We develop a Bayesian model (BayesRR-RC) that provides robust SNP-heritability estimation, an alternative to marker discovery, and accurate genomic prediction, taking 22 seconds per iteration to estimate 8.4 million SNP-effects and 78 SNP-heritability parameters in the UK Biobank. We find that only ≤10% of the genetic variation captured for height, body mass index, cardiovascular disease, and type 2 diabetes is attributable to proximal regulatory regions within 10kb upstream of genes, while 12-25% is attributed to coding regions, 32–44% to introns, and 22-28% to distal 10-500kb upstream regions. Up to 24% of all cis and coding regions of each chromosome are associated with each trait, with over 3,100 independent exonic and intronic regions and over 5,400 independent regulatory regions having ≥95% probability of contributing ≥0.001% to the genetic variance of these four traits. Our open-source software (GMRM) provides a scalable alternative to current approaches for biobank data. Improving inference in large-scale genetic data linked to electronic medical record data requires the development of novel computationally efficient regression methods. Here, the authors develop a Bayesian approach for association analyses to improve SNP-heritability estimation, discovery, fine-mapping and genomic prediction. As whole-genomes are collected for hundreds of thousands of individuals, we require regression methods that are not only computationally efficient, but which also provide improved inference. Rather than relying on subsets of the SNPs, methods should fully utilise the data, exploiting computational power to facilitate discovery of additional genomic regions, to improve understanding of the genomic architecture of common disease, and to provide more informative genomic prediction.4 highlight the importance of accounting for minor allele frequency (MAF) and LD structure of the genomic data. Generally, assessment of the relative contribution of different genomic regions is currently made assuming that markers within a category all contribute to the variance, with enrichment defined as the estimated share of the variance explained divided by its expected share6. However ideally, the estimated distribution of marker effects for each category would be directly obtained, accounting for MAF and LD structure and allowing for some of the marker effects to be zero, as this would yield a better understanding of the polygenicity of genomic effects across different genomic annotation groups.For example, when estimating the proportion of phenotypic variance attributable to different categories of genetic markers  is then typically conducted on the summary statistics generated. The advantage of a multi-step approach is that large sample size can be easily obtained through meta-analyses, combining summary statistics from different studies and avoiding the need for individual-level data sharing. However, as large-scale biobank data is increasingly available, methods that provide joint estimates of the marker effects in a single step by estimating the effect sizes as random under flexible prior formulations may become beneficial as they: (i) can account for differences in the variance contributed across MAF, LD or annotation groups providing unbiased MAF-LD annotation-specific genetic effect size estimates and gene architecture of complex traits and the uncertainty over the estimates; and (iii) provide improved genomic prediction, whilst providing a posterior predictive distribution for each individual.Furthermore, statistical inference usually follows a multi-step approach. Current mixed-linear association models such as those implemented in the software fastGWAHere, we outline the fastest Bayesian penalised regression model to date, with a hybrid-parallel algorithm for analysing large-scale genomic biobank using a single command-line tool implemented in our grouped mixture regressions model (GMRM) software. We validate our approach in large-scale simulation study and provide an empirical example using four traits measured in both the UK Biobank and Estonian Biobank data.13. Like these former methods, we consider a spike probability at zero (Dirac delta function), and a scale mixture of Gaussian distributions as a slab probability density. Unlike these models, we have genetic markers grouped into MAF-LD-annotation specific sets, with independent hyper-parameters for the phenotypic variance attributable to each group, so that the mixture proportions, the variance explained by the SNP markers, and the mixture constants are all unique and independent across SNP marker groups. This enables estimation of the phenotypic variance attributable to the group-specific effects, and differences in the underlying distribution of the βφ effects among MAF-LD-annotation groups, with different degrees of sparsity. Assuming N individuals and p genetic markers, our model of an observed phenotype vector y is:1μ and a single error term, a vector (N × 1) of residuals ϵ, with N by p matrix of single nucleotide polymorphism (SNP) genetic markers, centred and scaled to unit variance, which we denote as Xφ. The effects are allocated into groups . Each group has a set of model parameters βφ as a pφ × 1 vector of partial regression coefficients, where jth covariate within the φth group. The spike and slab prior, contains what is called a Dirac spike15 for βφ, which induces sparsity in the model through a Dirac-delta at zero, excluding variables from the model by setting their coefficients to zero. A finite scale mixture of normal distributions centred at zero constitute the slab component. The slab shrinks the non-zero coefficients towards zero according to the slab’s width, and by having a scale mixture of Gaussians, the distribution has heavier tails and can accommodate big and small effects16. Therefore, each φ, which, like all the other parameters, is estimated directly from the data. Here, we use 78 MAF-LD-annotation SNP marker groups. SNPs are partitioned into seven location annotations preferentially to coding (exonic) regions first, then to intronic regions, then to 1 kb upstream regions, then to 1–10 kb regions, then to 10–500 kb regions, then to 500–1 Mb regions. Remaining SNPs were grouped in a category labelled “others" and also included in the model so that variance is partitioned relative to these also. Thus, we assigned SNPs to their closest upstream region, for example if a SNP is 1 kb upstream of gene X, but also 10–500 kb upstream of gene Y and 5 kb downstream for gene Z, then it was assigned to be a 1 kb region SNP. This ensures that SNPs 10–500 kb and 500 kb–1 Mb upstream are distal from any known gene. We further partition upstream regions to experimentally validated promoters, transcription factor binding sites (tfbs) and enhancers (enh) using the HACER, snp2tfbs databases (see “Code availability” section). All SNP markers assigned to 1 kb regions map to promoters; 1–10 kb SNPs, 10–500 kb SNPs, 500 kb–1 Mb SNPs are then split into enh, tfbs and others (unmapped SNPs) extending the model to 13 annotation groups  is conducted as a series of look-up tables. We provide publicly available open source software (GMRM) that requires as little as 22 s per MCMC sample to estimate 78 group-specific One of the major limitations preventing the application of Bayesian approaches to large-scale genomic data is the view that the computation of a posterior distribution is too expensive. In Supplementary Note entclass1pt{minimaR2 < 0.1) causal SNP markers. For each SNP marker set, we then simulated effect sizes from a normal distribution with zero mean and variance of 0.1, 0.3 or 0.6 divided by the number of causal variants and ∝N]−0.25), with p the allele frequency (see “Methods” section). This simulates stronger effect sizes for rare variants in line with recent empirical estimates and we simulated ten replicate phenotypes for each of the nine different genetic architectures. We then additionally repeat each simulation, sampling the SNP marker effects this time from 13 different distributions, one for each of 13 different genomic annotation groups with different proportions of 17 with the same 78 MAF-LD-annotation groups enabling a direct comparison, (ii) a Haseman–Elston (HE) regression using the same 78 group model implemented in the software RHEmc18, (iii) summary statistic linkage disequilibrium score regression (LDSC)19, with LD scores calculated using the same data, and the same 78 non-overlapping annotations in a 78 component LDSC annotation model, and (iv) summary statistic SumHer6 (LDAK) with the same 78 non-overlapping annotations.We first compare the model performance of BayesRR-RC to existing approaches across 18 different genetic architectures. We randomly selected 40,000 unrelated UK Biobank individuals and used 596,741 imputed SNP markers from chromosomes 19 to 22. We randomly selected either 1000, 10,000 or 100,000 LD independent  that contain causal variants, and compare this to using LD to clump mixed-linear model association estimates obtained using the BoltLMM software  effect sizes estimated by BayesRR-RC, (ii) fixed-effect SNP effect sizes estimated in the MLMA approach implemented in bolt, and (iii) effect size estimates obtained from four different genomic prediction models proposed in a recent paper4. We explore the performance of our model in theory, with highly correlated genetic markers in Supplementary Note We then conduct a number of follow-up simulation studies. Recent work has highlighted differences in statistical model performance depending upon the relationship of SNP marker effect size, LD and MAFmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimmentclass2pt{minimWe confirmed our genomic prediction results, finding that BayesRR-RC outperforms all methods implemented in the LDAK software across all generative models, with BayesRR-RC very marginally outperforming a single variance component BayesR model in the enrichment simulations of each of the 20 generative genetic models  of selecting credible sets of markers with high probability of association, finding that BayesRR-RC has higher power to localise associations to sets of SNP markers , type-2 diabetes (T2D), body mass index (BMI) and height measured for 382,466 unrelated individuals from the UK Biobank data genotyped at 8,433,421 imputed SNP markers. These markers were selected as they overlap with the Estonian Genome Centre data (see “Methods” section) and have minor allele frequency >0.0002. We adjust each phenotype for age, sex, year of birth, genotype batch effects, UK Biobank assessment centre, and the leading 20 principal components of the SNP data. We conducted a series of convergence diagnostic analyses of the posterior distributions to ensure we obtained estimates from a converged set of four Gibbs chains, each run for 6000 iterations with a thin of five for each trait  for height, 0.02  for BMI, 0.103  for CAD, and 0.064  for T2D. Similarly, we find small positive correlations between introns and cis regions . This highlights that selecting on the top SNP markers identified by standard association studies would give a different set of variants than those obtained from selecting high PIP SNPs.Finally, our approach provides automatic fine-mapping of SNP loci, and of these region-level and gene-level associations, 360 SNPs for height, 20 for BMI, 2 for CAD and 9 for T2D could be mapped to a single SNP with greater than 95% inclusion probability across all four chains , has a prior that is flexible enough to show robust model performance across the data analysed here, improving inference in many settings over commonly applied approaches. We develop a range of computational and statistical approaches which allow this, or any similar Gibbs sampling algorithm, to scale to whole genome sequence data on many hundreds of thousands of individuals. This has enabled us to compare and contrast the inferred underlying genetic distribution for four complex phenotypes under this prior, providing novel insight into the genetic architecture of these traits. We observe that all phenotypes simply appear to be predominantly underlain by very many common variants, with SNPs within distal regulatory regions, coding and intronic regions each contributing