The advances of hyperspectral technology provide a new analytic means to decrease the gap of phenomics and genomics caused by the fast development of plant genomics with the next generation sequencing technology. Through hyperspectral technology, it is possible to phenotype the biochemical attributes of rice seeds and use the data for GWAS.NDSI2 = 0.68. Based on GWAS analysis using all the traits, NDSI was able to identify the same SNP loci as rice protein content that was measured by traditional methods. In total, hyperspectral trait NDSI identified all the 43 genes that were identified by biochemical trait PC. NDSI identified 1 extra SNP marker on chromosome 1, which annotated extra 22 genes that were not identified by PC. Kegg annotation results showed that traits NDSI annotated 3 pathways that are exactly the same as PC. The cysteine and methionine metabolic pathway identified by both NDSI and PC was reported important for biosynthesis and metabolism of some of amino acids/protein in rice seeds.The results of correlation analysis indicated that Normalized Difference Spectral Index (NDSI) had high correlation with protein content (PC) with RThis study combined hyperspectral technology and GWAS analysis to dissect PC of rice seeds, which was high throughput and proven to be able to apply to GWAS as a new phenotyping tool. It provided a new means to phenotype one of the important biochemical traits for the determination of rice quality that could be used for genetic studies.The online version of this article (10.1186/s13007-019-0432-x) contains supplementary material, which is available to authorized users. Oryza sativa L.) is one of the major staple food in the world feeding over half of the world’s population [Cultivated rice  technologies has greatly improved the speed and accuracy of resequencing a large number of genomes, which facilitated the study of rice functional genomics and molecular breeding , 7. In aHyperspectral technology has been greatly applied in plant phenotyping including biochemical attributes such as estimating the canopy water content , assessiBiochemical contents are one essential rice seed parameter that is used for grading rice quality, and it was time-consuming, labor intensive and expensive to measure, so in order to achieve high throughput phenotyping for genetic studies on rice seed quality, such as molecular breeding programs and functional genome study, we attempted to investigate the possibility of using hyperspectral traits extracted from an ASD FieldSpec4 Hi-Res spectroradiometer for GWAS analysis to identify SNP markers and genes that are related to the represented biochemical traits in this research. To our knowledge, there are no published studies that have applied hyperspectral indices of any biochemical contents related to rice quality in GWAS.In our study, we attempt to extract hyperspectral indices representing biochemical contents that could be used for GWAS analysis, which had never been reported in any published research. The objects of this study were (1) to select hyperspectral indices that could represent the according biochemical trait, (2) using the selected hyperspectral variables as substitutions of biochemical measurements of rice to achieve high-throughput phenotyping for genetic studies and verify the results of GWAS on the extracted hyperspectral indices by comparing the identified SNP markers, Genes and pathways with those of biochemical traits. Eventually through this study, we hope to introduce a possible high throughput plant phenotyping method of biochemical contents that could be used in genetic studies based on hyperspectral technology.Seeds of eighty cultivated rice accessions (including 56 Japonica type rice and 24 Indica type rice) were grown in an experimental rice field at Rice Breeding Research Station in Jiaxing Academy of Agricultural Sciences, Zhejiang Province, China (N30°50′5″E120°42′59″). The rice field was allocated into 80 rice plots, with each rice variety grown in one rice plot. Rice seeds from five plants of each rice variety, 400 samples in total were collected for 9 phenotypic traits as designed , Zhejiang province, China, to measure 4 biochemical components that were important for rice quality determination basted on national rice standards NY/T593, including Crude Protein Content (PC), Amylose Content (AC), Gel consistency (GC) and Alkali Spreading Value (ASV) Table . The detAn ASD FieldSpec4 Hi-Res Spectroradiometer  with a range of 350–2500 nm was used to acquire hyperspectral data. The spectral resolution is 3 nm @ 700 nm, 8 nm @ 1400/2100 nm with sampling intervals (bandwidths) of 1.4 nm @ 350–1000 nm 1.1 nm @ 1001–2500 nm. Rice grains were put in a petri dish (diameter: 8 cm). The sensor of spectroradiometer was fixed vertically down to the opposite to the center of the sample by a detachable rack system and the height between the spectroradiometer sensor and rice sample in petri dish was 20.7 cm. The light source was a 50 W halogenate lamp, which was 27.4 cm in height and 60 degree from the sample surface. The details of the hyperspectral data acquisition system and the spectral data acquisition process are shown in Additional file Ical, Iraw, Iwhite and Idark represented calibrated reflectance intensity, original intensity, white reference intensity and dark current, respectively. Idark was collected by the spectroradiometer automatically; Iwhite was measured using a white Teflon tile with reflectance close to 100%. Data before 400 nm and after 2450 nm was removed due to the low signal-to-noise ratio before they were used for further analysis.The hyperspectral data process followed published protocols with minor changes –33. The Ra and Rb stand for reflectance of two different wavelengths in each formula, respectively. The optimal wave lengths were selected by the following procedure. Reflectance of two random wavelengths was used in the aforementioned formulas to calculate the value of SRI, NDSI and DSI respectively, until all the wavelength combinations were applied. The resulting SRI, NDSI and DSI were then subjected to Pearson correlation analysis. The index of the best performance (the highest the determination coefficient) was selected as the hyperspectral trait for the according biochemical component.After calibration, the data were applied for the following analysis. The average spectrum of all samples was extracted. Three indices including Simple Ratio Index (SRI), Normalized Difference Spectral Index (NDSI) and Differential Spectral Index (DSI) were induced for the correlation analysis and as a means to select the optimal wavelength combination for biochemical components. These three indices were used because a number of research had reported normalized difference vegetation index derived indices could be used to estimate biochemical components such as protein content of rice based on the hyperspectral data from rice canopy –37. The e stands for the sequencing error rate, Qphred represents the quality score of nucleotides.One fresh leaf from each rice variety was collected for next generation sequencing. Leaf samples were wrapped in aluminum foil and put in liquid nitrogen for 2 h, prior to being stored at − 80 °C overnight before re-sequencing. Sample Re-sequencing was performed on the Illumina HiSeq X Ten platform . Raw sequencing data was first processed with software Illumina Casava 1.8. Raw data was filtered for cleaner reads before further analysis. The filtering process includes the deletion of the adapter sequences, reads with over 10% N contents and reads with over 50% nucleotides whose quality score was lower than 10. The quality score of nucleotides was calculated using the following formula:Oryza sativa_IRGSP_1.0 was used as the reference genome which is available on the website of National Center for Biotechnology Information (NCBI). The sequencing depth, genome coverage, and other information of each sample were collected through the alignment process, and mutations were called.The BWA software  was usedThe detection of SNPs was achieved mainly using GATK  softwareA neighbor-joining tree of all rice accessions was constructed using MEGA5 software  based onQ stands for the population structure calculated using admixture software, K stands for kinship of samples from SPAGeDi software. X is the genotype while y stands for phenotype. The genome-wide significance thresholds of all tested traits were evaluated with Bonferroni correction:n stands for the effective number of independent SNPs. Bonferroni correction was applied here to control the type I error genome-wide. The P value threshold for significance in the Oryza sativa population was set to be p = 3.788e−09 and p = 3.788e−09  for the studied population. In this study, only the associations that exceeded the significant P-value threshold were considered. The extent of local LD was evaluated for each selected significant SNP to determine the interval of each locus.The resulted SNPs  ≥ 0.05) was used for the following GWAS with the selected biochemical and hyperspectral traits. The GWAS analysis was performed using the