predictive power. To continue the example from above, imagine an extreme scenario of exact assortative mating on where a person grew up. That is, everyone has a mother and a father who are from the same region. In this scenario, there will be more people with very high and very low educational attainment polygenic indexes compared to a scenario where people marry at random across regions. That is because people from regions with high average polygenic indexes are marrying other people from the same region and having offspring that are relatively more likely to also have a high polygenic index. Similarly, people from regions with low polygenic indexes are marrying other people from their same region and having offspring that are relatively more likely to also have a low polygenic index. Thus, relative to the scenario of people marrying at random across regions, there is more variation of the polygenic index across people in the scenario with assortative mating. Consequently, variation in the polygenic index across people will be associated with (and hence “statistically predict”) more of the variation in educational attainment across people.

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2.9       What did you find in the analysis of the X chromosome?

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Like our most recent GWAS of educational attainment (Lee et al., 2018)—but unlike most GWASs—this study also examined genetic variants on the X chromosome. In addition to the 3,952 variants identified on the autosomes (the non-sex chromosomes), we identified 57 variants associated with educational attainment on the X chromosome.

The results of our analysis of the X chromosome in this study are fully consistent with the results from the previous GWAS of educational attainment (but our confidence in these results is even greater in the current study because of our larger sample size). For example, as in the previous study, we found fewer SNPs associated with educational attainment on the X chromosome than on other chromosomes of similar length. Also as in the previous study, in separate GWASs of men and women, we found that, in aggregate, SNPs on the X chromosome predict similar amounts of variation in educational attainment in men and in women. Some researchers had hypothesized that genetic influences on the X chromosome are an important source of differences in the variance in cognitive performance across men and women. While there were compelling scientific reasons to view such claims skeptically even prior to the publication of our earlier study, the results of both of our studies provide further evidence against the hypothesis.

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2.10     What did you do in the “dominance GWAS” of educational attainment? What did you find?

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In addition to our standard GWAS of educational attainment on the autosomes (i.e., the non-sex chromosomes) described in FAQ 1.3 above, we also conducted a “dominance GWAS” of educational attainment on the autosomes. As in a standard GWAS, in a dominance GWAS we test each SNP for its association with educational attainment. The only difference is that, unlike in a standard GWAS, in a dominance GWAS, we allow for the possibility that each SNP has a non-linear relationship with educational attainment. A linear relationship is one where an increase in one variable is associated with a correspondingly-sized increase or decrease in another variable. Specifically, suppose (as is typical) there are three possible combinations of alleles at a given SNP: let’s call them AA, AB, and BB. And let’s assume that the B allele is associated with greater educational attainment. A standard GWAS assumes the “additive model,” according to which the effect of going from zero to one B allele (i.e., AA to AB) is assumed to be equal to the effect of going from one to two B alleles (i.e., AB to BB). In contrast, a dominance GWAS separately estimates each of these two effects and thereby allows us to test whether or not they are equal. 

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(In this context, the term “dominance” originally comes from the idea of “dominant” and “recessive” alleles. In the classical usage, often called “complete dominance,” an organism has a trait—for example, a pea is smooth rather than wrinkled—if there are any B alleles. In that case, AB and BB would both yield the dominant trait of a smooth pea, and only AA would yield the recessive trait of a wrinkled pea. A dominance GWAS allows for this possibility: a large effect of going from AA to AB but no effect of going from AB to BB. It also allows for other, more common possibilities. For example, in “incomplete dominance,” the effect of going from AA to AB is larger than the effect of going from AB to BB, but both effects are non-zero. Another possibility is “overdominance,” where an organism with the AB combination of alleles has more of the trait than an organism with AA or BB.)

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To many researchers, it seems natural to expect that relationships between SNPs and outcomes like educational attainment would be non-linear—that is, that there might be less of an effect, or no effect at all, of going from one B allele to two B alleles. Indeed, there is a long tradition in behavior genetics research (much of which compares outcomes across identical and fraternal twins) of assuming that non-linear relationships between SNPs and socio-behavioral outcomes account for a non-trivial fraction of the variation in such outcomes across individuals (e.g. Jinks and Eaves, 1974).

Perhaps surprisingly, there is an equally long tradition in a field of research called quantitative genetics showing that, theoretically, for outcomes like educational attainment that are influenced by many SNPs, deviation from linear relationships are likely to be small and account only for a small fraction of the variation in outcomes across individuals (e.g. Hill, Goddard and Visscher, 2008). There are a variety of theoretical arguments, which stem from both biological and statistical considerations. Based on other kinds of studies that are not dominance GWAS, for many outcomes (but not educational attainment), there is also evidence that dominance deviations account for only a small fraction of the variation across individuals (e.g. Pazokitoroudi et al., 2020; Hivert et al., 2021).

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Thus, researchers are divided about whether the relationship between SNPs and socio-behavioral outcomes are likely to be largely linear or to have significant dominance effects. Partly because a dominance GWAS needed to answer that question is more complex than a standard GWAS, ours is one of the first large-scale dominance GWAS conducted for any outcome. We conducted our dominance GWAS in a sample of individuals from 23andMe and the UK Biobank. It was a slightly smaller sample than our standard GWAS, but still a very large sample: ~2.6 million individuals.

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Our results strongly support the view of those researchers who believe that with respect to educational attainment, deviations from linear relationships are likely to be small and account only for a small fraction of the variation in outcomes across individuals. We cannot identify any SNPs with such a non-linear relationship to educational attainment, despite our very large sample size. While some non-linear relationships between SNPs and educational attainment probably exist, our results indicate that such SNPs must be at least an order of magnitude smaller than the (already very small) linear effects of SNPs on educational attainment. 

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Even though we cannot identify any dominance effects of specific SNPs, we can use the aggregate results of our dominance GWAS to estimate how much of the variation in educational attainment is explained by the dominance effects that do exist among SNPs in our analysis. Our results suggest that, taken altogether, dominance effects of the SNPs included in our GWAS account for only roughly 0.02% (two hundredths of one percent) of the variation in educational attainment across individuals.

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We note two important qualifications about how our findings should be interpreted. First, our results leave open the possibility that there are rare SNPs that have large non-linear relationships with educational attainment. The data included in our GWAS, as in almost all GWASs, are common SNPs (see FAQ 2.1). These common SNPs capture most of the information about common ways in which people vary genetically (e.g., at least 1% of the population has a different genotype than the remainder of the population). However, these common SNPs do not capture information about rare SNPs (e.g., over 99% of the population has the same genotype, but a small percentage of people differ). Our results are therefore silent about whether these rare SNPs may have substantial non-linear relationships with educational attainment.

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Second, although the dominance effects of SNPs included in our GWAS account for only a tiny fraction of the variation across individuals, the combined effect of dominance across many SNPs on a particular individual can nonetheless be substantial. In particular, when two close relatives have offspring, the offspring will have an unusually large number of AA and BB SNPs and an unusually small number of AB SNPs (because the parents are more likely than unrelated individuals to both have the same allele, either A or B). While there is a lot of variation across SNPs and outcomes, on average, having the same two alleles at a SNP, i.e., having AA or BB rather than AB, is known to be harmful to an organism. When an individual’s recent genetic ancestors are closely genetically related, there can be a noticeably harmful effect on certain outcomes due to the unusually large number of AA and BB genetic variants. Using our dominance GWAS results, we estimate that the offspring of first cousins will have, on average, roughly 1 fewer month of formal schooling than the offspring of unrelated individuals.