more to the phenotypic variance and having higher allele substitution effects.4 and here we validate that one approach could be to split SNP markers by LD to improve genetic effect size estimates. Our results suggest that the proportion of genomic variation attributable to mutations in regulatory regions and mutations in the closest genic regions are largely independent. Additionally our model tests association within groups in a probabilistic way and we find 290 independent coding, 2888 independent intronic, and 5406 independent cis regions with ≥95% probability of contributing at least 0.001% of the SNP heritability. Understand how these coding, intronic and proximal and distal regulatory regions combine to contribute to phenotypic variance remains a substantial challenge and our results suggest a predominant role for introns and for distal, and thus likely more global enhancers, rather than locally dominant proximal expression QTL. The recent “omnigenic” model24, suggests that trait-associated variants in regulatory regions influence a local gene which is not directly causal to the disease, and also co-regulate other disease causal genes (or “core” gene). Our findings of little correlation of exonic and proximal regulatory variance and a large number of trait-associated intronic and cis regions do not rule this out, but suggest a more complex infinitesimal picture with differences occurring among traits, potentially due to their evolutionary history.There has been debate on how to best estimate SNP heritabilityThere are important caveats and limitations to consider. Here, we present an approach for analysing large-scale biobank data, which is becoming increasingly available, However, a substantial number of GWAS have already been conducted, with associated published genome-wide summary association statistic estimates. Many methods have been developed to take advantage of these estimates, with downstream analysis models making use of various summary statistics resources in efficient and flexible ways. We show here that two leading summary statistic approaches perform poorly as compared to individual-level models for estimation of enrichment and genomic prediction. Despite this, the sample sizes obtained in consortia study meta-analyses will exceed those from single biobanks, especially for disease, and thus the genomic prediction accuracy of consortia study meta-analysis summary statistic prediction models may exceed those from individual-level analyses. Combining the posterior distribution obtained from BayesRR-RC across different individual-level biobank studies would alleviate this issue.Additionally, in this work we do not extend past a limited number of functional annotations and thus we do not provide a model capable of further partitioning the variation into specific regulatory functions  or directly modelling the relationships among components. LDSC functional methods take the approach that SNPs can be assigned to different categories , with the categories competing against each other to explain the signal, with the downside that enrichment is relative and that the total variance is not partitioned. Here, the total variance is partitioned but this is based on preferential allocation of SNPs to coding regions, then introns, and then to their nearest upstream gene position. These SNPs are most likely to be allocated accurately, with 1 and 1–10 kb groups being more ambiguous in high gene density regions and likely mislabelled. However, if this was the case then variance would still be partitioned to these mislabelled groups and it would just be evenly split across them, with experimentally validated promotor, enhancer and tfbs regions assisting to some degree in alleviating this. Rather, here we see a clear pattern of increasing variance contributed, increasing average effect size, and an increasing pattern of higher rare allele substitution effects by individual markers as distance from the nearest gene increases. 10–500 kb distal regions may contribute more variance as marker density and marker coverage is higher in these regions, with missing variation within 10 kb upstream as causal variants are poorly correlated with SNPs. The posterior distributions for the variance explained by 1 kb, 1–10 kb regions, and 10–500 kb regions are negatively correlated , each of which having it’s own set of model parameters We extend the BayesR model to a BayesRR-RC model as follows25 and BayesRS26), which have used additional mixtures for different SNP groups, but kept a single global variance component. Importantly, a single variance component with more mixtures serves only to change the amount of mass allocated at different sizes of the distribution, but does not alter the sizes of the effects themselves as there is still a single distribution. In contrast, the formulation presented here of having an independent variance parameter Thus the mixture proportions, variance explained by the SNP markers, and mixture constants are all unique and independent across SNP marker groups. This extends previous models . If we take the whole genotype matrix, the pattern would be closer to a block diagonal matrix of correlations, in refs. 27 it is showed that the former case requires weaker conditions in order to recover the true vector β consistently than the latter. Although the sampling scheme was different, we have shown that a similar model with only two groups: genetic markers and epigenetic markers, is successful in identifying BMI and smoking epigenetic signatures13. The baseline model derivations for this model are outlined in Supplementary Note In our model the conditional posterior is:mentclass2pt{minimR2 < 0.1) causal SNP markers. For each SNP marker set there were two settings.We first compare the model performance of BayesRR-RC to existing approaches across 18 different genetic architectures. We randomly selected 40,000 unrelated UK Biobank individuals and used 596,741 imputed SNP markers from chromosomes 19 to 22. We randomly selected either 1000, 10,000, or 100,000 LD independent ]−0.25), with p the allele frequency. We sampled individual-level environmental  variance from a normal distribution with zero mean and variance equal to 1 minus either 0.1, 0.3, or 0.6 to give phenotypes with zero mean and unit variance. This gave N]−0.25) to give In the first setting, we simulated effect sizes from a normal distribution with zero mean and variance of 0.1, 0.3, or 0.6 divided by the number of causal variants ∝ Thus, in the first setting we simulate variance explained by annotation groups that is on average proportional to the number of SNPs within each annotation . In the second setting, the variance and average effect size differ across annotation groups. We refer to these as two different enrichment settings: “random”, or “enriched”.A restricted maximum likelihood model implemented in the software GCTA with a single relationship matrix providing an estimate of the variance attributable to SNPs genome-wide.17. Here, we used a 78 MAF-LD-annotation group model using the non-overlapping genomic annotation groups described below in the UK Biobank analysis providing an estimate of the variance attributable to SNPs genome-wide and an estimate of the variance attributable to SNP markers of each annotation group.A restricted maximum likelihood model implemented in the software BoltREML18, providing an estimate of the variance attributable to SNPs genome-wide and an estimate of the variance attributable to SNP markers of each annotation group.A Haseman-Elston regression using the same 78 group model implemented in the software RHEmc8, Regenie9, and GCTA to fit these models. These approaches provided estimates of the SNP regression coefficients (marker effect sizes).Mixed linear association model (MLMA), which is a two-stage approach where the variance attributable to the SNP markers genome-wide is estimated and this estimate is then used in a second generalised least squares step to test for SNP-phenotype associations one marker at a time. There are two forms of this model. In the first, the SNP is fitted twice as it is included in both the fixed and random terms (MLMAi). In the second, the SNP to be tested as fixed is removed from the random term alongside those on the same chromosome (MLMA). We used the software BoltLMM28, whilst fitting 20 principal components of the marker data as covariates.Single marker marginal least squares regression using plink219), with LD scores calculated using the same data, and the same 78 non-overlapping annotations in a 78 component LDSC annotation model. We included SNPs with MAF > 1% following the software instructions. This model is intended to approximate an individual-level REML analysis with 78 annotations and provides an estimate of the variance attributable to SNPs genome-wide and an estimate of the variance attributable to SNP markers of each annotation group.Linkage disequilibrium score regression ]0) with w the LD score of the marker and p the allele frequency.We simulated effect sizes from a normal distribution with zero mean and variance 0.6 divided by the number of markers  with no relationship to the LD or MAF of the markers. Thus, effects had variance ∝ N]−0.25). This simulates stronger effect sizes for rare variants and those in low LD.We simulated effect sizes from a normal distribution with zero mean and variance 0.6 divided by the number of markers  ∝ N]−0.25). This simulates stronger effect sizes for rare variants and those in high LD.We simulated effect sizes from a normal distribution with zero mean and variance 0.6 divided by the number of markers  ∝ N]0.75). This simulates equivalent effect sizes for common and rare variants, and greater effects for markers in low LD.We simulated effect sizes from a normal distribution with zero mean and variance 0.6 divided by the number of markers  ∝ N]0.75). This simulates equivalent effect sizes for common and rare variants, and greater effects for markers in high LD.We simulated effect sizes from a normal distribution with zero mean and variance 0.6 divided by the number of markers  ∝ Having created four different ways of selecting associated markers  we then created five different ways of assigning effect sizes to them: For each of the four different sets of markers, each with five different effect size sampling schemes, we then created two additional settings. In the first setting markers were sampled from the various normal distribution, as described above, for the five different effect size sampling schemes. In the second setting, for each of the five different effect size sampling schemes we simulated effects from 13 different distributions, one for each of 13 different genomic annotation groups with different proportions of total SNP heritability , each with five different marker effect size sampling schemes, which we refer to in the main text as the 20 different generative genetic models  variance from a normal distribution with zero mean and variance 0.4 to give phenotypes with zero mean and unit variance.We then conducted another large-scale, but this time well-powered simulation study, where we ascertained the causal variant SNP markers in different ways and varied the relationship between effect size, minor allele frequency and LD. We used the same randomly selected 40,000 unrelated individuals and all 596,741 imputed (version 3) genetic markers from chromosomes 19 through 22 from the UK Biobank. We simulated a wide-range of different possible underlying genetic effect size distributions as follows:This range covers generative genetic models discussed in the literature and provides models that both fit and violate the assumptions of the range of variance component statistical models. This includes both individual-level and summary statistic approaches, that are currently applied in the literature for estimation of the variance attributable to the SNP markers, for testing association of genetic markers with phenotypes genome-wide, and for genomic prediction.This simulation provides a range of different scenarios for which we can explore the model performance of BayesRR-RC and compare it to existing approaches. In Supplementary Fig. We then extend our model comparisons in a number of ways. While