mixed linear model (MLM) of TASSEL software . The forFunctional annotation analysis of genes in the associated regions was performed using different databases including NCBI non-redundant (NR), The Gene Ontology (GO), Clusters of Orthologous Groups (COG), Kyoto Encyclopedia of Genes and Genomes (KEGG) Pathway analysis. A gene was annotated based on the principle that at least 2 databases provided the annotation description. Further validation of candidate genes was obtained by manually screening based on published research and gene function descriptions of the aforementioned databases.Table ASV and AC are two of the multidimensional characteristics relating to rice grain quality that has been used worldwide in rice breeding and process technologies. The degree of degradation test was evaluated visually by inspectors which was graded by a range of scores from 1 to 7. Since a number of the ASV scores of the rice collection reached maximum measurement limit, which was 7, the distribution of ASV value was not normalized and heavily skewed, thus not suitable for Pearson Correlation analysis. Therefore, it was not selected for the following Pearson correlation analysis. ASV is the inverse indicator of the gelatinization temperature (GT) of rice starch granules , which iSRI2 = 0.21, RNDSI2 = 0.21 and RDSI2 = 0.26 for GC; RSRI2 = 0.24, RNDSI2 = 0.24 and RDSI2 = 0.31 for AC), while PC showed high determination coefficient with all three indices, especially NDSI RNDSI2 = 0.68. Therefore, NDSI was selected for the final GWAS analysis as a hyperspectral trait for PC. The correlation between hyperspectral data and biochemical traits of AC and GC were low (R2 < 0.6). This might be because that due to a relatively small sample size and large dispersed data set of AC, the correlation between hyperspectral traits and AC became low. In order to construct a hyperspectral index that could be applied for AC, a bigger sample size would be selected in the future. In addition, because the GC is a complex trait and the nature of the GC data set was not a measurement of the content of a certain chemical/compound, but the length of flow distance [Overall, the data size of hyperspectral data from the spectrometer was 6.5 MB. Based on the summary of Pearson correlation analysis of GC, AC and PC with all three hyperspectral indices shown in Table distance , which mdistance . There idistance , 50. At distance –53.TableNDSI2 = 0.68)  Fig. b.Fig. 3TSequencing results showed that approximately 12-fold coverage was achieved, generating a total of 419.53 Gbp clean data, with Q30 up to 94.65%. Detailed sequencing data statistics was listed in Additional file 2) dropped to half its maximum value, was applied to evaluate the linkage disequilibrium. The longer LD50 indicated a smaller chance of gene recombination [The neighbor-joining tree of all rice varieties is shown in Fig. bination . On averbination . Howeverp = 3.788e−09 was used to identify SNPs relating to selected traits PC and NDSI. Manhattan plots and quantile–quantile plots for other traits were shown in Additional file The threshold of SAS3 and EL5, respectively  for S-adenosyl-l-methionine synthetases (SAMS) on chromosome 1 was previously recorded to be important for histone H3K4me3 in rice, because it regulates the expression of genes related to flowering development by DNA methylation. By knocking down SAS3, the expression of the flowering key genes including Early heading date 1 (Ehd1), Hd3a and RFT1 (rice FT-like genes) were greatly decreased, which lead to severe late flowering. This might cause decreasing of rice milking stage, which was important for the accumulation of seed nutrition including rice protein content [EL5 belongs to an ATL family gene, which is characterized by a transmembrane domain at the N-terminal and a RING-H2 finger domain (RFD). Koiwai et al. [SAS3  content . Meanwhii et al. , 61 repo2 < 0.6) which indicates a relatively low correlation with each other. These LD regions indicated relatively strong inheritability with their traits accordingly, which might not be due to LD block effects.LD block heatmaps based on the LD of each identified SNP loci are shown in Fig. glx-1, a glyoxalase gene, could express protein OsGlyI, which might be relating to improving abiotic stress tolerance and grain yield in rice [ORR2 was reported to cause rice morphology variation and cytokinin metabolism [Potential candidate gene loci that could be related to PC content based on KEGG annotation, GO annotation and NR annotation (NCBI) were summarized in Table  in rice . During tabolism .Table 5SbHLH genes in the rice genome. These conserved TFs have a diverse variety of functions in many plant signaling processes that regulates the expression of functional proteins involved in different biological processes including cell proliferation and differentiation [bHLH142 played an important role in pollen development, which could potentially affect the flowering date and the development of grains. According to Liu, the flowering time was associated with rice seed protein content [bHLH-150 were evidently down-regulated 10–25 and 15–35 days after anthesis [bHLH-150 in regulating the accumulation of rice storage protein. It indicates that SNP locus sf017837287 identified by NDSI but not PC is related to rice protein content. To further validate this result, a gene function analysis of bHLH-150 in rice would be conduct in the future studies. However, this further illustrates the promising potential of hyperspectral traits in GWAS study which is rapid to acquire and can identify promising genes while biochemical traits could not. The detailed gene annotations were listed in Additional file The basic helix-loop-helix (bHLH) proteins, a superfamily of TFs, are one of the largest TF families in plants, which includes 177 ntiation , root dentiation , mineralntiation  and seedntiation , etc. Inntiation  it was f content . Most inanthesis . This reOs01g0293000) in NCBI gene bank was annotated to be related to the biosynthesis of amino acids. Gene function analysis of genes identified by NDSI but not detected by PC on chromosome 1 position 7837287 was able to identify annotated gene bHLH-150 which was reported to be involved in the regulation of grain storage protein, which indicates that NDSI could possibly serve as a substitute of PC and identify more genes than PC involved in rice protein content in GWAS.Kegg annotation histogram shows that traits PC Fig. a and NDSThe distribution of pathways and gene loci that were identified by PC and NDSI based on Kegg database were summarized in the Venn diagrams in Fig. Traditionally, it is time-consuming and labor-intensive to acquire most of the biochemical component traits, but using spectroradiometer we not only obtained standardized phenotypic traits accurately but achieved high-through, which could be applied to keep up with the advancing speed of genotyping , 10. SinIn the future study, more hyperspectral traits representing different biochemical traits, such as starch, components relating to rice fragrance and texture, need to be extracted for GWAS analysis to improve application of the SNP identification process. Meanwhile, more gene function analysis of GWAS on hyperspectral traits are needed to fully address the effect of hyperspectral traits in genetic studies. Other information related to this research is listed in Additional files In this study, we tried to apply high through-put spectroradiometer hyperspectral data to extract hyperspectral traits that were highly related to biochemical attributes for rice quality. One resulted hyperspectral trait NDSI was used for GWAS as an alternative for rice protein content to investigate the possibility of using hyperspectral trait for genetic study. The results showed that the application of hyperspectral trait NDSI had the potential to identify the same genes/pathways as PC and in addition, NDSI detected one more SNP locus that is related to grain protein content which could not be identified by PC. In conclusion, hyperspectral traits have the potential to be applied to GWAS as an alternative to traditional time-consuming and labor-intensive biochemical component measurements, which could greatly improve the phenotyping speed and decrease bias caused by human operation for genetic study. This research provides a potential new method to phenotype biochemical traits of rice for genetic studies based on the hyperspectral technology.Additional file 1: Table S1. Information of all rice accessions.Additional file 2: Fig. S1. The setting of the hyperspectral data acquisition system.Additional file 3: Table S2. Summary of re-sequencing results.Additional file 4: Fig. S2. LD decay of all rice accessions.Additional file 5: Fig. S3. GWAS results of other traits.Additional file 6: Table S3. Summary of gene annotation.Additional file 7: Table S4. Measurements of biochemical traits.Additional file 8: Table S5. MAF of all identified SNPs.Additional file 9: Fig. S4. Distribution of reflectance for signal-to-noise ratio.Additional file 10: Fig. S5. The distribution of accumulative SNP depth.


