Here, we briefly introduce the BADGERS model. The workflow of BADGERS is shown in Figure 1. A brief flowchart including all the analyses we contained in the manuscript was shown in the supplementary material (Figure 1—figure supplement 1). Complete statistical details are discussed in the Methods section. BADGERS is a two-stage method to test associations between traits. First, polygenic risk scores (PRS) are trained to impute complex traits using genetic data. Next, we test the association between a disease or trait of interest and various genetically-imputed traits. Given a PRS model, the imputed trait can be denoted asT^=XW

where XN×M is the genotype matrix for N individuals in a GWAS, and WM×1 is the Mx1 matrix denotes pre-calculated weight values on SNPs in the PRS model. Then, we test the association between measured trait Y and imputed trait T^ via a univariate linear model.Y=α+T^γ+δ

The test statistic for γ can be expressed as:Z=γ^se(γ^)≈WTΓZ∼

where Z~ is the vector of SNP-level association z-scores for trait Y, and Γ is a diagonal matrix with the j^th diagonal element being the ratio between the standard deviation of the j^th SNP and that of T^ .

This model can be further generalized to perform multivariate analysis. If K imputed traits are included in the analysis, we use a similar notation as in univariate analysis:T^∗=XW∗

Here, WM×K* is a matrix and each column of W* is the pre-calculated weight values on SNPs for each imputed trait. Then, the associations between Y and K imputed traits T^i(1≤i≤K) are tested via a multivariate linear model.Y=α∗+T^∗γ∗+δ∗

where γ*=(γ1,…,γK)T is the vector of regression coefficients. The z-score for γi(1≤i≤K) can be denoted as:Zi=γ^ise(γ^i)≈1UiiIiTU(W∗)TΘZ∼

where U is the inverse variance-covariance matrix of T^∗ ; Ii is the K×1 vector with the i^th element being 1 and all other elements equal to 0; is a M×M diagonal matrix with the i^th diagonal element being varXi ; and Z~ is defined the same as the univariate case as the vector of SNP-level association z-scores for trait Y.

We used real genotype data from the Genetic Epidemiology Research on Adult Health and Aging (GERA) to conduct simulation analyses (Methods). First, we evaluated the performance of our method on data simulated under the null hypothesis. We tested the associations between randomly simulated traits and 1738 PRS from the UK biobank and did not observe inflation in type-I error (Supplementary file 1). Similar results were also observed when we simulated traits that are heritable but not directly associated with any PRS. Since BADGERS only uses summary association statistics and externally estimated linkage disequilibrium (LD) as input, we also compared effect estimates in BADGERS with those of traditional regression analysis based on individual-level data. Regression coefficient estimates and association p-values from these two methods were highly consistent in both simulation settings (Figure 2A and Figure 2—figure supplements 1–3), showing minimal information loss in summary statistics compared to individual-level data indicating highly consistent performance compared to methods based on individual-level data. To evaluate the statistical power of BADGERS, we simulated traits by combining effects from randomly selected PRS and a polygenic background (Methods). We set the effect size of PRS to be 0.02, 0.015, 0.01, 0.008, and 0.005. BADGERS showed comparable statistical power to the regression analysis based on individual-level genotype and phenotype data (Figure 2B, Supplementary file 1). Overall, our results suggest that using summary association statistics and externally estimated LD as a proxy for individual-level genotype and phenotype data does not inflate type-I error rate or decrease power. The performance of BADGERS is comparable to regression analysis based on individual-level data. We also studied if more sophisticated polygenic risk prediction methods could potentially lead to higher statistical power in downstream association tests. We compared the performance of PRS based on marginal effect sizes with that of LDpred, a more sophisticated PRS model that jointly estimates SNP effects via a Bayesian framework (Vilhjálmsson et al., 2015). Imputation models based on multivariate analysis indeed improved the results. When using marginal PRS to impute traits, the correlation between γ^i and γi was 0.79. This correlation improved to 0.91 when using LDpred PRS (Figure 2—figure supplement 4). However, such improvement did not substantially affect the statistical power in association testing. Using marginal PRS, our analysis achieved a statistical power of 86% to identify associations at a type-I error rate of 0.05, and the power was 88% when using multivariate effect estimates to calculate PRS. These results suggest that while more sophisticated PRS methods can improve the results in BADGERS, simple PRS based on marginal effects also shows reasonably good performance.