direct comparisons of frequentist and Bayesian approaches are difficult and often ill advised, we wished to show that BayesRR-RC provides accurate effect size estimation in the presence of LD. We provide three simple comparable metrics to assess model performance of BayesRR-RC against frequentist mixed linear association models (MLMA) applied as two-stage approaches, where either the SNP is fitted twice as it is included in both the fixed and random terms (MLMAi implemented in GCTA), or the SNP to be tested as fixed is removed from the random term alongside those on the same chromosome (MLMA implemented in BoltLMM and Regenie).z-scores of the marker effect estimates from their true simulated value. As MLMA approaches estimate marker effects one-at-a-time, we calculated the z-score of the estimate from the true simulated value for the causal variants in each simulation replicate, across generative genetic models. For the Bayesian methods, at any one iteration, LD among the markers is controlled for (see Supplementary Note R2 ≥ 0.1 within 1 MB) of each simulation replicate, took the posterior mean across iterations, and then calculated the z-score of the estimate from the simulated value. This metric provides an assessment of the ability of BayesRR-RC to accurately estimate the contribution of a genomic region to the phenotypic variance as compared to MLMA approaches. We present these results in Supplementary Fig. z-scores of the estimated BayesRR-RC effects are generally stable across generative genetic models and comparable to those obtained from BayesR but with slightly elevated variance in many cases as the model is less sparse  across the genome. True associations were defined as selected SNPs that were in LD with a simulated causal variant (LD R2 ≥ 0.01). False associations were defined as selected SNPs that were not in LD (LD R2 ≤ 0.01) with a simulated causal variant. Precision and recall were calculated across thresholds of the chi-squared statistics of the selected markers, and the area under the curve was calculated using the trapezoid rule for calculating the integrals, assuming the curve is linear between the points. FDR is then calculated as the proportion of markers with p-value ≤ 5 × 10−8 that were not in LD with a causal variant (LD R2 ≥ 0.01). This provides a way to directly compare model performance for the discovery of associated genomic regions across Bayesian and frequentist approaches and tests our hypothesis that a PPWV approach controls FDR well in comparison with Bonferroni p-value correction  fitted as random when testing for the effects of a focal SNP. For two markers, FST among the two populations at each SNP. Second, we selected the same high-LD SNPs as the causal variants, but simulated effect sizes to have correlation 0.5 with the allele frequency differences of the SNPs among the two populations, and thus not only is the effect size proportional to the FST, but there is also directional differentiation . For each of these two scenarios, we simulated 50 replicate phenotypes where the phenotypic variance attributable to the causal SNPs is 0.5, there is a phenotypic difference in which Croydon individuals have a phenotype that is 0.5 SD higher than Glasgow individuals (contributing variance 0.05), and residual variance was simulated from a normal with variance 0.45, to give a phenotype with mean of zero and variance of 1. The data were then analysed using a mixed-linear model association (MLMAi implemented in GCTA) and a grouped Bayesian dirac spike and slab models (BayesR implemented in GMRM). In the analysis, we either adjusted the phenotype by the first 20 PCs of the genetic data used in the simulation study, or we did not adjust the phenotype for the PCs, to examine the effects of this common methods of population stratification control. In a two-population scenario the leading eigenvector encapsulates the allele frequency differentiation between the populations and thus the expectation is that this should adjust for these differences when estimating the marker associations. The results are presented in Fig. FST and underestimates the variance when there is a directional associations, with this underestimation being less severe with PC adjustment.We conducted a simulation study using real genomic data from chromosome 22 where 10,000 individuals were selected from two UK Biobank assessment centres (Glasgow and Croydon). First, causal variants were allocated to 5000 high-LD SNPs with effect sizes simulated from a normal distribution with variance proportional to the Finally, we also assess the influence of relatedness on the estimates obtained from a BayesR model using real genomic data from chromosome 21 and 22  and 10,000 families randomly selected from the UK Biobank . Here, we selected 2000 LD blocks with a single causal SNP per block at random, where an LD block is defined as a group of SNP markers with absolute LD of at least 0.01. We assigned effect sizes to these 2000 selected SNPs, drawing them from a normal distribution with zero mean and variance 0.5/2000. We then multiplied effect sizes by the simulated marker values scaled to zero mean and unit variance to create the genetic values with variance 0.5. In addition to the genetic component, we added a common environment component to simulate effects coming from shared familial environment. We simulated four scenarios where each family was assigned the same common environment effect drawn from a normal distribution with variance 0 (no common environment), 0.1, 0.2, and 0.3. Finally, we added an environmental component simulated from a normal distribution with mean zero and variance 1 minus the genetic variance and minus the common environment variance. We analysed 20 replicates of each of the four scenarios with BayesRR-RC with six MAF-LD groups . In Supplementary Fig. We further validate the use of PPWV in an another simulation study with 500 replicate data sets of 10,000 SNP markers for 5000 individuals for each of two scenarios. In the first scenario, 1000 SNPs are randomly selected to be causal variants and all 10,000 SNP markers are LD independent. In the second, the 1000 causal variants are each in LD with four other variants with LD = 0.95, with the remaining 5000 variants having zero effect size and LD = 0. For each scenario, we simulate effect sizes as an equally spaced sequence from an effect size of −0.04 SD, to 0.04 SD giving genetic variance of 0.55, and we simulate residual variance from a normal distribution with zero mean and variance 0.45, to give a phenotype with zero mean and unit variance. For the first scenario, we calculate the posterior inclusion probability of each causal SNP. For the second scenario, we calculate the PPWV for each 5-SNP group. Across the 500 replicates of each scenario, we take the mean PPWV and mean PIP for each of the 1000 different effect sizes and compare these in Fig. R2 ≥ 0.15 with 348 other SNPs, rs2096537 with MAF 0.14 which had LD R2 ≥ 0.15 with 295 other SNPs, rs131538 with MAF 0.05 which had LD R2 ≥ 0.15 with 82 other SNPs, rs141962840 with MAF 0.007 which had LD R2 ≥ 0.15 with 11 other SNPs, rs117873986 with MAF 0.02 which had LD R2 ≥ 0.15 with 12 other SNPs, rs9606483 with MAF 0.005 which had LD R2 ≥ 0.15 with 1 other SNP, and rs78881648 with MAF 0.009 which had LD R2 ≥ 0.15 with 1 other SNP. To these seven SNPs, we assigned the same effect sizes in four different scenarios, either 0.05, 0.025, 0.0125, or 0.01 on the SD scale. On the remainder of chromosomes 19, 20, 21 and 22, we randomly selected 1000 SNPs as causal variants to give a polygenic background, sampling their effects from a normal distribution with zero mean and variance 0.5/1000. We repeated each of the four scenarios 20 times. We selected these regions to compare the performance of BayesRR-RC to the fine-mapping approach SuSiE as outlined in a recent paper22. For BayesRR-RC, we calculate the PPWV of the LD blocks containing the seven focal SNPs, and then prune these blocks based on the LD among the markers in the block (described as “purity" in the SuSiE paper22) to identify a credible set with LD R2 ≥ 0.9. We then count the proportion of times across the simulations that each causal variant was contained with one of the credible sets. For SuSiE, we ran the model from the individual-level data of the whole block of chromosome 22 using the suggested settings and setting K = 10. We then calculate the proportion of times that the identified credible sets contained one of the seven causal variants. We present these results in Supplementary Fig. We also focused on the ability of our approach to fine-map associated regions to identify candidate SNPs and to provide a probabilistic assessment of the most likely associated set of SNP markers. To do this we used our large-scale simulation data and focused on seven focal regions within a blocks of chromosome 22. We allocated effect sizes to the following SNPs: rs131529 with MAF 0.32 which had LD We restricted our discovery analysis of the UK Biobank to a sample of European-ancestry individuals. To infer ancestry, we used both self-reported ethnic background (UK Biobank data code 21000-0) selecting coding 1 and genetic ethnicity (UK Biobank data code 22006-0) selecting coding 1. We also took the 488,377 genotyped participants and projected them onto the first two genotypic principal components (PC) calculated from 2504 individuals of the 1000 Genomes project with known ancestries. Using the obtained PC loadings, we then assigned each participant to the closest population in the 1000 Genomes data: European, African, East-Asian, South-Asian or Admixed, selecting individuals with PC1 projection < absolute value 4 and PC 2 projection < absolute value 3. This gave a sample size of 456,426 individuals.p-value for Hardy–Weinberg test larger than 10-6, as determined in the set of unrelated Europeans) were selected those with minor allele frequency (MAF) > 0.0002 and rs identifier, in the set of European-ancestry participants, providing a data set 9,144,511 SNPs, short indels and large structural variants. From these, we took the overlap with the Estonian Genome centre data to give a final set of 8,430,446 markers. From the UK Biobank European data set, samples were excluded if in the UKB quality control procedures they (i) were identified as extreme heterozygosity or missing genotype outliers; (ii) had a genetically inferred gender that did not match the self-reported gender; (iii) were identified to have putative sex chromosome aneuploidy; (iv) were excluded from kinship inference. Information on individuals who had withdrawn their consent for their data to be used was also removed. These filters resulted in a data set with 382,466 individuals.To facilitate contrasting the genetic basis of different phenotypes, we then removed closely related individuals as identified in the UK Biobank data release. While the BayesRR model can accommodate relatedness similar to mixed linear models, we wished to simply compare phenotypes at markers that enter the model due to LD with underlying causal variants. Relatedness leads to the addition of markers within the model to capture the phenotypic covariance of closely related individuals, and this will vary across traits in accordance with the genetic and environmental covariance for each phenotype. For these unrelated individuals, we used the imputed autosomal genotype data of the UK Biobank provided as part of the data release. We used the genotype probabilities to hard-call the genotypes for variants with an imputation quality score above 0.3. The hard-call-threshold was 0.1, setting the genotypes with probability ≤0.9 as missing. From the good quality markers (with missingness less than 5% and We then selected the recorded measures of BMI (UK Biobank variable identifier 21001-0.0) and height (variable identifier 50-0.0) collected during initial assessment visit (year 2006-2010). BMI and height phenotypes six standard deviations (SD) away from the mean were not included in the analyses. For Type 2 Diabetes (T2D) in UKB, we selected cases very broadly as individuals who have main or secondary diagnosis (UKB fields 41202-0.0–41202-0.379 and 41204-0.0–41204-0.434) of “non-insulin-dependent diabetes mellitus” (ICD 