We propose FEATHER, a method for fast permutation-based testing of marker sets and of heritability, which properly controls for false-positive results. FEATHER eliminated 47% of methylation sites found to be heritable by the parametric test, suggesting a substantial inflation of false-positive findings by alternative methods. Our approach can rapidly identify heritable phenotypes out of millions of phenotypes acquired via high-throughput technologies, does not suffer from model misspecification and is highly efficient.Testing for association between a set of genetic markers and a phenotype is a fundamental task in genetic studies. Standard approaches for heritability and set testing strongly rely on parametric models that make specific assumptions regarding phenotypic variability. Here, we show that resulting  p-values. Here, the authors develop a fast method for permutation-based testing of marker sets and of heritability that does not suffer from model misspecification.Standard approaches for heritability and set testing in statistical genetics rely on parametric models that might not hold in reality and give inflated  A similar notion to heritability has been tested in other fields as well, beyond genetics. For example, in metagenomics, it is a common practice to test for an association between a phenotype and the relative abundance vector obtained from either shotgun sequencing or targeted 16S sequencing11. Heritability is commonly studied using the linear mixed model (LMM); this model is a linear model that implicitly assume a very small effect for each of the SNPs12.One of the most fundamental problems in genetics is testing whether a particular phenotype is associated with a set of markers. For instance, it is often desired to understand whether a specific phenotype is heritable. The heritability of a phenotype is defined as the proportion of the variance explained by a genetic component. In this example, the set of single-nucleotide polymorphisms (SNPs) that are tested for association with the phenotype includes the entire set of SNPs of the genome; when local heritability is tested, then the set of SNPs includes the SNPs in particular regions such as chromosomes or with a particular functional annotation. Furthermore, these variants are often tested against a large number of phenotypes, such as expression profiles of genes16. Set testing is especially important when analyzing data with rare variants. Rare variants are becoming widely available, with sequencing costs rapidly decreasing, resulting in many whole-genome sequencing studies. Rare variants are particularly important since a large part of human genetic variation can be explained by these variants.Naive association testing of single markers may be extremely underpowered, even in large datasets. The common technique to address this issue is set testing, which groups together markers and applies a joint test to them17). However, there is no guarantee that a sufficiently good transformation exists, and the dependency on the parametric model may not be robust to other types of model deviations.The success of the LMM depends on the degree to which it fits the data. For example, the LMM assumes the phenotype follows a normal distribution. However, phenotypes which are discrete, multimodal, bounded, truncated, or in general whose residuals, after adjusting for covariates, do not exhibit normality, might not be suitable for use with the LMM. The same argument holds for generalized LMMs (GLMMs), which replace the normality assumption with other parametric distributions. To mitigate such issues, one can attempt to pre-process the phenotypic values to make them as Gaussian as possible , re-estimate the heritability of each shuffled dataset, and compute the proportion of permutations for which we got a higher heritability value than the original estimate. This offers an intuitive notion of significance, which has little dependency on the underlying distribution of the phenotype.Our goal is to develop a practical and globally applicable test for existence of heritability, which will apply to the test statistic calculated via the LMM mechanism, whether or not the LMM assumptions actually fit the data well. Permutation testing is a non-parametric, assumption-free method for testing the null hypothesis of sample exchangeabilityp-values of 1/M requires 100M permutations19. Contemporary QTL studies3 often carry out hundreds of thousands (or more) of tests, calling for p-values smaller than, e.g., 0.05/100000 to establish significance after multiple testing correction. Thus, permutation-based testing of such studies will require on the order of 109 permutations, a formidable task.Unfortunately, permutation tests are computationally demanding, requiring the calculation of the test statistic for each permuted dataset. As a rule of thumb, accurate estimation of 16 or without such assumptions21. This approach was extended to be used in association with multiple traits22. A less restrictive permutation scheme was used in23 to test whether the distribution of survival endpoints varies among centers in an acute myeloid leukemia multicentre study, using the LMM for analysis. More generally, permutation and other nonparameteric bootstrapping schemes have been used to calibrate various statistics suggested for testing for a nonzero variance components in GLMMs. In ref.24, an alternative statistic based on the score test is suggested, with a corresponding non-permutation-based parametric bootstrap test. Other works follow a similar permutation procedure to the one presented in this work, but apply it to a newly suggested T-based statistic20 or to particular quadratic forms of the phenotype25. In9, one of the considered permutation tests is similar to ours, but they do not address computational issues, which limits their ability to detect small p-values.Previous works suggest permutation procedures as a way to calibrate the distribution of a statistic of choice, in the context of LMMs. For example, permutations are used to calibrate the likelihood ratio (LR) test statistic, assuming its distribution comes from a limited family of distributionsp-values calculated by assuming the parametric LMM. We analyze methylation measurement profiles from the longitudinal KORA study , and gene expression profiles from the GTEx project. We show that large discrepancies exist between the two tests. In particular, p-values from the parametric test are often much smaller than those obtained from the permutation test. We show that this likely stems from model mis-specification of the LMM, which suggests a large majority of methylation sites or expression profiles with seemingly significant heritability are in fact false positives, motivating the use of permutation tests.In this paper, we study the behavior of the permutation test compared to the p-value evaluation procedure26 based on the Stochastic Approximation Markov Chain Monte Carlo (SAMC) algorithm28, which allows us to estimate the significance of a heritability estimate with a fraction of the number of permutations required by the naive method. We apply our approach to the KORA dataset, to achieve a speed up of up to eight orders of magnitude in p-value calculation.We then propose a fast method for permutation testing for heritability and for set testing. To do so, we address two issues. First, for each permutation, we speed up evaluation by using the derivative of the likelihood of the permuted phenotype instead of a full estimation step. Second, we use an efficient y, the LMM assumes y = Xβ + g + e, where Xβ is the contribution of covariates, K is a kinship matrix capturing the genetic relatedness between individuals in the sample, which can be constructed in various ways, using genotypes or known familial relations. Heritability is then defined as For a phenotype p-value calculation  is to calculate the generalized likelihood ratio test statistic, and to assume it is distributed as a 50:50 mixture of zero and the chi-square distribution (see Methods). Other distributions are sometimes used16, as we discuss below. An alternative test, usually used in the context of set testing, is the score test for 30. The distribution of the SKAT test statistic is assumed to be a certain weighted mixture of chi-square distributions.Under the LMM, the common technique for parametric N = 1,000,000). This gives us an estimate of the p-value of the test under the model, for which we can construct accurate confidence intervals (CIs). One appealing property of the permutation test is that it is an exact test under the assumption that the true model for the data is invariant to relabeling of individuals, which holds specifically if the trait is non-heritable, and holds approximately when non-constant covariates are used, in a wide range of settings. For example, if we decide that a p-value of < 0.001 is our threshold for proclaiming a phenotype as heritable, then we will falsely label non-heritable phenotypes as heritable about 0.1% of the time.To avoid model mis-specification or relying on an asymptotic distribution of the test statistic, we consider the permutation test. In the context of heritability, it consists of permuting the phenotype, estimating the heritability for each permuted phenotype, and counting the proportion of permutations for which the estimate obtained was higher than that of the original phenotype (see Methods). In practice, we do not enumerate over the entire set of permutations, but rather sample random permutations , which consists of subjects