We applied BADGERS to conduct a biobank-wide association scan (BWAS) for AD risk factors from 1738 heritable traits (p<0.05; Methods) in the UK biobank. We repeated the analysis on two independent GWAS datasets for AD and further combined the statistical evidence via meta-analysis (Figure 3—figure supplement 1). We used stage-I association statistics from the International Genomics of Alzheimer’s Project (IGAP; n=54,162) as the discovery phase, then replicated the findings using 7050 independent samples from the Alzheimer’s Disease Genetics Consortium (ADGC). We identified 50 significant trait-AD associations in the discovery phase after correcting for multiple testing, among which 14 had p<0.05 in the replication analysis. Despite the considerably smaller sample size in the replication phase, top traits identified in the discovery stage showed strong enrichment for p<0.05 in the replication analysis (enrichment = 2.5, p=2.2e-5; hypergeometric test). In the meta-analysis, a total of 48 traits reached Bonferroni-corrected statistical significance and showed consistent effect directions in the discovery and replication analyses (Figure 3 and Supplementary file 2).

Unsurprisingly, many identified associations were related to dementia and cognition. Family history of AD and dementia showed the most significant associations with AD (p=3.7e-77 and 5.2e-28 for illnesses of mother and father, respectively). Having any dementia diagnosis is also strongly and positively associated (p=8.5e-11). In addition, we observed consistent and negative associations between better performance in cognition test and AD risk. These traits include fluid intelligence score (p=2.4e-14), time to complete round in cognition test (p=2.8e-9), correct final attempt (p=9.1e-11), and many others. Consistently, education attainment showed strong associations with AD. Age completed full time education (p=2.5e-7) was associated with lower AD risk. Four out of seven traits based on a survey about education and qualifications were significantly associated with AD (Figure 3—figure supplement 2). Higher education such as having a university degree (p=4.4e-12), A levels/AS levels or equivalent (p=6.9e-9), and professional qualifications (p=7.1e-6) were associated with lower AD risk. In contrast, choosing ‘none of the above’ in this survey was associated with a higher risk (p=1.6e-11). Other notable strong associations include high cholesterol (p=2.5e-15; positive), lifestyle traits such as cheese intake (p=2.5e-10; negative), occupation traits such as job involving heavy physical work (p=2.7e-10; positive), anthropometric traits including height (p=5.3e-7; negative), and traits related to pulmonary function, e.g., forced expiratory volume in 1 s (FEV1; p=1.9e-6; negative). Detailed information on all associations is summarized in Supplementary file 2.

Of note, associations identified in the marginal analysis are not guaranteed to be independent. We observed clear correlational structures among the identified traits (Figure 4). For example, PRS of various intelligence and cognition-related traits are strongly correlated, and consumption of cholesterol-lowering medication is correlated with self-reported high cholesterol. To account for the correlations among traits and identify risk factors that are independently associated with AD, we performed multivariate conditional analysis using GWAS summary statistics (Methods). First, we applied hierarchical clustering to the 48 traits we identified in marginal association analysis and divided these traits into 15 representative clusters. The traits showing the most significant marginal association in each cluster were included in the multivariate analysis (Figure 4—figure supplement 1). Similar to the marginal analysis, we analyzed IGAP and ADGC data separately and combined the results using meta-analysis (Supplementary file 2). All 15 representative traits remained nominally significant (p<0.05) and showed consistent effect directions between marginal and conditional analyses (Supplementary file 1). However, several traits showed substantially reduced effect estimates and inflated p-values in multivariate analysis, including fluid intelligence score, mother still alive, unable to work because of sickness or disability, duration of moderate activity, and intake of cholesterol-lowering spread. Interestingly, major trait categories that showed the strongest marginal associations with AD (i.e. family history, high cholesterol, and education/cognition) were independent from each other. Paternal and maternal family history also showed independent associations with AD, consistent with the low correlation between their genetic risk scores (correlation = 0.052).