10 code E11) or self-reported non-cancer illness (UKB field 20002-0.0–20002-2.28) “type 2 diabetes” (code 1223). From respondents self-reporting just “diabetes” (code 1220), we selected as cases those who did not self-report “type 1 diabetes” (code 1222) and had no Type 1 Diabetes (ICD code E10) diagnosis. Individuals with self-reported “diabetes” and “type 1 diabetes”/E10 were also left out from controls. We also defined coronary artery disease (CAD) cases broadly as participants with one of the following primary or secondary diagnoses or cause of death: ICD 10 codes I20 to I28; self-reported angina (code 1074) or self-reported heart attack/myocardial infarction (code 1075). Participants with self-reported “heart/cardiac problem” (code 1066) were not included as cases but also excluded from controls. This gave a sample size for each trait of 25,773 T2D cases and 359,730 T2D controls, 39,766 CAD cases and 344,054 CAD controls, 382,402 measures of height and 381,899 measures of BMI.http://www.ukbiobank.ac.uk/ethics/), and these ethical regulations cover the work in this study. Written informed consent was obtained from all participants. Data from this project were held under UK Biobank project ID 35520.UK Biobank has approval from the North West Multi-centre Research Ethics Committee (MREC) to obtain and disseminate data and samples from the participants , batch, and ancestry effects, and that the effects of each SNP is estimated jointly  environmentally induced covariance between SNP markers and a phenotype is still possible.All phenotypes were adjusted for age of attending assessment centre , year of birth , UK Biobank recruitment centre , Genotype batch  and final 20 leading principal components of 1.2 million LD clumped markers from the 8,430,446 markers included in the analysis, calculated using flashPCA (see “Code availability” section). The residuals were then converted to We partition SNP markers into seven location annotations using the knownGene table from the UCSC browser data (see “Code availability” section). We preferentially assigned SNPs to coding (exonic) regions first, then in the remaining SNPs, we preferentially assigned them to intronic regions, then to 1 kb upstream regions, then to 1–10 kb regions, then to 10–500 kb regions, then to 500–1 Mb regions. Remaining SNPs were grouped in a category labelled “others” and also included in the model so that variance is partitioned relative to these also. Thus, we assigned SNPs to their closest upstream region, for example if a SNP is 1 kb upstream of gene X, but also 10–500 kb upstream of gene Y and 5 kb downstream for gene Z, then it was assigned to be a 1 kb region SNP. This means that SNPs 10–500 kb and 500 kb–1 Mb upstream are distal from any known nearby genes. We further partition upstream regions to experimentally validated promoters, transcription factor binding sites (tfbs) and enhancers (enh) using the HACER, snp2tfbs databases (see “Code availability” section). All SNP markers assigned to 1 kb regions map to promoters; 1–10 kb SNPs, 10–500 kb SNPs, 500 kb–1 Mb SNPs are split into enh, tfbs and others (un-mapped SNPs) extending the model to 13 annotation groups. Within each of these annotations, we have three minor allele frequency groups , and then each MAF group is further split into two based on median LD score. This gives 78 non-overlapping groups for which our BayesRR-RC model jointly estimates the phenotypic variation attributable to, and the SNP marker effects within, each group. For each of the 78 groups, SNPs were modelled using five mixture groups with variance equal to the phenotypic variance attributable to the group multiplied by constants . We conducted a series of convergence diagnostic analyses of the posterior distributions to ensure we obtained estimates from a converged set of four Gibbs chains, each run for 6000 iterations with a thin of five and burn-in of 500 for each trait  and using 1 − p in a Plink clumping procedure to select LD independent (correlation2 ≤ 0.1) blocks of SNPs. We then repeat the estimation of the PPWV of 50 kb regions across the genome, then map SNPs to the coding region of genes, and to the closest gene +/− 50 kb from the SNP position. These are labelled as located in a coding region, an intron, 1 kb upstream of a gene using our functional annotations. Remaining SNPs are labelled as located in a cis-region  with “body mass index” entry for BMI, “standing height” for HT, “angina/heart attack” for CAD and “diabetes” for T2D  as reference and a window size of 1000 kb. Because SNPs included in groups others and rare 1Mb tfbs are not present in all chromosomes, tagging files are constructed using 70 non-overlapping annotations only. The remaining SNPs are modelled together in an extra partition. Finally, we merged the tagging files and regressed the summary statistics onto this file assuming the LDAK model. SNP heritability estimates, proportions of heritability, enrichment and standard errors per genetic component are reported in Supplementary Data Table We then compared our BayesRR-RC estimates for height, BMI, T2D and CAD to RHEmc28 summary statistics, we also applied Bolt-LMM8 and Regenie9 to height, BMI, T2D and CAD. In the first step, we pruned SNPs using plink30 with a pairwise r2 threshold of 0.5 and a window size of 1000 kb, resulting in a subset of 1,362,013 SNPs markers. We restricted the random effects in the mixed model for bolt-LMM and the ridge regression predictors for Regenie to this subset of pruned SNPs. In the second step, all 8,430,446 SNPs from the full genotype data were then tested for association in both methods. Following recommendations, we used the provided hg19 genetic map file and 1000 Genomes LD scores reference for Bolt-LMM and performed the default mixed linear model association test. For Regenie, the 1,362,013 SNP markers are split in blocks of 1000 consecutive SNP markers and ridge regression predictors are computed for a range of five shrinkage parameters within each block. For the association testing, we split the 8,430,446 SNP markers in blocks of 400 consecutive SNP markers and set the Firth correction p-value threshold to 0.01. We then applied an approximate and joint association analysis called GCTA-COJO31 to the summary statistics obtained with Bolt-LMM, Regenie and plink2. We ran GCTA-COJO using a subset of 20,000 individuals randomly selected from the 382,466 individuals as reference with a window size of 10,000 kb and a r2 cutoff value of 0.5 for the LD among the SNPs in the data. Finally, we set a p-value threshold to 5e−8 to report significant SNPs associated with height, BMI, CAD an T2D in Table In addition to plink232. From 11,130,313 markers with imputation quality score >0.3, we selected SNPs that overlapped with the UK Biobank, resulting in a set of 8,433,421 markers.For the Estonian Genome Centre Data, 32,594 individuals were genotyped on Illumina Global Screening (GSA) arrays and we imputed the data set to an Estonian reference, created from the whole genome sequence data of 2244 participantsz-scores after applying the same outlier removal procedure as in UKB and adjusting for the age at agreement. Prevalent cases of CAD and T2D in the Estonian Biobank cohort were first identified on the basis of the baseline data collected at recruitment, where the information on prevalent diseases was either retrieved from medical records or self-reported by the participant. The cohort was subsequently linked to the Estonian Health Insurance database that provided additional information on prevalent cases (diagnoses confirmed before the date of recruitment) as well as on incident cases during the follow-up.We selected height and BMI measures from the Estonian Genome Centre data, in 32,594 individuals genotyped on GSA array and converted them to sex-specific All Estonian biobank participants have signed a broad informed consent form and the study was carried out under ethical approval 1.1 12/2856 from the Estonian Committee on Bioethics and Human Research .z-score prior to analysis, all effect sizes obtained are on the SD scale. Thus when we create a genomic predictor, for say coding SNPs, by multiplying SNPs mapped to coding regions genotyped in Estonia to the effect sizes obtained in the UK Biobank for each iteration, we obtain a genetic predictor for each iteration, providing a posterior predictive distribution that is also on the SD scale. For each trait, we created 2000 genomic predictors for each individual in the Estonian Biobank, at each of the 13 annotation groups, by selecting effect size estimates obtained every tenth iteration from the last 3000 iterations of each of the four Gibbs chains and combining them together in a single posterior. We calculated prediction accuracy as the proportion of phenotypic variation explained by the genomic predictor, and area under the receiver operator curve (AUC) for T2D and CAD using each individual’s mean genetic predictor. For each of the 13 annotation groups, we calculated the partial correlation of the genetic predictor of each of the 2000 iterations and the phenotype. We then used this to estimate the independent proportional contribution of each group to the total prediction accuracy, providing a metric of replication for our UK Biobank enrichment results.As the UK Biobank marker effects are estimated from traits that were standardised to a For height and BMI, we determined the probability that each Estonian individual’s predictor accurately reflected their phenotypic value. To do this, we calculated the proportion of posterior samples with pth percentile of the distribution of genetic risk in the general population. We calculated the proportion of posterior samples for each individual with values in the top 25% of the distribution of genomic predictors for each trait. Thus for each individual, we calculate the probability that the posterior predictive distribution is in the top 25% of the distribution of genetic risk in the general population.For T2D and CAD, we extended the PCF metric, typically defined as the proportion of cases with larger estimated risk than the top 21 as recommended by the authors and as shown to have the best prediction performance out of the MegaPRS approaches in our simulation study. We clumped SNPs with r2 threshold of 0.5 resulting in 1,508,624 SNP markers to be included in the analysis and randomly selected 20,000 individuals to compute the LDAK weights. We then computed the tagging file using the same data set as reference and the 64 BLD-LDAK annotations. Here, weights are models as an extra annotation and we save the heritability matrix. We then regress the plink228 summary statistics for height, BMI, CAD and T2D onto the tagging file, saving the per-predictor heritabilities. We then created four reference panels with the same 1,508,624 SNP markers but randomly selecting different 5000 related individuals from the UK Biobank and we used these to: (i) calculate predictor-predictor correlations with a window size of 3000 kb to estimate the LD structure; (ii) compute pseudo summaries from the plink2 summary statistics including ambiguous alleles, which creates pseudo training and test summary statistics to be used in the construction of the prediction model; (iii) estimate effect sizes specifying a Bolt-LMM model for height, BMI, CAD and T2D, using the predictor–predictor correlations, the per-predictor heritabilities, the plink2 summary statistics and training pseudo summary statistics, whilst including ambiguous allele and specifying a 1000 kb window; (iv) test prior distributions to determine the most accurate model and obtain the best effect sizes. These steps resulted in 1,397,514 predictors for height, 1,471,586 for BMI, 1,397,514 for CAD and 1,389,364 for T2D and we ensured that at no point was the Estonian genome centre data used, nor was any overlapping individuals in the UK Biobank subsets used to train the models and the data used to generate the summary statistics. Finally, we then calculated genomic predictors for each individual in the Estonian Biobank using the best effect sizes. We report the squared correlations between the genomic predictor and phenotypes.As a comparison, we also estimated a boltLMM prediction model using MegaPRSFurther information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1-10Reporting Summary