from the general population living in the region of Augsburg, southern Germany. In this dataset, both whole-blood methylation levels and genotypes are available for 1799 individuals (see Methods). The phenotype in this study is the proportion of methylated samples at a specific site, averaged across cells. These proportions are often empirically bimodal for a given site, and their values are bounded between 0 and 1, and thus it is not clear that an assumption of normality or near-normality is suitable here.We compared the 5 and references therein). For example, heritable methylation sites were previously shown6 to be enriched for open chromatin regions and binding sites of regulators of transcription and chromatin architecture, and to be proximal to genes enriched in several known pathways, suggesting a potential regulatory mechanism through which genetic variation can affect phenotype.Several works have studied heritable DNA methylation effects and the role of such epigenetic variants in disease and genetic regulation  and using a permutation test with 10,000 permutations, using only an intercept covariate (see Methods). We observed that parametric p-values are often considerably smaller than the exact p-values obtained by the permutation test, frequently by several orders of magnitude, and thus they may incur false-positive findings , the discrepancy was less than 1 order of magnitude smaller, which can be accounted for by noise in p-value estimation. The remaining 19 sites showed discrepancies below 2 orders of magnitude, and 14 of them exhibit a tri-modal behavior. The results are summarized in Table Finally, to check for opposite discrepancies, we took the 6686 sites with permutation 31, and sex. Gene expression profiles were quantile-normalized before analysis (see32). As evident in Fig. p-value obtained from 10,000 permutations32. This exemplifies the need for a fast and accurate permutation testing procedure.In order to show the generality of the discrepancy phenomenon, we analyzed gene expression data in the GTEx dataset (see Methods). We first performed a cis-eQTL study, where for each of 22,171 genes, we created a kinship matrix from the SNPs located within 500 kbps from the gene transcription start site . For each gene, we used both the parametric and the permutation tests to test for association between the SNPs in the window and the gene expression profile, as measured in whole-blood samples. We used the same covariates used in the original GTEx study—namely, the first three genotyping principal components (PCs), the first 15 expression PEER factors p-value discrepancies, when permutation p-values did not detect significantly heritable expression profiles, while parametric p-values did. Further analysis showed that all profiles with significant parametric p-values obtained a heritability estimate of 33, so such discrepancies are expected. This presents another scenario where parametric p-values are not calibrated.In addition, we performed a heritability study over the same data, where now the set of tested markers includes the entire genome. We still observed p-value discrepancies. The analysis is given in Supplementary Note p-values, finding that it did not eliminate the discrepancies, and introduced a potential power loss , as well as sites empirically showing a multimodal behavior. However, p-value discrepancies remained. Fifth, we examined whether this discrepancy exists when using the score test instead of the LR test. We note that using the SKAT method30 to calculate p-values, we found that it generated significantly deflated p-values throughout the dataset, indicating that the statistic distribution is not calibrated35. Using RL-SKAT35 to calculate calibrated p-values, we observed the same discrepancies , we address these two considerations in turn, beginning with the task of speeding up the evaluation performed for each random permutation.Running time is a major obstacle to performing permutation tests. First, for each permutation, finding the heritability estimate of the permuted phenotype is a computationally intensive task. Second, in order to accurately estimate small H2. However, we are not in fact interested in the estimated heritability value of the permuted phenotype, but rather only if it is smaller or larger than that of the unpermuted phenotype. Recall that REML obtains the heritability estimate which maximizes the (restricted) likelihood of the permuted phenotype as a function of the suggested heritability value. Consider the derivative of the likelihood function at the point H2. Assuming the likelihood function is well behaved, this derivative points us to the direction of the maximum: If the derivative is positive, then the maximum is obtained at a value larger than H2, and conversely if it is negative  time. Moreover, the core of the computation is a single matrix-by-vector product, an operation enjoying an efficient implementation in existing software and hardware36, and thus a small constant factor (see Methods). The savings in computation complexity depend on the heritability estimation algorithm used in the naive approach. For example, when using the AI or the EM algorithms, as in GCTA29, the computational complexity is O(n3), which gives our approach a speed up factor of O(n). With approaches that utilize the eigendecomposition, such as pylmm37 or FaST-LMM38, the asymptotic complexity is the same; However, we still get a significant empirical speed up as a result of avoiding many evaluations of the likelihood functions. In practice, on the KORA dataset, we observed a speed up of four orders of magnitudes per permutation of the derivative-based approach compared to full estimation using the widely used GCTA tool, and an order of magnitude improvement compared to FaST-LMM  algorithm27. We give an overview of the method and its properties here. For the full description, see Supplementary Note A major computational hurdle of permutation testing is the potentially large number of random permutations that need to be used in order to estimate small H2, we want to calculate its p-value, i.e., the probability a randomly permuted phenotype obtains a higher heritability estimate. We divide the interval  to D + 1 intervals, where the interval  is divided into D equally sized intervals, and  is an additional interval. This induces a partitioning of the permutation space to D + 1 subsets. Each subset is the set of permutations of the phenotype for which the estimated heritability value falls in the corresponding interval. Then, the p-value is exactly the size of the subset corresponding to , divided by n!, the number of permutations of size n.In the context of heritability testing, we utilize SAMC as follows. Given an estimate 39, which ensures that the estimates can be improved continuously as the simulation goes on. Importantly, the number of random permutations required for convergence is much smaller than the estimated p-value.The SAMC algorithm estimates the size  of each subset in the partition. Starting with an arbitrary initial permutation, each SAMC iteration consists of two steps: (1) Given the current random permutation, sample a new random permutation according to a certain target distribution, using the Metropolis-Hastings (MH) sampling algorithm; (2) Given the subset in which the new permutation falls, update the partition probability estimates, and the target distribution of step 1. The update rule for subset probability estimates follows the stochastic approximation algorithmp-value.Additionally, in order to determine in which subset a permutation falls, we need not calculate the heritability estimate of the respective permuted phenotype. Instead, we can check the derivatives at the endpoints of the interval. If the derivative is positive at the left endpoint and negative at the right endpoint, then we know a maximum exists within that interval. Using the derivative allows us to avoid the heritability estimation step, as before. When the algorithm converges, its estimate for the last subset will be our estimate of the We implemented both the simple and SAMC derivative-based permutation testing, as an efficient, multi-threaded C++ program. The fact that only few of the values of the random permutation change between successive iterations allows SAMC to be faster than the standard permutation testing, per permutation , switch to SAMC for estimating the p-value for the remaining sites.SAMC requires using a minimal number of permutations before convergence. Therefore, given a large set of phenotypes for which we wish to test for heritability, we suggest the following scheme. First, perform simple (non-SAMC) permutation testing with a small  number of permutations. Filter out all sites whose permutation 40. However, under the mild conditions considered here, the probability of false positives will remain calibrated, although the test may be underpowered. Indeed, any statistic that captures a correspondence between a phenotype and genetics will be suitable here.One advantage of the permutation approach is that it allows using certain statistics while overlooking otherwise important methodological caveats. For example, it is known that using the REML estimator for ascertained case-control studies leads to incorrect estimates30, or the PCGC regression40 statistic.We note that our use of SAMC is also independent of our choice of the REML estimator as the statistic. Indeed, any other statistic, for which it is possible to determine in which region of a partition the statistic of a permuted