Furthermore, we evaluated the impact of APOE on identified associations. We removed the extended APOE region (chr19: 45,147,340–45,594,595; hg19) from summary statistics of the 48 traits showing significant marginal associations with AD and repeated the analysis. We observed a substantial drop in the significance level of many traits, especially family history of AD, dementia diagnosis, and high cholesterol (Figure 5, Figure 5—figure supplement 1, and Supplementary file 2). 38 out of 48 traits remained significant under stringent Bonferroni correction after APOE removal. Interestingly, the associations between AD and almost all cognition/intelligence traits were virtually unchanged, suggesting a limited role of APOE in these associations.

Next, we investigated the evidence for causality among identified associations. We performed Mendelian randomization (MR-IVW; Methods) in IGAP and ADGC datasets separately and meta-analyzed the results on the complete set of 1738 heritable traits from the UK biobank. A total of 48 traits reached Bonferroni-corrected statistical significance and showed consistent effect directions in the discovery and replication analyses using BADGERS. In contrast, MR-IVW only identified nine traits with Bonferroni-corrected statistical significance. Among these nine traits, seven were also identified by BADGERS (Supplementary file 1). The signs of all significant causal effects identified by MR-IVW were consistent with results from BADGERS. The most significant effect was family history (p=1.1e-233 and 1.7e-69 for maternal and paternal history, respectively). Dementia diagnosis (p=9.1e-7), high cholesterol (p=4.1e-6), A levels/AS levels education (p=1.7e-4), and time spent watching television (p=2.4e-4) were also among the top significant effects. Of note, the fluid intelligence score, one of the most significant associations identified by BADGERS, did not reach statistical significance in MR (p=0.06), which may be explained by its polygenic genetic architecture. It is also worth noting that if we scan all 1738 traits using BADGERS and then apply MR-IVW on the 48 Bonferroni-corrected significant traits, 23 could reach nominal significance (p<0.05) in MR, and seven could reach significance under Bonferroni correction (p<0.05/48; Supplementary file 1).

We also compared BADGERS with another more recent method GSMR (Zhu et al., 2018). Due to the smaller sample size in the ADGC dataset, we only applied GSMR to the IGAP summary statistics. In total, 18 traits reached statistical significance under Bonferroni correction (Supplementary file 1). However, these results showed only moderate consistency with MR-IVW and BADGERS. Among the 18 significant traits, only 1 trait, maternal family history of Alzheimer’s disease and dementia, overlapped with significant traits identified by MR-IVW. Six out of 18 traits overlapped with significant traits identified by BADGERS. Among the 18 significant traits, eight are related to body fat mass and two are related to educational attainment. The most significant effect was illnesses of mother (p=2.4e-294). College or University degree (p=4.84e-6), education; none of the above (p=3.6e-4), A levels/AS levels education (p=3.8e-6), and time spent watching television (p=4.0e-3) were also among top significant effects. Notably, GSMR failed to identify paternal family history or high cholesterol as risk factors for Alzheimer’s disease. If we only consider the 48 significant traits identified by BADGERS, 11 were nominally significant (p<0.05). However, 23 traits did not have enough significant SNPs to perform the GSMR analysis (at least 10 SNPs are required). The signs of all significant causal effects identified by GSMR were consistent between association effects in BADGERS.

Additionally, we included GSMR analysis results after removing APOE region from the 48 identified traits. Only maternal family history reached Bonferroni-corrected statistical significance, further demonstrating the lack of statistical power in MR when performing biobank-wide scans (Supplementary file 1).

To further investigate the mechanistic pathways for the identified risk factors, we applied BADGERS to a variety of AD subgroups, biomarkers, and neuropathologic features (Supplementary file 1). Overall, 29 significant associations were identified under a false discovery rate (FDR) cutoff of 0.05, and these endophenotypes showed distinct association patterns with AD risk factors (Figure 6; Figure 6—figure supplement 1). First, we tested the associations between the 48 AD-associated traits and five AD subgroups defined in the Executive Prominent Alzheimer’s Disease (EPAD) study, i.e., memory, language, visuospatial, none, and mix (Methods) (Mukherjee et al., 2018; Crane et al., 2017). Maternal family history of AD and dementia was strongly and consistently associated with all five EPAD subgroups (Supplementary file 2), with memory subgroup showing the strongest association (p=3.3e-16), which is consistent with the higher frequency of APOE ε4 in this subgroup (Mukherjee et al., 2018). Paternal family history was not strongly associated with any subgroups, but the effect directions were consistent. Interestingly, intelligence and cognition-related traits such as correct final attempt in cognitive test (p=2.7e-5) and fluid intelligence score (p=6.8e-5) were specifically associated with the ‘none’ subgroup – AD samples without relative impairment in any of the four cognitive domains. High cholesterol and related traits were associated with language, memory, and mix (i.e. AD samples with relative impairment in two or more domains) subgroups but showed weaker associations with the visuospatial and none subgroups.