N = 97, 170 observations; age 13–21 years old). It also explores pT interactions with pubertal stage and timing. PT concentrations were measured from amniotic fluid extracted in the 2nd trimester of gestation via amniocentesis conducted for clinical purposes. Autistic traits were measured by self- and parent-reports on the Autism Spectrum Quotient (AQ) which provides a total score and 5 sub-scores . Self-reported pubertal stage was regressed on age to provide a measure of relative timing. We found no statistical evidence for a direct association between pT and autistic traits in this adolescent sample . Exploratory analyses suggested that pT correlated positively with autistic traits in adolescents with earlier puberty-onset, but statistical robustness of this finding was limited. Further exploratory post-hoc tests suggested the pT-by-pubertal timing interaction was stronger in males relative to females, in self-reported compared to parent-reported AQ and specifically for social traits. These findings require replication in larger samples. Findings have implications for understanding the effects of pT on human behavior, specifically existence of effects in adolescence.Prenatal testosterone (pT) is a crucial component in physiological masculinization in humans. In line with the Prenatal Sex Steroid Theory of autism, some studies have found a positive correlation between pT and autistic traits in childhood. However, effects in adolescence have not been explored. Hormonal and environmental changes occurring during puberty may alter the strength or the nature of prenatal effects on autistic traits. The current study examines if pT relates to autistic traits in a non-clinical sample of adolescents and young adults  may be associated with autistic traits in children.•An association was not observed in our adolescent sample.•The association between pT and autistic traits may be moderated by pubertal factors.•Higher pT related to higher autistic traits in adolescents with earlier-onset/faster puberty.•This interaction of pT and pubertal timing was most evident for social traits. Autism is more commonly diagnosed in males than females . In the Some support for the link between pT and autistic traits has come from several study designs. First, correlations have been reported between pT found in amniotic fluid and parent-reported autistic traits in childhood , parent-Second, Congenital Adrenal Hyperplasia (CAH) is an autosomal recessive disorder characterized by cortisol deficiency and elevated androgens beginning prenatally. This elevation is particularly marked in females with CAH. Males with CAH have normal to high androgen concentrations prenatally. Two studies found that girls with CAH score higher on measures of autistic traits than matched relatives , howeverThird, an association between pT and autism is supported by studies on children of mothers with Polycystic Ovary Syndrome (PCOS), a condition characterized by excess circulating androgens. A meta-analysis found maternal PCOS increases the odds of an autism diagnosis in their children by 66% , an effeFourth, masculinized morphology may be associated with autism. Male-type shifts in the facial morphology of autistic individuals have been reported compared to their non-autistic peers  and sex The timing of pT measurement may be important. Studies measuring testosterone from umbilical cord blood or infant saliva have not found associations with autistic traits . Cord-deTwo main caveats surround the association between pT and autistic traits. First, studies using the Danish Biobank found no significant difference in amniotic fluid testosterone between autistic and non-autistic boys, showing that other steroid hormones beyond pT are likely involved . This ha1.2One unknown is whether pT exposure can impact behavior beyond childhood and into adolescence. To date, all studies on amniotic pT and autistic traits have assessed outcomes in mostly pre-pubertal children, but it is possible that the hormonal and neuronal changes of puberty could interact with the initial effect of pT on neurodevelopment. Puberty may alter the number or strength of autistic traits, particular social traits. Adolescence is a time of accelerated structural and functional change in the brain, partially mediated by the increase in sex hormones and resulting in a hypersensitivity to social stimuli . HoweverThere is some evidence to suggest the effects of pT on brain structure and function are altered during adolescence. Twins sharing the womb with a male, who are thought to be exposed to higher levels of pT, have larger total brain volumes at age 9 . However, this effect of pT on brain volumes was attenuated and non-significant in adults suggesting it may be developmentally specific . Beking Animal experiments suggest puberty may be a second sensitive period of neuroendocrine organization . ManipulTaken together, these animal and human studies highlight the importance of taking puberty into account when assessing the behavioral effects of pT in adolescence.1.3We test whether pT is related to scores on the Autism Spectrum Quotient (AQ) in individuals aged 13–21. This is a follow-up of the longitudinal study of neurotypical children whose pT was measured from amniotic fluid during gestation and who were assessed for autistic traits as infants  and chil22.1Mothers in Cambridgeshire (UK) who had undergone a routine amniocentesis for clinical purposes (1996–1999) and who gave birth to healthy singletons were invited to take part in a study on the effects of pT on the child’s cognition, behavior and brain development . Those w2.2t = −7.66, p < 0.001, Cohen’s d = 1.51; PT concentration was measured via radioimmunoassay in amniotic fluid samples collected between 13 and 20 weeks of gestation . Amnioti2.3Adolescents completed the self-report Adult AQ  while paThe internal consistency for the AQ total is adequate  for inclusion. Most (78%) participants had both versions of the AQ, so while the Adult-AQ has only been validated for individuals over 16  and the 2.4Participant ages ranged from 13 to 21 years . There was 1 participant with missing age which was imputed with the mean. We refer to all participants as adolescents given recent proposals that the definition of adolescence should be extended to 10–24 years, within which continued biological and social development occurs .2.5The Pubertal Developmental Scale  was used2.6Pubertal timing was the deviation of an individual’s pubertal stage from the mean stage for their age and sex, within this sample. We regressed pubertal stage on age for males and females separately (standard linear regressions) and the residuals of these tests  were tak2.7Certain gestational factors may be associated with pT levels and autistic traits and are therefore potential confounds. The time of amniocentesis (in weeks gestation) for instance is correlated with autistic traits in infants . Unfortu2.82.8.1lmer function from the lme4 package . Linear mixed models were used to predict AQ scores using the  package . ParametWhile linear mixed models are robust to violations of distributional assumptions , we alsosimr, determined that our linear mixed model and sample size  had sufficient power (83%) to detect a main effect of pT on AQ similar in magnitude to that found in younger children (β = 12), moderate (β = 6) and small (β = 3) interactions between pT and our pubertal measures could be observed with power of 100%, 60% and 20% respectively. The interaction between pT and sex was likely to be underpowered (required sample size for 80% power estimated between 320 and 2000 participants). Allowing estimates to vary by sex is crucial to any test of testosterone effects, therefore we could not exclude the pT x sex interaction despite power issues. Details of power calculations are described in A power analysis, using R package children . Large , rater (parent/self), (and continuous variables) pT, pubertal stage, pubertal timing, maternal age at birth and time of amniocentesis. To avoid multicollinearity between pubertal stage and pubertal timing (due to the latter being generated from the former), two separate models were run. The pubertal stage model included 4 main effects  and 2 interactions  at baseline. The pubertal timing model simply replaced pubertal stage with pubertal timing. Maternal age and time of amniocentesis were added in consecutive models  as their inclusion reduced the sample size to 74 and 50 respectively. Inclusion of a pT x sex interaction allows the slope of the pT-outcome relationship to differ for males and females which was deemed necessary given differences in pT distribution observed across sex  and the 2 term was included as an additional fixed effect. A quadratic effect of pT on AQ total would be supported if the model including a quadratic term was a better model fit to the data than the model including linear terms only  and if the pT2 term itself was significant.We tested whether the relationship between pT and AQ total score was better described as quadratic (versus linear). An pTSensitivity analyses were performed to verify results of the linear mixed models: (1) simpler models predicting AQ from pT (less covariates and rater-stratified models) (2) sex-stratified analyses (3) generalized linear mixed models to account for violations of assumptions of normality and homoscedasticity and (4) a repeat of main analyses without participants with an autism diagnosis (n = 1).2.8.3p = .01) for reference . We also conducted sensitivity analyses with these sub-score results (as in 2.8.2).The five AQ subscales were dependent variables in five separate tests. We had no specific hypotheses about the how pT would relate to the AQ subscales therefore, on the basis of AQ total results, we included pubertal timing only  in prediction models of AQ subscales to restrict the number of tests performed. The baseline model (M1) used to predict each AQ subscale therefore included 4 main effects  and 2 interactions . In subsequent models, we also controlled for maternal age at birth (M2) and time of amniocentesis (M3). We report Bonferroni corrected significance levels (33.1r(74) = .42, p < .001), there was also a significant difference whereby adolescents rated themselves higher than parents on average (t(75) = −4.38, p < .001; r (71)= −0.35, p = .002) but not AQ totals. Time of amniocentesis was weakly correlated with both amniotic pT levels (r (48) = 0.24, p = 0.10) and rater-averaged AQ totals (r (48)= −0.27, p = .05).3.23.2.1r = −0.11  and for females was r = 0.17 . No significant correlation was observed between pT and specifically parent-reported AQ total  or self-reported AQ total . The quadratic relationship between pT and AQ total was not significant i.e., the pT2 term was not significant and its inclusion did not improve model fit  only overlapped to a small extent with the interval previously reported in younger children , time of amniocentesis (M2) and maternal age (M3). No significant interaction between pT and sex was observed either . The Peaodel fit . The hypstage on AQ totals was not significant at the Bonferroni-corrected threshold (0.0167) in the baseline model M1 or after adjusting for maternal age (M2) but was significant in M3, adjusted for both maternal age and time of amniocentesis . β = 7.28, SE = 2.74, t = 2.65, p = 0.01; N = 73) and time of amniocentesis  but not in the baseline model M1. x pubertal timing interaction among the AQ subscales.Of all predictors of AQ total, rater had the most reliable effect. On average, adolescents rated themselves over 3.0–3.7 points higher than their parents did on the 50-point AQ scale . Sex als3.2.2β = 2.20, SE = 0.83, p = 0.008; M2: β = 2.52, SE = 0.90, p = 0.006; M3: β = 4.24, SE = 1.14, p < 0.001). To limit the number of tests performed on AQ subscales, we explored the pubertal timing model only, as pubertal timing had shown more reliable interaction effects with pT on AQ total score, and as pubertal variables were highly correlated. β = 3.34, SE = 0.86, p < 0.001) and generalized linear mixed models , therefore this result should be interpreted with caution.An interactive effect of pT and pubertal