phenotype falls, can be used. Natural candidates are the score test statisticOne critical issue that is not covered by our current approach is the limitation to one variance component. Many applications currently use LMMs using multiple variance components, specifically by dividing the genome into regions and constructing a variance component from each region. In those cases, the contribution of each variance component is then estimated or tested for being significant. Estimating multiple variance components with REML is computationally intensive, and the derivative does not appear to lend itself to a simple analytical expression as in the single variance component case. However, as PCGC regression provides an alternative, faster estimation method, using its statistic is a particularly attractive avenue of research in the context of multiple variance components.41, thus avoiding the cubic complexity. A natural extension of our proposed method is to derive a procedure that calculates the derivative of the restricted likelihood function using conjugate gradient methods. Such a procedure could result in a quadratic complexity, as it avoids the eigendecomposition.Typically, a preliminary step in heritability estimation is the eigendecomposition of the kinship matrix. This procedure is not very efficient, as it is cubic in the number of individuals, and may therefore be too computationally inefficient for large datasets that include many individuals. Recently, it has been suggested to use conjugate gradient methods in order to estimate heritability26. Preliminary results appear encouraging, but a more thorough study of this tradeoff remains a direction for future research, as well as other variants of SAMC42.One disadvantage of SAMC is that, unlike the simple permutation test, it has to be run sequentially. However, it is possible to run multiple shorter chains simultaneously, each with a less strict convergence criteria, and then to aggregate the results in order to obtain a more accurate estimate43.Finally, the ideas presented here can be readily extended to the testing of genetic correlations, which determine if there is evidence that two phenotypes have common underlying genetic drivers 33 and the SAMC algorithm.For clarity of presentation, we begin by defining the heritability under the LMM. We then introduce our improved method for fast permutation testing for heritability, while reviewing relevant results from the ALBI method44. Let n be the number of individuals  and let y be a n × 1 vector of phenotype measurements for each individual. Let X be a n × p matrix of p covariates, associated with fixed effects . Let β be a p × 1 vector of fixed effects. Let Z be a n × m standardized  genotype matrix containing the m SNPs we test. Finally, let K be a kinship matrix, which can be taken to be any symmetric positive-definite matrix that encodes similarity between individuals, using any biomarkers, e.g., a set of SNPs. A standard choice for K is a weighted dot product12; formally, define K = ZWZT, where W is a non-negative m × m diagonal matrix assigning a weight per SNP .We first present the standard variance components modely is assumed to follow:Then, β and the coefficients The fixed effects 45:The narrow-sense heritability due to genotyped common SNPs is defined as the proportion of total variance explained by a genetic componentDefining mentclass2pt{minimh2 is REML estimation. REML consists of maximizing the likelihood function associated with the projection of the phenotype onto the subspace orthogonal to that of the fixed effects of the model46. The logarithm of the REML function is, up to additive and multiplicative constants:The most common way of estimating K are zero or near-zero. This occurs, for example, when K is constructed from a mean-centered Z, in which case the constant vector 1 would be an eigenvector with the eigenvalue 0. Another example is when Z has fewer SNPs than samples, in which case K will be low rank. When this is the case, the likelihood at h2 = 1 may be undefined or prone to numerical instability. To avoid this, we project both the phenotype and covariates to the subspace spanned by eigenvectors corresponding to nonzero eigenvalues. Let U be the matrix whose columns are the eigenvectors of K, and let di be the eigenvalues of K, for i = 1,…,n. If there are z eigenvalues larger than a sufficiently small threshold, denote by Uz the matrix with the first z eigenvectors. Effectively, this amounts to replacing In practice, often some of the eigenvalues of The common way to test for the statistical significance of a nonzero heritability value is using the generalized restricted likelihood ratio test statistic48.p-value of the full permutation test is calculated by enumerating over all permutations to calculateMonte Carlo permutation testing: The π(y) is the application of the permutation π on the phenotype y, and Sn is the set of all permutations of n elements. This is an exact test—that is, under a null hypothesis invariant to permutations, pperm is distributed uniformly. However, since the number of permutations, n!, is huge, the common approach is to employ a Monte Carlo approximation. In detail, let π1,…,πN be N random permutations of n elements; the p-value of the test is:where p-value pMC is an approximation of the required p-value pperm. Moreover, since each permutation was chosen randomly and with replacement, pMC can be seen as the result of a binomial experiment. Therefore, we can calculate accurate confidence intervals for pperm given pMC, e.g., using the Cloppe–Pearson method49.The X = 1n), then the permutation test does not require taking covariates into consideration. In the general case, we apply the same permutation on each covariate vector as we do on the phenotype. We note that the permutation approach requires exchangeability of the residuals, which are not observed in general in presence of non-constant covariates in the model. However, we verified in simulations that the test remains exact or approximately exact under various settings; this is theoretically supported in recent works on permutation tests in linear regression52. See Supplementary Note Covariates: If there are no covariates, or the only covariate is the constant vector , the estimation of its heritability using REML, The naive calculation above requires, for each permuted phenotype 33, it is shown that when X = 1n, checking if u = UTπ(y), and checking ifInH2. Therefore, assuming the restricted likelihood function is well behaved, a positive derivative indicates that the REML heritability estimate is larger than H2. Similar expressions are defined for a general X in33.entclass1pt{minimaK is obtained, calculating pMC may be performed in a time complexity quadratic in n:y and its heritability estimate H2, calculate O(n)).Given π1,…,πN Sn (complexity: O(nN)).Draw t = 1,…,N:ut = UTπt(y) (complexity: O(n2)).Calculate bt = 1 if bt = 0 otherwise (complexity: O(n)).Let For O(N)).Return Therefore, once the eigendecomposition of O(n2N). For a general covariate matrix X, the only change will be in the condition checked in step (b), whose complexity is O(np2 + p3) instead of O(n), resulting in a final complexity of O((n2 + np2 + p3)N), as detailed in33.The total complexity is p-value evaluation procedure based on the Stochastic Approximation Markov Chain Monte Carlo (SAMC) algorithm27. A description of the SAMC algorithm and its tuning is given in Supplementary Note To cope with the major computational hurdle of permutation testing, we use an efficient q define the probability of choosing a new permutation τ, given that the current permutation is πt. Let D + 1 be the number of intervals in the partitioning of . For a permutation π∈Sn, let J(π) be the index of the interval in which Initialize a uniform estimate, π1.Choose a random initial permutation t = 1,…,T (or until convergence): πt + 1 by a single Metropolis-Hastings update, as follows:i.τ according to the proposal distribution q.Generate ii.Calculate the ratio iii.r). If accepted, set πt+1 = τ. Otherwise, set πt+1 = πt.Accept the proposed move with a probability of min .Update the estimates: For For Return In summary, let the proposal distribution n = 1799 individuals from the general population living in the region of Augsburg, southern Germany53. The measured phenotype is the proportion of methylated samples at a specific site, averaged across DNA samples of an individual. We used whole-blood samples of the KORA F4 study, as described elsewhere54. Briefly, DNA methylation levels were collected using the Infinium HumanMethylation450K BeadChip array (Illumina). Beta Mixture Quantile (BMIQ)55 normalization was applied to the methylation levels. Further processing was performed as in ref.56; briefly, genotyping was performed with the Affymetrix 6.0 SNP Array , with further imputation using HapMap2 as a reference panel. A total of 657,103 probes remained for the analysis. In summary, a total of 431,366 methylation site phenotypes, and 657,103 SNPs, were available for analysis. Covariates used in this study are age, sex, and smoking status.The KORA project studies 52 Project is a US National Institutes of Health (NIH) Common Fund project that aims to collect a comprehensive set of tissues from 900 deceased donors  and to provide the scientific community with a database of genetic associations with molecular traits such as mRNA levels. We used 22,171 gene expression profiles obtained from whole-blood samples of 338 individuals, as preprocessed and using the same covariates as described in32.The Genotype-Tissue Expression (GTEx)29 and pylmm57. We used the C++ implementation of FaST-LMM, FastLmmC v2.07.2014072338 and calculated the kinship matrix and its eigendecomposition in advance using the -eigen flag. We only considered the GWAS analysis but not the data loading time, as reported by FaST-LMM.We used GCTA version 1.26https://github.com/cozygene/feather.FEATHER is available at Supplementary InformationPeer Review file