Next, we extended our analysis to three biomarkers of AD in cerebrospinal fluid (CSF): amyloid beta (Aβ₄₂), tau, and phosphorylated tau (ptau₁₈₁) (Deming et al., 2017). Somewhat surprisingly, AD risk factors did not show strong associations with Aβ₄₂ and tau (Supplementary file 2). Maternal family history of AD and dementia was associated with ptau₁₈₁ (p=4.2e-4), but associations were absent for Aβ₄₂ and tau. It has been recently suggested that CSF biomarkers have a sex-specific genetic architecture (Deming et al., 2018). However, no association passed an FDR cutoff of 0.05 in our sex-stratified analyses (Supplementary file 2).

Furthermore, we applied BADGERS to a variety of neuropathologic features of AD and related dementias (Methods), including neuritic plaques (NPs), neurofibrillary tangles (NFTs), cerebral amyloid angiopathy (CAA), lewy body disease (LBD), hippocampal sclerosis (HS), and vascular brain injury (VBI) (Beecham et al., 2014). Family history of AD/dementia (p=3.8e-8, maternal; p=1.4e-5, paternal) and high cholesterol (p=2.1e-5) were strongly associated with NFT Braak stages (Supplementary file 2). NP also showed very similar association patterns with these traits (p=2.7e-19, maternal family history; p=2.6e-7, paternal family history; p=0.001, high cholesterol). The other neuropathologic features did not show strong associations. Of note, despite not being statistically significant, family history of AD/dementia was negatively associated with VBI, and multiple intelligence traits were positively associated with LBD, showing distinct patterns with other pathologies (Figure 6—figure supplement 2). We also note that various versions of the same pathologies all showed consistent associations in our analyses (Figure 6—figure supplement 2). The complete association results for all the endophenotypes and all the traits are summarized in Supplementary file 2. We further identified the influence of the APOE region in these results. The association results for all the endophenotypes with APOE Region being removed are summarized in Supplementary file 2.

Finally, we studied the associations between AD risk factors and pre-clinical cognitive phenotypes using 1198 samples from the Wisconsin Registry for Alzheimer’s Prevention (WRAP), a longitudinal study of initially dementia-free middle-aged adults (Johnson et al., 2018). Assessed phenotypes include mild cognitive impairment (MCI) status and three cognitive composite scores for executive function, delayed recall, and learning (Methods). A total of 12 significant associations reached an FDR cutoff of 0.05 (Supplementary file 2). Somewhat surprisingly, parental history and high cholesterol, the risk factors that showed the strongest associations with various AD endophenotypes, were not associated with MCI or cognitive composite scores in WRAP. Instead, education and intelligence-related traits strongly predicted pre-clinical cognition (Figure 7). A-levels education and no education both showed highly significant associations with delayed recall (p=4.0e-5 and 7.7e-7) and learning (p=7.6e-6 and 5.0e-8). No education was also associated with higher risk of MCI (p=2.5e-4). Additionally, fluid intelligence score was positively associated with the learning composite score (p=7.5e-4), and time to complete round in cognition test was negatively associated with the executive function (p=1.1e-5).

The goal of this method is to study the association between Y, a measured trait in the study, and T^ , a trait imputed from genetic data via a linear prediction model:T^=XW

Here, XN×M is the genotype matrix for N individuals in a study of trait Y. WM×1 is the pre-calculated weight values on SNPs in the imputation model. M denotes the number of SNPs. We use Y, a N×1 vector, to denote the trait values measured on the same group of individuals. We test the association between Y and T^ via a linear model.Y=α+T^γ+δ

where α is the intercept, δ is the term for random noise, and regression coefficient γ is the parameter of interest. The ordinary least squares (OLS) estimator for γ can be denoted as,γ^=cov(T^,Y)var(T^)=cov(XW,Y)var(T^)=1var(T^)WT(cov(X1,Y)⋮cov(XM,Y))

Here, Xj is the j^th column of X. Additionally, we derive the formula for the standard error of γ^ :se(γ^)=var(δ)N×var(T^)≈var(Y)N×var(T^)

The approximation in this formula is based on the assumption that trait Y has complex etiology and imputed trait T^ only explains a small proportion of its phenotypic variance. When an accurate estimate of var(δ) is difficult to obtain, this approximation approach provides conservative results and controls type-I error in the analysis.