timing was also observed for the communication subscale, though it was only significant at the corrected threshold for the fully-adjusted model in the restricted sample  in both linear mixed models  in the full sample, or either sex. A number of sensitivity analyses verified this null finding  and equi4.1n = 97 Vs n = 235) or sample age  and autistic traits  are affe4.2Findings from other human studies support the plausibility of our trend interaction between pT and pubertal timing on autistic traits. One study in 14–16-year-old adolescents showed prenatal and pubertal testosterone levels had an interactive effect on male-typical patterns of brain lateralization during a visuospatial task . SpecifiIt may be that both high pT and early/fast pubertal timing are by-products of a polygenetic tendency to autism. The majority of genetic contribution to autism is likely due to common variants  which mamain effect of pubertal timing on AQ total was not significant. Our results may therefore be consistent with a “double-hit” model of autistic traits  than males  and the inclusion of multiple trait scales . Finally, the use of multiple statistical models with different underlying assumptions  allowed us to probe the robustness of findings.4.6This is the first study to investigate behavioral correlates of mid-gestational pT in adolescents and young adults, and the first to assess the contribution of puberty. Our findings suggest that the positive correlation between pT and autistic traits, previously observed in infants and children of the same cohort, does not persist into adolescence. However, an exploratory analysis suggested pT and pubertal timing may have interactive effects on autistic traits. This interaction was stronger for social aspects of autism and for males. This finding was explorative and additional research in both humans and animals is needed to test its robustness. Our results also highlight the importance of including pubertal measures and multi-rater behavioral assessments when investigating hormone-behavior links in adolescents.The data used in this report were from a longitudinal study led by the Autism Research Center in Cambridge. The authors have no conflicts of interest to disclose.


However, the current genomic selection software faces several issues such as low prediction accuracy, low computational efficiency, or an inability to handle large-scale sample data. We report the development of a genomic prediction model named FMixFN with four zero-mean normal distributions as the prior distributions to optimize the predictive ability and computing efficiency. The variance of the prior distributions in our model is precisely determined based on an F2 population, and genomic estimated breeding values (GEBV) can be obtained accurately and quickly in combination with an iterative conditional expectation algorithm. We demonstrated that FMixFN improves computational efficiency and predictive ability compared to other methods, such as GBLUP, SSgblup, MIX, BayesR, BayesA, and BayesB. Most importantly, FMixFN may handle large-scale sample data, and thus should be able to meet the needs of large breeding companies or combined breeding schedules. Our study developed a Bayes genomic selection model called FMixFN, which combines stable predictive ability and high computational efficiency, and is a big data-oriented genomic selection model that has potential in the future. The FMixFN method can be freely accessed at  Based on the use of genomic information and prediction of the genetic merit of animals, genomic selection is changing breeding strategies and approaches in livestock . Among mediction . In the Although Bayes-based models have the potential for the development of more faithful genetic models and seem to be the best choice for estimating GEBV, they require long computing times since they use computer-intensive MCMC techniques . For pravariance . Using thttps://queries.uscdcb.com/Genotype/cur_freq.html), more than 5,000,000 Holstein cows have been genotyped as of July 2021. With the accumulation of breeding data, there is an urgent need for a genomic selection model that can handle large-scale sample data.For genomic selection, most of the focus has been on prediction accuracy and computational efficiency, but the computing limits are an increasingly important aspect that needs to be taken into account. The direct method of genomic selection can provide GEBV in a short computing time when the number of individuals in the population is small, but some studies have shown that when the dimensions of the kinship matrix exceed hundreds of thousands or even millions, the process to inverse the matrix inverse becomes very difficult due to the limitations in computer memory and computational time . AccordiIn our study, we presented an ICE-based prediction model with four zero-mean normal distributions as the prior distribution and the variance of which have been obtained accurately based on the 374 standardized phenotypes in an F2 population. This model with four normal distributions and variances classified into four categories was referred to as FMixFN, where MixFN refers to the prior distribution of FMixFN was a mixture of four normal distributions, and the first “F” refers to “Fast.” As a test, the predictive ability and computation time obtained with GBLUP, SSgblup, Bayesian mixture regression (MIX), BayesR, BayesA, BayesB, and FMixFN were compared first based on six traits with different heritabilities and different genetic architectures by using cross-validation. Then FMixFN was evaluated by using data from Duroc and Asian rice experiments, respectively . This stAll procedures including experimental animals established and tissue collection were performed in accordance with the guidelines approved by the Ministry of Agriculture of China. This study was approved by the ethics committee of Jiangxi Agricultural University.n = 1,912) in six batches. All the F2 animals were kept under standard indoor conditions at the experimental farm of Jiangxi Agricultural University (China). Then the F2 piglets were weaned at 46 days, and males were castrated at 90 days. At 240 ± 6 days of age, 1,030 F2 animals including 549 gilts and 481 barrows were slaughtered at 70–120 kg live weight.An F2 design resource population was developed between 2000 and 2006  as folloGenomic DNA was isolated from ear tissue with a standard phenol/chloroform extraction method. All DNA samples were diluted to a final concentration of 50 ng/μl in 96-well plates. In total, 933 F2 were genotyped with the Illumina PorcineSNP60 BeadChip on an iScan System  following the manufacturer’s protocol . QualityWe used the GEMMA software to calculate the substitution effects of 14,320,159 SNPs on the 374 traits included in the standard linear model . Sex wasThree genotypes “AA,” “Aa,” and “aa” were assumed each locus and were represented by 0, 1, and 2, respectively, with  2pqβ2 . In the Group of traits with high heritability:Group of traits with a moderate heritability:Group of traits with a low heritability:The linear model for genomic prediction was as follows:In this study, the prior distribution with four zero-mean normal distributions was written as a function of prior distributions of SNP variance as determined above:lgorithm . In brieTherefore, the equation The first term of Here, the last term of this formula equals Here, the derivation process for the remaining terms of Here, the fixed effects are estimated at each iteration by the formula: In the following analysis, we used GBLUP , SSgblupGBLUP: GBLUP was used to estimate the effects of the markers by BLUP, assuming that each marker explains an equal proportion of the total genetic variance. The software GEMMA was used to implement the GBLUP calculation process .https://hiblup.github.io/).SSgblup: Single-step genomic BLUP (SSgblup), which was developed by https://cran.r-project.org/web/packages/VIGoR/index.html).MIX: the MIXTURE model assumed that the marker effects came from a mixture of two distributions: one distribution with large variance (accommodating large marker effects) and one with small variance . The distribution to which the marker belongs is sampled from the Bernoulli distribution. The variances of the two distributions underlying the mixture are estimated using a noninformative chi-square distribution. Implementation of MIX is completed by the R package “VIGoR” (https://cnsgenomics.com/software.html).BayesR: BayesR starts the hierarchical model and poses a mixture of four zero-mean normal distributions as a conditional prior for a specific SNP effect. We use BayesR software to implement the calculation process  .In this study, all traits of the F2 population were divided into three groups based on the heritability of the traits: high, moderate, and low. For the group of traits with high heritability, the calculated In this study, we selected phenotype 3 and phenotype 4 to verify the unbiasedness of the variance ratio of the prior distribution. When the variance ratio was assumed to be 0.5, 0.25, 0.125, and 0.125, the predictive ability of phenotype 3 and phenotype 4 are 0.4773 and 0.4911, respectively. When the variance ratio is assumed to be 0.9, 0.005, 0.045, 0.005, the predictive ability of each of these phenotypes are 0.4789 and 0.4911, respectively. In contrast, the predictive ability of these two phenotypes estimated by using the original parameters is 0.4787 and 0.4913, respectively.The predictive ability of each of the six F2 traits under the six predictive methods is shown in The computational time per iteration of FMixFN increases almost linearly as the number of individuals increases in the reference group, as shown in In conclusion, when there are fewer individuals in the reference group, the computational speeds for ICE-based FMixFN are on the same order of magnitude with GBLUP, and they were much faster than the MCMC-based Bayesian methods. When the number of individuals in the reference dimension of the kinship matrix exceeds hundreds of thousands or even millions, the process to inverse the matrix becomes very difficult for the direct method of genomic selection. FMixFN has excellent computational efficiency and can handle large-scale sample data.Our results show that the accuracy of genomic selection is affected by many factors, among which the a priori hypothesis on the size of the QTL effect values for traits is crucial. Usually, the most accurate method to predict genetic values or phenotypes based on SNP genotypes is to fit all SNPs simultaneously, treating the SNP effects as they are drawn from a prior distribution that matches the true distribution of SNP effects as closely as possible . To dateNarrow-sense heritability is defined as the proportion of additive variance to phenotype variance , which mThe results showed that the predictive ability of BayesR, BayesA, and BayesB was similar in phenotype1, 3, and 5, and was higher than that of the three other methods, which means the MCMC based Bayes genomic selection model has an advantage in predicting genomic breeding values when the trait is affected by large-effect QTL. This result confirms those reported by In addition to resulting in stable predictive ability, two other advantages of FMixFN are computational efficiency and its ability to deal with large-scaled sample data. The level of the computational efficiency of the direct method of genomic selection was the same as that of FMixFN when the number of individuals in the reference population was small, but if this number increases, the direct method will not be efficient because the process to invert the matrix will become very difficult due to the limitations in computer memory and computational time. Our study demonstrates the stability of FMixFN and its potential for use on large-scale sample data.We have developed a Bayes-based genomic selection model called FMixFN, which combines stable predictive ability and computational efficiency. Besides, when the number of individuals in the reference population is large, FMixFN is one of the best choices for genomic selection. FMixFN is a stable, big data-oriented genomic selection model, which could meet the needs of large breeding companies or combined breeding schedules.