We developed the high resolution MAGIC wheat population WM-800, consisting of 910 FRht-B1 and Rht-D1 and a potentially novel QTL on chromosome 5A. Additionally, epistatic effects controlled plant height. For example, two loci on chromosomes 2B and 7B gave rise to an additive epistatic effect of 13.7 cm.Genotyping WM-800 with 7849 SNPs revealed a low mean genetic similarity of 59.7% between MAGIC lines. WM-800 harbours distinct genomic regions exposed to segregation distortion. These are mainly located on chromosomes 2 to 6 of the wheat B genome where founder specific DNA segments were positively or negatively selected. This suggests adaptive selection of individual founder alleles during population development. The application of a genome-wide association study identified 14 quantitative trait loci (QTL) controlling plant height in WM-800, including the known semi-dwarf genes The present study demonstrates that plant height in the MAGIC-WHEAT population WM-800 is mainly determined by large-effect QTL and di-genic epistatic interactions. As a proof of concept, our study confirms that WM-800 is a valuable tool to dissect the genetic architecture of important agronomic traits.The online version of this article (10.1186/s12864-018-4915-3) contains supplementary material, which is available to authorized users. Triticum aestivum L., 2n = 6× = 42, AABBDD) is one of the three most important crop species globally, with a world production of more than 710 million metric tons [Arabidopsis [Bread wheat  genes controlling the gibberellic acid (GA) pathway in wheat, served as a catalyst for the green revolution [Rht-B1 on 4B and Rht-D1 on 4D represented major sources to achieve reduced plant height in European wheat breeding programs since the 1960s. This resulted in markedly increased grain yields in most environments [Rht8 is widely used in dry environments of Southern and Eastern European environments [Rht4, Rht5, Rht6 [Rht7 [, Rht9 [Rht11 [Rht12 [Rht13 to Rht20 [Plant height is a key trait in wheat as it affects grain yield, grain quality  and pathFusarium . The intvolution . The semronments . Furthert5, Rht6 , Rht7 [2t6 [Rht7 , Rht9 [2 [, Rht9 , Rht11 [9 [Rht11 , Rht12 [1 [Rht12 , Rht13 tto Rht20 , howeverRht genes, several genetic regions were identified by QTL analysis investigating plant height in various wheat mapping populations [Rht-B1 and Rht-D1, supporting the idea that these two genes are widely used in modern wheat breeding to control plant height.In addition to the known ulations , 26, 27.Epistasis, the genetic interaction between independent loci, is one additional factor known to play an important role in dissecting quantitative traits . EpistasIn this study, we report on the new MAGIC winter wheat population WM-800. WM-800 was characterized based on genotypic data derived from a 15 k Infinium iSelect SNP array. This data was applied to investigate genetic diversity, linkage disequilibrium, allele frequency and segregation distortion. We further proved that WM-800 is a powerful mapping tool by dissecting the genetic architecture of plant height. We also demonstrated that epistatic interactions play a significant role controlling plant height in WM-800.1 seeds: Patras x Meister (AB), Linus x JB Asano (CD), Tobak x Bernstein (EF) and Safari x Julius (GH). Single F1 plants of each 2-way cross were intercrossed, resulting in two 4-way crosses (ABCD) and (EFGH). Subsequently, 141 seeds of the 8-way cross (ABCDEFGH) were produced by Syngenta, where 56 seeds derived from intercrossing 18 4-way F1 plants (ABCD x EFGH) and 85 reciprocal 4-way F1 plants (EFGH x ABCD), respectively, to assure a balanced allele frequency for each of the eight founders. On average 15 selfed F2 seeds per 8-way plant were produced. These seeds were further advanced by single seed descent (SSD) to yield 2125 F4 recombinant inbred lines (RILs). Each WM line is expected to hold 12.5% of the genome of each of the eight WM founders. Altogether, 1323 WM lines were randomly selected and analysed with KASP marker on the presence of double dwarfism at KWS SAAT SE, Einbeck. Out of these, 935 RILs were not homozygous at both loci for the dwarfing allele Rht-B1 and Rht-D1 according to the KASP marker analysis. These were propagated (F4:5) for one round of bulk propagation to establish the MAGIC wheat population WM-800, which is composed of a final set of 910 RILs in F4:6.WM-800 was developed following the crossing scheme reported by Cavanagh et al. . The WM-2) in 2016. Subsequently, analysis of variance for plant height was carried out with SAS 9.4  using PROC MIXED to test for genotype and year effects. Least squares means (LSmeans) per genotype were calculated using PROC MIXED (SAS 9.4) assuming fixed genotype effects and random year effects. PROC VARCOMP (SAS 9.4) was used to estimate variance components. Broad-sense heritability (h2) was calculated applying the formula h2 = VG / (VG + VGY/y + VR/(y*r)), where VG, VGY and VR denote the variance components genotype, genotype by year and residual, respectively. Y and r denote the number of years and replicates per genotype, respectively.Bulk propagation of WM-800 RILs took place at Syngenta’s breeding station in Hadmersleben, Germany . Plant height (HEI) was measured in one replication on single plants in 2015 and in one replication in field plots . Infinium 15 k iSelect SNP array was used for genotyping. It contains 13,006 SNPs selected from the wheat 90 k SNP array [Ppd, Rht, Vrn-1 and Vrn-2.Bulked DNA from 12 FNP array , includiwww.wheatinitiative.org) and since a BLAST database of wheat genome assemblies, including Julius, is available (see webblast.ipk-gatersleben.de/wheat_ten_genomes/).Polymorphic SNP data was quality checked. SNPs with missing data > 10%, heterozygous genotypes > 10% and minor allele frequency < 1% were removed . The genPROC FREQ (SAS 9.4). Subsequently, Bonferroni-Holm correction of the p-values (pBon-Holm) was used for multiple testing with PROC MULTTEST (SAS 9.4) [Bon-Holm < 0.01 [The IBS-SNP matrix was used to calculate allele frequencies and segregation distortion (SD) for each SNP in WM-800. Bi-allelic SNPs do not follow a Mendelian segregation in an 8-way MAGIC population. The segregation ratio of the two alternative SNP alleles in the population depends on their frequency in the founder set. Thus, the SNPs were classified into seven allele frequency groups (AFG 1 – AFG 7), depending on the presence of the Julius allele among the founders. Segregation distortion within each AFG was estimated by chi-square testing, using SAS 9.4) . A chromm < 0.01 . AFG 1 aPROC DISTANCE (SAS 9.4) with method simple matching was used to calculate genetic similarity (GS) between WM-800 lines and their eight founders. Subsequently, population structure within WM-800 and their founders was investigated based on GS values applying a principal component analysis (PCA) with PROC PRINCOMP (SAS 9.4).Procedure 2) [2 values were plotted against the genetic distance according to [PROC LOESS (SAS 9.4). A population-specific background LD (r2) was estimated as the 95th-percentile of r2 values for unlinked markers [Linkage disequilibrium (LD) was calculated as the squared allelic correlation linkage (r2)  using thrding to . The sec markers .PROC GLMSELECT (SAS 9.4) including 20 times five-fold cross-validation. Stepwise forward and backward selection of significant SNPs was conducted with model selection criteria of p ≤ 0.001. SNPs were accepted as significant marker-trait associations (MTA) if they were included in the final model in at least 35 cross-validation runs (detection rate ≥ 35%) and if pBon-Holm < 0.01 after adjusting p-values for multiple testing with the Bonferroni-Holm procedure using PROC MULTTEST (SAS 9.4) [The multiple linear regression model “Model-A” was used to conduct GWAS mapping based on plant height LSmeans for each WM-800 line. The model  was succSAS 9.4) . MTAs wePROC MIXED (SAS 9.4) procedure including a five-fold cross validation based on LSmeans of WM-800 lines as input and a marker 1 by marker 2 interaction to test for fixed interaction effects including a forward selection procedure. At first, markers with a single marker probability below 0.15 were included in pairwise marker interaction analysis. Second, a forward and backward selection procedure was applied for all significant marker by marker combinations. A FDR corrected p-value of ≤0.01 was chosen as a significance threshold to accept the presence of an epistatic effect. Explained marker by marker variance was calculated by comparing the sum of squares of the respective M by M interaction to the sum of squares of the genotypes. Values are given in percent. Marker interactions were grouped to a single interaction if significant SNP interactions were placed in a window ≤7 cM. Subsequently, the additive by additive epistatic effect (aa) was estimated [Epistatic effects between SNPs were estimated with the stimated : aa =   in WM-800 was based on 7849 SNPs and revealed a low degree of genetic similarity among the eight founders, ranging from 51.6% (between Patras and Safari) to 65.5% (between