In practice, individual-level genotype (i.e. X) and phenotype data (i.e. Y) may not be accessible due to policy and privacy concerns. Therefore, it is of practical interest to perform the aforementioned association analysis using summary association statistics. Standard genetic association analysis tests the association between trait Y and each SNP via the following linear model:Y=μj+Xjβj+εj(1≤j≤M)

The OLS estimator for βj and its standard error have the following forms.β^j=cov(Xj,Y)var(Xj)se(β^j)=var(εj)N×var(Xj)≈var(Y)N×var(Xj)

Again, the approximation is based on the empirical observation in complex trait genetics – each SNP explains little variability of Y (Manolio et al., 2009).

Next, we derive the test statistic (i.e. z-score) for γ:Z=γ^se(γ^)≈Nvar(Y)×var(T^)WT(cov(X1,Y)⋮cov(XM,Y))≈1var(T^)WT(var(X1)β1^se(β1^)⋮var(XM)βM^se(βM^))=WTΓZ∼

where Γ is a diagonal matrix with the j^th diagonal element beingΓjj=var(Xj)var(T^)

and Z∼ is the vector of SNP-level z-scores obtained from the GWAS of trait Y, i.e.,Z∼j=β^jse(β^j)

Without access to individual-level genotype data, var(Xj) and var(T^) need to be estimated using an external panel with a similar ancestry background. We use X~ to denote the genotype matrix from an external cohort, then var(Xj) can be approximated using the sample variance of X~j . Variance of T^ can be approximated as followsvar(T^)≈WTD∼W

where D~ is the variance-covariance matrix of all SNPs estimated using X~ . However, when the number of SNPs is large in the imputation model for trait T, calculation of D~ is computationally intractable. Instead, we use an equivalent but computationally more efficient approach. We first impute trait T in the external panel using the same imputation modelT∼=X∼W

Then, var(T^) can be approximated by sample variance var(T∼) .

Thus, we can test the association between Y and T^ without having access to individual-level genotype and phenotype data from the GWAS. The required input variables for BADGERS include a linear imputation model for trait T, SNP-level summary statistics from a GWAS of trait Y, and an external panel of genotype data. With these, the association test can be performed.

To adjust for potential confounding effects, it may be of interest to include multiple imputed traits in the same BADGERS model. We still use Y to denote the measured trait of interest. The goal is to perform a multiple regression analysis using K imputed traits (i.e. T^1 ,..., T^K) as predictor variables:Y=T^∗γ∗+δ∗

Here, we use T^∗=(T^1,…,T^K) to denote a N×K matrix for K imputed traits. Regression coefficients γ*=(γ1,…,γK)T are the parameters of interest. To simplify algebra, we also assume trait Y and all SNPs in the genotype matrix X are centered so there is no intercept term in the model, but the conclusions apply to the general setting. Similar to univariate analysis, traits T^1,…,T^K are imputed from genetic data via linear prediction models:T^∗=XW∗

where WM×K* are imputation weights assigned to SNPs. The i^th column of W denotes the imputation model for trait Ti . Then, the OLS estimator γ^∗ and its variance-covariance matrix can be denoted as follows:γ^∗=((T^∗)TT^∗)−1(T^∗)TYcov(γ^∗)≈var(Y)((T^∗)TT^∗)−1

The approximation is based on the assumption that imputed traits T^1,…,T^K collectively explain little variance in Y, which is reasonable in complex trait genetics if K is not too large. We further denote:U:=N((T^∗)TT^∗)−1=(var(T^1)⋯cov(T^1,T^K)⋮⋱⋮cov(T^K,T^1)⋯var(T^K))−1

All elements in matrix U can be approximated using a reference panel X~ (Dudbridge, 2013):cov(T^i,T^j)≈cov(T∼i,T∼j)