Genetic association studies for blood cell traits, which are key indicators of health and immune function, have identified several hundred associations and defined a complex polygenic architecture. Polygenic scores (PGSs) for blood cell traits have potential clinical utility in disease risk prediction and prevention, but designing PGS remains challenging and the optimal methods are unclear. To address this, we evaluated the relative performance of 6 methods to develop PGS for 26 blood cell traits, including a standard method of pruning and thresholding (P + T) and 5 learning methods: LDpred2, elastic net (EN), Bayesian ridge (BR), multilayer perceptron (MLP) and convolutional neural network (CNN). We evaluated these optimized PGSs on blood cell trait data from UK Biobank and INTERVAL. We find that PGSs designed using common machine learning methods EN and BR show improved prediction of blood cell traits and consistently outperform other methods. Our analyses suggest EN/BR as the top choices for PGS construction, showing improved performance for 25 blood cell traits in the external validation, with correlations with the directly measured traits increasing by 10%–23%. Ten PGSs showed significant statistical interaction with sex, and sex-specific PGS stratification showed that all of them had substantial variation in the trajectories of blood cell traits with age. Genetic correlations between the PGSs for blood cell traits and common human diseases identified well-known as well as new associations. We develop machine learning-optimized PGS for blood cell traits, demonstrate their relationships with sex, age, and disease, and make these publicly available as a resource.  •Evaluated the performance of 6 polygenic scoring methods•Developed machine learning-optimized PGSs for blood cell traits•PGSs showed interaction with sex and stratify age-dependent blood cell trait levels•PGSs of blood cell traits were genetically correlated with common diseases Xu et al. develop and validate polygenic scores (PGSs) for 26 blood cell traits using 6 PGS methods. PGSs developed using machine learning methods show improved polygenic prediction and allow for jointly modeling the effect of correlation, interaction, and low MAF variants. Blood cell trait PGSs were used to stratify the age-based trajectories of blood cell trait levels and showed genetic correlation with common diseases. Blood cells play essential roles in a variety of biological processes, such as oxygen transport, iron homeostasis, and pathogen clearance.,Blood cell traits are heritable, and their genetic architecture has been found to be polygenic. Analyses of the UK Biobank (UKB),PGSs for blood cell traits show the potential for utility in clinical practice. A recent study examining the effects of known pathogenic variants and blood cell trait PGSs on patients with rare blood disorders showed that a 1-standard deviation (SD) increase in PGS was comparable in risk to carrying a rare coding variant in heterozygosity.,A PGS is most commonly constructed as a weighted sum of genetic variants, typically single-nucleotide polymorphisms (SNPs), carried by an individual, in which the genetic variants are selected and their weights are set via the per-SNP univariate analysis in a genome-wide association study (GWAS).In this study, we evaluate 6 PGS methods to develop optimized PGS for 26 blood cell traits across 3 blood cell types—platelets, red blood cells, and white blood cells—using data from UK Biobank and INTERVAL . With any of these 4 learning methods, PGSs for 11 blood cell traits achieved a nearly ≥0.02 increase in Pearson r score in internal validation. The following 5 blood cell traits each achieved ≥0.02 improvement in both internal and external validation using EN or BR, in comparison with the P + T method   . We founr score), while PGS for MCHC saw little improvement in internal validation  and the EN/BR methods . We founlidation . In spitr2 > 0.1. As expected, for variants in moderate to high LD, EN and BR tended to assign weights that were more different from univariate analysis than for variants not in LD, with some variant effects even changing direction  variants for each trait included many correlated variants, with those with irection .In addition, univariate analysis does not model SNP-SNP interaction effects on the trait; however, modeling interactions can improve PGS construction.r score in the external validation, in which 6 traits achieved >0.05 additional improvement. When compared with the P + T method, EN achieved greater improvements for PGSs of most blood cell traits by using the largest expanded variant set. For example, 25 of the 26 traits had ≥10% improvement over their r scores achieved using P + T, in which 2 traits had >20% improvement .The above analysis has shown that EN, BR, and LDpred2 are the most promising methods for PGS construction of blood cell traits. We further explored potential improvements by incorporating larger variant sets for LDpred2 and EN . Our results showed that EN further improved PGS for almost every trait with the expanded variant sets, when compared with EN using conditional analysis variants only  and S2. r score using EN are within 0.01 for all of the traits between the smaller variant set with p value threshold = 10−4 and the largest variant set . Using a more lenient p value threshold  can result in overfitting problems. By incorporating the variant set with a p value threshold of 10−2, EN significantly outperformed that of using other variant sets in the internal validation with UKB, while it experienced a substantial performance decrease in the external validation with INTERVAL (−6 or lower) could limit the predictive power of EN.By applying different p value thresholds on all the LD-thinned variants, we also obtained smaller variant sets for each trait. Our results suggested that it is possible that by using a smaller variant set with p value thresholding, EN can achieve performance comparable to when using the largest expanded variant set. For example, the performance differences in terms of INTERVAL  and S2, −6 and 10−4) as compared with using CA variants only. However, LDpred2 models showed overfitting on variant sets with lenient or no p value thresholding . Nevertheless, EN consistently outperformed LDpred2 in the external validation with INTERVAL data on almost every expanded variant set for every trait  of both methods. In addition, LDpred2 failed to construct a PGS for the trait MPV on 2 expanded variant sets, indicating that EN may be more robust when using large variant sets.LDpred2 also showed improved performance for PGSs of 24 traits when using the expanded variant sets with more stringent p value thresholds . Blood cell traits exhibited well-known sex differences.Maximizing the accuracy and performance of PGS for blood cell traits raises opportunities for insights into the underlying biology, which is potentially of relevance to disease risk. We next compared the extent to which EN-trained PGS would be used to stratify the levels of blood cell traits in men and women over the age ranges of individuals in INTERVAL  and S3. −4), which are consistent with well-known associations between the blood cell traits themselves and the disease. For example, prior studies have demonstrated a strong association of asthma with eosinophil indices,Finally, we examined the landscape of genetic correlations for the EN-trained PGS of blood cell traits and PGS of several common human diseases . We founImproved polygenic models of blood cells traits aid our understanding of myriad biological processes and diseases. This study demonstrated that common machine learning methods such as EN and BR show improved polygenic prediction of blood cell traits and consistently outperform other methods, likely due to their implicit modeling of SNP-SNP correlations, interactions, and controlling the effect of underrepresented low-MAF variants. We showed that blood cell trait PGSs are able to stratify age-dependent trait levels in both men and women in a population-based setting, and that many blood cell trait PGSs have sex-specific interactions. The landscape of genetic correlations between blood cell traits and common diseases identified well-known trait-level associations, such as eosinophils and asthma, and intriguing associations such as IRF and CAD, MONO# and schizophrenia.Our analysis indicated that EN and BR can jointly model the effect of correlation, interaction, and low MAF variants, and result in improved PGSs over P + T for blood cell traits. To overcome the scalability problem in PGS methods such as MLP and CNN and provide directly comparable results across these methods, the comparative analysis was conducted based on the optimal variant sets identified by the P + T method. Due to the use of hard cut-off thresholds in P + T, this unified way for variant selection may limit the potential of the regularization-based methods EN and BR, which are known for their strength in feature selection. Our follow-up analysis demonstrated including a larger set of genome-wide variants in EN further improved PGS for almost every blood cell trait. These results suggest the EN/BR method as the top choice for PGS development of these (or similar) traits when sufficient individual-level data are available. However, the increased number of input variants can cause increased requirements for the amount of training data, computational resources when using these methods, which could constrain their utilization in PGS development. To address these issues, we also demonstrate that tightening p value thresholds offers a way to not only reduce the size of input variants but also maintain its performance. However, we also find that overly stringent or lenient p value thresholds could cause either deteriorated performance or overfitting problems, so that these should be applied with caution. Our analyses suggest that selecting an appropriate p value threshold through an external validation step could be the key to the better application of these methods in PGS construction.LDpred2 is specifically designed to consider LD correlation in polygenic prediction, but it still relies on cutoff thresholds to remove the impact of other factors such as low-MAF variants.Deep learning models MLP and CNN are based on looser model assumptions than the other methods and are capable of modeling more complex relationships among data. The increased model complexity of MLP and CNN did not result in improvements for PGS construction of blood cell traits, indicating that explicit incorporation of non-linearity factors in the two models does not offer an advantage in this setting. However, it is well known that the design of customized network structures plays a pivotal role in addressing a specific task in deep learning, which encourages us to further design and optimize networks beyond these