Meister and Bernstein) with a mean GS of 58.1%. These results indicate the high level of diversity between the selected elite soft winter wheat cultivars originating from diverse European breeding programs. Genetic similarity between WM lines ranged from 44.7 to 97.2% with a mean of 59.7%  depending on the expected allele frequency of the Julius allele Table . Julius Segregation distortion (SD) is a common phenomenon in plant genome analysis and has been described in many species, like barley , 52, triBon-Holm ≤ 0.01 . Only four QTL explained more than 4% of the genetic variation. This indicates, that plant height in WM-800 is controlled by a small number of genes revealing strong effects and a larger number of genes exposing small effects. However, approximately 50% of the genetic variation remains unexplained. This hidden part of genetic control may point to an even larger number of additional genes with small effects. To locate these QTL, an increase of population size, marker density and number of tested environments may be necessary.The relatively low average genetic similarity of 59.7% between WM-800 lines, the strong phenotypic variation of plant height and its high heritability are promising features for a successful GWAS. Consequently, 14 highly significant QTL were estimated regulating plant height in WM-800 with p01 Table , Fig. 4.Rht-D1 and Rht-B1 on chromosomes 4D and 4B [Rht-D1) and 6.7% (Rht-B1) of the genotypic variance  and reduced plant height by − 14.9 cm (Rht-D1), respectively. These effects are in accordance with the expected effects inherited by the WM founders  concept proposed by Tuinstra et al.  and succ2 values ranging from 3.4 to 45.1%  of − 13.2 cm .The genetic structure of the multi-parental population WM-800 enables to conducted detailed studies on the genetic architecture of important agronomic traits in wheat, exemplified by plant height as a proof of concept. In the present study we demonstrated that plant height in WM-800 is mainly determined by large-effect QTL and di-genic epistatic interactions. The semi-dwarf genes Our first findings demonstrate the high value of WM-800 to support both - genetic studies to explain genetic networks regulating quantitative traits as well as breeding improved wheat cultivars. Regarding the latter aspect, we propose to evaluate WM-800 for direct selection of improved winter wheat cultivars. Both routes are currently followed up in our MAGIC-WHEAT consortium consisting of wheat geneticists and applied wheat breeders.Additional file 1Table S1. SNP genotypes, plant height, QTL detection rate and genotype and allele frequencies for 910 MAGIC WHEAT lines and eight founders. Table S2. Plant height (cm) raw data for MAGIC WM-lines and founders for year 2015 and 2016. Table S3. Distribution of polymorphic SNPs within WM-800 according to genome positions of Wang et al.... [Table S4. Mean, minimum, maximum and coefficient of variation  of linkage disequilibrium (r2) in WM-800, calculated per chromosome, subgenome and across the whole wheat genome. Table S5. Genetic similarity (GS) between founders and WM-800 lines based on 7849 polymorphic SNPs. Table S6. Principle Component Analysis (PCO) based on genetic similarities (GS) between founders and WM-800 lines. Table S7. Distribution of segregation distortion (SD) SNPs and segregation distortion regions (SDR) across the wheat genome and across allele frequency groups. Table S8. Selection of unique SNPs from AFG 1 and AFG 7 in WM-800. Major selection events, represented by > 10 SNPs, are indicated in bold. (ZIP 2660 kb)t al.... . Table SAdditional file 2:Figure S1. Linkage disequilibrium (r2) as a function of genetic distance (mean of whole genome) within WM-800. The horizontal line (0.02) indicates the 95th percentile of the LD distribution of unlinked pairs of loci, representing the population-specific critical r2 value. The curve (red line) was fitted with second-degree LOESS. (PNG 30 kb)


It is often assumed that selection (including participation and dropout) does not represent an important source of bias in genetic studies. However, there is little evidence to date on the effect of genetic factors on participation.N = 7486) and children (N = 7508) from the Avon Longitudinal Study of Parents and Children, we: (i) examined the association of polygenic risk scores for a range of sociodemographic and lifestyle characteristics and health conditions related to continued participation; (ii) investigated whether associations of polygenic scores with body mass index  and self-reported smoking differed in the largest sample with genetic data and a subsample who participated in a recent follow-up; and (iii) determined the proportion of variation in participation explained by common genetic variants, using genome-wide data.Using data on mothers  and depression were associated with lower participation. Associations between the polygenic score for education and self-reported smoking differed between the largest sample with genetic data [odds ratio (OR) for ever smoking per standard deviation (SD) increase in polygenic score: 0.85, 95% confidence interval (CI): 0.81, 0.89} and subsample . In genome-wide analysis, single nucleotide polymorphism based heritability explained 18–32% of variability in participation.Genetic association studies, including Mendelian randomization, can be biased by selection, including loss to follow-up. Genetic risk for dropout should be considered in all analyses of studies with selective participation. Polygenic scores for a range of sociodemographic, health and lifestyle factors are related to continued participation after enrolment in the Avon Longitudinal Study of Parents and Children.There was evidence that associations between polygenic scores and measured phenotypes differed between the full sample with genetic data and a more selected subsample, indicating that genetic association studies can be biased by selection.Common genetic variation explained a moderate amount (18–32%) of variability in participation.Researchers should consider selective participation as a potential source of bias in genetic and non-genetic association studies.,,Missing data are a pervasive problem in cohort studies, with decreasing participation over the duration of the study, and concern about the extent to which this biases analyses.,,,,Sample representativeness is critical for estimating prevalence of exposure or disease,,To estimate the impact of selective participation for a given analysis, we need to know which factors cause participation. Here, we extend previous work relating participation and polygenic risk for schizophrenia and autism in ALSPAC,http://www.bris.ac.uk/alspac/researchers/data-access/data-dictionary]. Ethical approval for the study was obtained from the ALSPAC Ethics and Law Committee and the local research ethics committees.ALSPAC is a longitudinal birth cohort that recruited 14 541 pregnant women resident in Avon, UK, with expected dates of delivery between 1 April 1991 and 3 December 1992. Of these initial pregnancies, there were a total of 14 676 fetuses, resulting in 14 062 live births and 13 988 children who were alive at 1 year of age. The children and their mothers have been followed up through postal questionnaires and at clinics.IJE online. From these, we calculated the following continuous phenotypes by summing the number of questionnaires/clinics completed: total participation [all questionnaires and clinics for both mother and child (including child-based and child-completed)]; total questionnaire ; mother questionnaire (mother questionnaires); child questionnaire (child-completed questionnaires); and child clinic (child clinics attended). We created two binary variables for the mothers and children indicating: (i) participation in the most recent clinic; and (ii) completion of the most recent questionnaire. For both mothers and the offspring, we generated variables from data collected at clinics 17–18 years after the child’s birth and from questionnaires 19–20 years after birth.Participation was defined by responding to a questionnaire or attending a clinic for which the whole cohort was eligible to participate (i.e. we excluded clinics and questionnaires targeted at a subset of the cohort). The ALSPAC mothers have answered questionnaires about themselves (mother questionnaires) and about their children (child-based questionnaires). The ALSPAC children have answered questionnaires about themselves (child-completed questionnaires). A full list of the questionnaires and clinics included is provided in IJE online).ALSPAC children were genotyped using the Illumina HumanHap550 quad chip genotyping platforms. ALSPAC mothers were genotyped using the Illumina Human660W-quad array at the Centre National de Genotypage (CNG), and genotypes were called with Illumina GenomeStudio. Imputation was performed using Impute V2.2.2 against the 1000 genomes phase 1 version 3 reference panel. Quality control procedures removed related individuals and individuals of non-European genetic ancestry  and the first 10 genetic principal components.http://prsice.info/]P-value thresholds: 0.0005, 0.005, 0.05, 0.1, 0.5 (see IJE online). In addition, we generated scores in PRSice by inputting only the independent genome-wide significant SNPs reported by the discovery samples (IJE online). We assessed associations of standardized polygenic scores with participation phenotypes using linear and logistic regression in Stata (version 14.1).Polygenic scores were derived using the PRSice software  ] . The ass, 0.89)] . In