Therefore, the z-score for γk(1≤k≤K) isZk=γk^se(γk^)=IkTU(W∗)TXTYNUkkvar(Y)=1UkkIkTU(W∗)TΘZ∼

where Ik is the K×1 vector with the k^th element being 1 and all other elements equal to 0, is a M×M diagonal matrix with the i^th diagonal element being var(Xi) , and similar to the notation in univariate analysis, Z~ is the vector of SNP-level z-scores from the GWAS of trait Y. Given imputation models for K traits (i.e. W*), GWAS summary statistics for trait Y (i.e. Z~), and an external genetic dataset to estimate U and , multivariate association analysis can be performed without genotype and phenotype data from the GWAS.

Any linear prediction model can be used in the BADGERS framework. With access to individual-level genotype and phenotype data, the users can train their preferred statistical learning models, e.g., penalized regression or linear mixed model. When only GWAS summary statistics are available for risk factors (i.e. T), PRS can be used for imputation. We used PRS to impute complex traits in all analyses throughout the paper. Of note, more advanced PRS methods that explicitly model LD (Vilhjálmsson et al., 2015) and functional annotations (Hu et al., 2017) to improve prediction accuracy have been developed. However, additional independent datasets may be needed if there are tuning parameters in PRS. In general, higher imputation accuracy will improve statistical power in association testing (Hu et al., 2018). The BADGERS software allows users to choose their preferred imputation model.

We simulated quantitative traits using genotype data of 62,313 individuals from the GERA cohort (dbGap accession: phs000674). Summary association statistics were generated using PLINK (Purcell et al., 2007). We ran BADGERS on summary statistics based on the simulated traits and PRS of 1738 traits in the UK biobank. To compare BADGERS with the traditional approach that uses individual-level data as input, we also directly regressed simulated traits on the PRS of UK biobank traits to estimate association effects.

Summary statistics for 4357 UK biobank traits were generated by Dr. Benjamin Neale’s group and were downloaded from (http://www.nealelab.is/uk-biobank). AD summary statistics from the IGAP stage-I analysis were downloaded from the IGAP website (http://web.pasteur-lille.fr/en/recherche/u744/igap/igap_download.php). ADGC phase 2 summary statistics were generated by first analyzing individual datasets using logistic regression adjusting for age, sex, and the first three principal components in the program SNPTest v2 (Marchini et al., 2007). Meta-analysis of the individual dataset results was then performed using the inverse-variance weighted approach (Willer et al., 2010).

GWAS summary statistics for neuropathologic features of AD and related dementias were obtained from the ADGC. Details on these data have been previously reported (Beecham et al., 2014). We analyzed a total of 13 neuropathologic features, including four NP traits, two traits for NFT Braak stages, three traits for LBD, CAA, HS, and two VBI traits. Among different versions of the same pathology, we picked one dataset for each pathologic feature to show in our primary analyses. Six AD subgroups were defined in the recent EPAD paper (Mukherjee et al., 2018) on the basis of relative performance in memory, executive functioning, visuospatial functioning, and language at the time of Alzheimer’s diagnosis. Four subgroups include AD samples with an isolated substantial relative impairment in one of four domains; the ‘none’ subgroup includes samples without substantial relative impairment; the ‘mix’ subgroup includes samples with relative impairment in multiple domains. Each domain was compared with healthy controls in case-control association analyses. We did not include the executive functioning subgroup in our analysis due to its small sample size in cases. Detailed information about the design of CSF biomarker GWAS and the recent sex-stratified analysis has been described previously (Deming et al., 2017; Deming et al., 2018). Details on the association statistics for AD subgroups, CSF biomarkers, and neuropathological features are summarized in Supplementary file 2.

We applied LD score regression implemented in the LDSC software (Bulik-Sullivan et al., 2015) to estimate the heritability of each trait. Among 4357 traits, we selected 1738 with nominally significant heritability (p<0.05) to include in our analyses. We removed SNPs with association p-values greater than 0.01 from each of the 1738 summary statistics files, clumped the remaining SNPs using a LD cutoff of 0.1 and a radius of 1 Mb in PLINK (Purcell et al., 2007), and built PRS for each trait using the effect size estimates of remaining SNPs.