standard structures for PGS construction. Meanwhile, it was noted that the scalability problem of existing deep learning frameworks in ultrahigh-dimensional genotype data will be a major challenge for the widespread application of neural network-based methods in PGS development. Thus, deep learning frameworks based on efficient genotype data format , and their respective PGSs reflected these associations. Knowledge of their shared genetics and corresponding PGSs may enable early stratification of individuals at increased risk of EO- or NEUT-related RA. Such insights represent new avenues for using PGSs to interrogate disease biology. To facilitate the use of this resource, we have made the blood cell trait PGSs constructed using EN  publicly available at the PGS Catalog.Overall, this study evaluated a variety of learning methods to construct PGSs for blood cell traits using individual-level genotype data. We demonstrate how the learning methods outperform univariate analysis-based methods, including by adjusting the effects of correlation, interaction, and low-MAF variants. This work highlights the importance of moving beyond standard summary statistics-based methods for PGS, particularly as the biobank-scale cohorts are becoming more common. We have made these PGSs available to the community, demonstrated that they can stratify sex- and age-dependent trajectories, and identify their shared polygenic basis with various common diseases. Future studies leveraging the totality of genetic variation  for blood cell traits, as identified in recent studiesyx322@medschl.cam.ac.uk).Further information and requests may be directed to the lead contact Yu Xu , that are not only significantly associated with the trait but also independently contribute to the trait. Our previous work−9 was applied as it is widely utilized for common, low frequency and rare variants.,r2 threshold of 0.9 was further performed to identify the variants that are independently associated with a trait and can best represent the underlying genetic signals of that trait.A GWAS was first performed for each trait on the UKB cohort to select variants significantly associated with the trait, in which a MAF threshold of 0.005% was applied and an genotype imputation INFO threshold of 0.4. For each variant tested, a genome-wide significance threshold of p = 8.31 × 10,−9) and have a LD r2 score lower than 0.9. Then, it fits a multivariate linear regression to remove variants that have a p value larger than the genome-wide significance threshold, which step is iterated until no more variants can be removed from the model. Note that we only keep those CA variants whose genotype data are available on both UKB and INTERVAL studies for the convenience of external tests in this study.The conditional analysis was performed using a stepwise multiple linear regression approach.indep-pairwise method implemented in plink version 2.00r2 = 0.5, which resulted in a total of 1,090,437 variants. Finally, several levels of p value thresholding  were applied on these selected variants to form different variant sets for each trait, each of which was incorporated to the CA variant set of the trait for its PGS construction.There are PGS methods that are scalable to much higher dimensional genetic data, such as EN and LDpred2, so we further investigated their performance on larger sets of genome-wide variants that were selected with more lenient thresholds. In details, we first selected all the biallelic variants that are shared between UKB and INTERVAL, on which filters, MAF > 0.01, INFO score > 0.4 and variant missing rate < 0.1, were applied to control the quality and total number of selected variants using UKB samples. Then, a LD thinning step was performed on UKB to remove SNP-SNP LD correlations using the r2 was used to evaluate the correlation between two variants. The multivariate linear regression: y = β0 + β1SNP1 + β2SNP2 + β3SNP1SNP2 was employed for interaction tests with the interaction terms passing the threshold of p = 2.3 × 10−7  were deemed significant. The term “interaction” used here refers to statistical interactions and does not imply  epistasis.To investigate capability of learning methods in modeling correlations and interactions, we focused on the CA variant sets and performed correlation and interaction tests between any pairs of CA variants for each trait on the UKB cohort. The coefficient of determination We constructed PGS for 26 blood cell traits using a conventional P+T method, summary statistics based learning method LDpred as well as a variety of widely used machine learning and deep learning methods. This subsection describes fundamental aspects of the P+T method, elastic net (EN), Bayesian ridge (BR), LDpred method, multilayer precepton (MLP) and convolutional neural network (CNN) methods.S is the set of SNPs that are identified in the variants selection step; βjis the effect size of the SNP j that is obtained through the univariate statistical association tests in the GWAS using the UKB cohort; xij is the genotype dosage of SNP j of the individual i. As discussed previously, P+T relies on LD pruning and p value thresholding, or maybe other thresholding strategies, for variants selection. The best set of thresholding parameters is usually identified by comparing their performance on a validation set.P+T method assumes that the genetic variants have linear additive effects on PGS of the trait and constructs polygenic scores of a blood cell trait using the weighted sum of genotypes of the selected variants for that trait:N is the set of training samples for a given trait and yi is the trait level of the training sample i; the second term is L1 norm and the third term is L2 norm; α and λ are coefficients used to control the contribution of L1 and L2 norms in the model, which are usually set via cross-validation. In EN, effect sizes of the variants selected for a trait are jointly estimated which provides an implicit way to model the correlations among these variants, and the use of L1 and L2 norms helps to control model complexity to address the over-fitting problem in which L1 controls the sparsity of the model and L2 controls the contribution of each variable. It has been shown that the application of these regularized multivariate models offers an effective way to improve PGS construction in practice.,EN also assumes that the variants have linear additive effects on the PGS of a trait, i.e., 1, α2) and Gamma. These two prior Gamma distributions can be set via a validation step. The β, α, λ are then estimated by maximizing the log of the corresponding posterior distribution with respect to β by combining Similarly, BR also has a linear assumption for the effects of the variants, i.e., Equation p(β|λ)∼N method using the summary statistics and a variants-variants correlation matrix (learned from a reference panel). The latest LDpred2The LDpred method (both version 1 and version 2) also has a fundamental linear assumption as EN and BR. Differently, it considers the prior for effect sizes of variants by a Gaussian mixture model:f1 in w11, w12 and w13, are weights of the three inputs of function f1 and b10 is the intercept (or bias); SNP1, SNP2 and SNP3 are the genotype dosages of three SNPs in our context; fact is an activation function which typically plays the role of introducing non-linearity into the model. Thus, the network architecture and its components of an MLP, e.g., activation function, determine a linear/non-linear mapping space, from which a model, i.e., all the weights across the given network that can best represent the data, is supposed to be learned. Details on the selection of network architectures for this study are given in the next subsection. This learning process is typically implemented by minimizing the difference, i.e., cost function, between the training data and the model distribution, through a back-propagation algorithm.MLP is also named Deep Forward Neural Networks. Unlike other statistical learning methods, e.g., EN and BR, MLP makes no prior assumptions on the data distribution and can be trained to approximate virtually any smooth, measurable functions including non-linear functions.CNNs are a specialized neural network for processing data that have a grid-like topology,r to measure the performance of various polygenic scoring methods. For each trait and each learning method, we randomly and equally partitioned the UKB samples into 5 portions, from which any 4 portions (80% of the samples) were used as training data to learn a model, and test the respective model’s performance on the remaining 20% of UKB samples, as well as an external validation using the whole INTERVAL cohort. For each learning method and each trait, we obtained 5 different models, each with a performance measurement for both the internal UKB test and the external INTERVAL test. By doing so, the training and internal testing covered the whole UKB cohort, affording an effective way to avoid evaluation bias. The P+T method was also tested on the five different UKB testing sets, and the whole INTERVAL cohort.We used Pearson 1, α2, λ1 and λ2, a grid search across the set  was conducted on the training set in which 10% of the samples were used as a validation set. BR was implemented using the scikit-learn package.h2, p, and sparsity were applied when running LDpred2. Randomly selected 10,000 samples from training data were used to obtain the variants-variants correlation matrix and all the training samples for each trait were used to validate the performance of different hyperparameter combinations for the optimal model selection.Hyperparameter turning is a crucial step for machine learning and deep learning methods as the choice of hyperparameters can greatly influence the model performance. In this study, we employed SNPNETAs this work is, to our knowledge, the first attempt to employ MLPs and CNNs for genomic prediction of blood cell traits, there was no prior information that could be used for the design of network architecture for this task. Therefore, similar to the previous work,r2 = 0.9 threshold in UK Biobank .The polygenic risk score used for coronary artery disease (CAD) was our previously published CAD meta-GRS;2 < 0.9), high-confidence (imputation INFO score > 0.4), common (MAF > 1%), unambiguous SNPs (A/T and G/C SNPs excluded) in the UK Biobank version 3 genotype data,40PGS for schizophrenia, Crohn’s disease, rheumatoid arthritis, allergic disease and asthma were derived from summary statistics from their respective genome wide association studies (GWAS) by filtering to variants that overlapped with a set of 2.3 million linkage disequilibrium (LD)-thinned (rscore method implemented in plink version 2.00.Levels of each PGS in each INTERVAL participant were calculated using the The quantitative and statistical analyses are described in the relevant sections of the