Throughout the paper, we used samples of European ancestry in the 1000 Genomes Project as a reference panel to estimate LD (Abecasis et al., 2012). In univariate analyses, we tested marginal associations between each PRS and AD using the IGAP stage-I dataset and replicated the findings using the ADGC summary statistics. Association results in two stages were combined using an inverse variance-weighted meta-analysis (Willer et al., 2010). A stringent Bonferroni-corrected significance threshold was used to identify AD-associated risk factors. For associations between identified risk factors and AD endophenotypes, we used an FDR cutoff of 0.05 to claim statistical significance. We applied hierarchical clustering to the covariance of 48 traits we identified from marginal association analysis, then divided the result into 15 clusters and selected one most significant trait from each cluster and used them to perform multivariate conditional analysis. We analyzed IGAP and ADGC datasets separately, and combined the results using meta-analysis.

We used MR-IVW approach (Burgess et al., 2013) implemented in the Mendelian Randomization R package (Yavorska and Burgess, 2017) to study the causal effects of 48 risk factors identified by BADGERS. For each trait, we selected instrumental SNP variables as the top 30 most significant SNPs after clumping all SNPs using a LD cutoff of 0.1.

WRAP is a longitudinal study of initially dementia-free middle-aged adults that allows for the enrollment of siblings and is enriched for a parental history of AD. Details of the study design and methods used have been previously described (Johnson et al., 2018; Sager et al., 2005). After quality control, a total of 1198 participants whose genetic ancestry was primarily of European descent were included in our analysis. On average, participants were 53.7 years of age (SD = 6.6) at baseline and had a bachelor’s degree, and 69.8% (n=836) were female. Participants had two to six longitudinal study visits, with an average of 4.3 visits, leading to a total of 5184 observations available for analysis.

DNA samples were genotyped using the Illumina Multi-Ethnic Genotyping Array at the University of Wisconsin Biotechnology Center. Thirty-six blinded duplicate samples were used to calculate a concordance rate of 99.99%, and discordant genotypes were set to missing. Imputation was performed with the Michigan Imputation Server v1.0.3 (Das et al., 2016), using the Haplotype Reference Consortium (HRC) v. r1.1 2016 (McCarthy et al., 2016) as the reference panel and Eagle2 v2.3 (Loh et al., 2016) for phasing. Variants with a quality score R² <0.80, MAF <0.001, or that were out of HWE were excluded, leading to 10,499,994 imputed and genotyped variants for analyses. Data cleaning and file preparation were completed using PLINK v1.9 (Chang et al., 2015) and VCFtools v0.1.14 (Danecek et al., 2011). Coordinates are based on the hg19 genome build. Due to the sibling relationships present in the WRAP cohort, genetic ancestry was assessed and confirmed using Principal Components Analysis in Related Samples (PC-AiR), a method that makes robust inferences about population structure in the presence of relatedness (Conomos et al., 2015).

Composite scores were calculated for executive function, delayed recall, and learning based on a previous analysis (Clark et al., 2016). Each composite score was calculated from three neuropsychological tests, which were each converted to z-scores using baseline means and standard deviations. These z-scores were then averaged to derive executive function and delayed recall composite scores at each visit for each individual. Cognitive impairment status was determined based on a consensus review by a panel of dementia experts. Resulting cognitive statuses included cognitively normal, early MCI, clinical MCI, impairment that was not MCI, or dementia, as previously defined (Koscik et al., 2016). Participants were considered cognitively impaired if their worst consensus conference diagnosis was early MCI, clinical MCI, or dementia (n=387). Participants were considered cognitively stable if their consensus conference diagnosis was cognitively normal across all visits (n=803).

The 48 PRSs were developed within the WRAP cohort using PLINK v1.9 (Chang et al., 2015) and tested for associations with the three composite scores (i.e. executive function, delayed recall, and learning) and cognitive impairment statuses. MCI status was tested using logistic regression models in R, while all other associations, which utilized multiple study visits, were tested using linear mixed regression models implemented in the lme4 package in R (Bates et al., 2015). All models included fixed effects for age and sex, and cognitive composite scores additionally included a fixed effect for practice effect (using visit number). Mixed models included random intercepts for within-subject correlations due to repeated measures and within-family correlations due to the enrollment of siblings.

The BADGERS software is freely available at https://github.com/qlu-lab/BADGERS, copy archived at qlu-lab, 2024.