contIJE online). Genome-wide hits were all in strong linkage disequilibrium (R2 > 0.8), indicating that this represents a single genetic signal. The SNP with the smallest P-value was rs10626545 for total (P = 1.50 x 10–9) and total questionnaire (P = 8.55e-10), and rs406001 for mother questionnaire (P = 8.27 x 10–9). SNPs in this region reached genome-wide significance or close to genome-wide significance (P <7 x 10–7) with dichotomized total participation, total questionnaire and mother questionnaire (data not shown). However, the minor allele frequency of these variants was relatively low (0.012) and beta-coefficients large , suggesting that this association is driven by a few individuals.Only one locus reached genome-wide significance with participation in the ALSPAC mothers. In the mothers, variants located in an intergenic region on chromosome 7: 51995163–52042976 were associated with total participation, total questionnaire and mother questionnaire (IJE online). SNPs in the bradykinin receptor B1 gene (BDKRB1) (chromosome 14: 96721850–96729885) were associated with total participation, total questionnaire and child questionnaire. The SNP with the smallest P-value was rs28631073 for all three participation measures (P between 1.29 x 10–8 and 2.27 x 10–8) and the beta with total participation was −3.20. Two SNPs in an intergenic region on chromosome 1 reached genome-wide significance with child clinic participation: rs1336852  and rs74626786 . Plots showing linkage disequilibrium and nearest genes for each of the genome wide significant loci (created using LocusZoomIJE online).In the children, two loci reached genome-wide significance  (IJE online).Estimates of heritability of participation phenotypes from SNPs included in the genome-wide analyses ranged 20–27% for the mothers and 18–32% for the children .Our findings show that genetic variants which are related to specific phenotypes are also related to participation. Using a Mendelian randomization framework, this could imply that these phenotypes cause continued participation. For example, the polygenic risk score for education was the score most robustly associated with participation—implying that higher education causes greater continued participation in ALSPAC. This interpretation requires that the key assumptions of Mendelian randomization are met,P-value thresholds could explain more of the variance in that trait than genome-wide significant scores,P-value thresholds than those created using low P-value thresholds. We found traits for which genome-wide scores were not associated with participation, but scores at higher P-value thresholds were, for example depression. This could be explained by low power in the original GWAS, meaning that truly associated SNPs are less likely to be included in a score constructed using a low significance threshold,P-value threshold increases, this also introduces more noise into the polygenic scores and may explain why some scores at the P = 0.5 threshold are less strongly associated with participation than the scores created at lower thresholds.Polygenic scores created using higher We also showed that it is possible to introduce bias into genetic analyses even when sample sizes are relatively modest. Therefore, we cannot assume that genetic-association studies, including GWAS, candidate gene studies and Mendelian randomization, are not biased by incomplete participation. We recommend that researchers consider how likely non-participation is as a potential source of bias when running genetic association studies and acknowledge this when reporting findings. The same implications hold for non-genetic studies—e.g. a study of the association between education levels and BMI in a selected subsample is likely to be biased by selection, since our genetic results show that both exposure and outcome cause participation.For both genetic and non-genetic studies, there are potential methods to correct for this bias. For example, where there is some information about participants who have dropped out, it may be possible to apply inverse probability weighting.BDKRB1). Bradykinin is a peptide hormone which is a pro-inflammatory mediator and is involved in vascular permeability and mitogenesis.,We found three loci associated with participation at genome-wide significance level. SNPs in the genomewide locus in mothers (e.g. rs406001) were identified in a previous GWAS of post-traumatic stress disorder (PTSD), but not replicated in the original GWAS.There are a number of limitations to this analysis. First, our analysis sample was restricted to just over half of the enrolled sample, due to availability of DNA samples for GWAS and exclusion criteria . Individuals in the analysis sample had higher participation rates than the full sample, meaning that associations between polygenic scores and participation are likely to be weaker than we would observe if we had full genetic data for the whole cohort. Second, our results may not be generalizable to studies with different selection criteria or specific cultural or contextual factors influencing participation. It is also possible that characteristics influencing participation will change over time and with age. We have shown here that genetic associations can be used to shed light on the selection mechanisms operating in a given study, but this will need repeating in studies in different populations or with different recruitment mechanisms. These are context-specific, rather than biological associations—although there is evidence that some associations (e.g. with education) may be fairly replicable.In conclusion, we demonstrate that polygenic scores related to a wide range of traits are associated with degree of participation in ALSPAC, and that this may introduce bias into genetic and non-genetic analyses. This highlights the importance of considering selection bias in all studies, and the need for the development of statistical methods to account for this issue.The UK Medical Research Council and Wellcome (Grant ref: 102215/2/13/2) and the University of Bristol provide core support for ALSPAC. Funding from British Heart Foundation, Cancer Research UK, Economic and Social Research Council, UK Medical Research Council and the National Institute for Health Research, under the auspices of the UK Clinical Research Collaboration, is gratefully acknowledged. This work was supported by the UK Medical Research Council . This study was supported by the NIHR Biomedical Research Centre at University Hospitals Bristol NHS Foundation Trust and the University of Bristol. The views expressed in this publication are those of the author(s) and not necessarily those of the the MRC, Wellcome, the NHS, the National Institute for Health Research or the Department of Health.Supplementary DataClick here for additional data file.


The methods commonly used to test the associations between ordinal phenotypes and genotypes often treat either the ordinal phenotype or the genotype as continuous variables. To address limitations of these approaches, we propose a model where both the ordinal phenotype and the genotype are viewed as manifestations of an underlying multivariate normal random variable. The proposed method allows modeling the ordinal phenotype, the genotype and covariates jointly. We employ the generalized estimating equation technique and M-estimation theory to estimate the model parameters and deduce the corresponding asymptotic distribution. Numerical simulations and real data applications are also conducted to compare the performance of the proposed method with those of methods based on the logit and probit models. Even though there may be potential limitations in Type I error rate control for our method, the gains in power can prove its practical value in case of exactly ordinal phenotypes. The unknown parameters In this subsection, we construct a test statistic to test First, based on the marginal density function (11) of G and Y are ordinal variables, whose realizations are determined by the intervals in which the values of two standard normal random variables G and Y to intuitively estimate G and Y, respectively. Recall that Second, in our model both The parameter According to the delta method, Now, we can propose a new Wald test statistic for the null hypothesis https://doi.org/10.25387/g3.8226650.The authors affirm that all data necessary for confirming the conclusions of the article are present within the article, figures, and tables. Supplemental material available at FigShare: In this subsection, we present a series of simulation studies to investigate the performance of our proposed latent variable model (abbreviated as lvm), and compare it with the probit and logit models, which both regressing an ordinal phenotype on a genotype. We compared these under multiple simulation scenarios, so that different modeling assumptions would be favored. Two types of data generation mechanism were considered throughout our simulation studies: (i) generating data from a multivariate normal random variable (named the ND mechanism) and (ii) generating data under the proportional odds model (named the PO mechanism). In addition, three genetic models  were considered.Y is set to five. Under the ND mechanism, the three-dimensional latent variable G being a manifestation of Y being a manifestation of G varied according to the type of the true genetic model. Let A  and a  denote two alleles at the single biallelic locus corresponding to the genotype G. Under the Hardy–Weinberg equilibrium (HWE) conditions, the expected genotype frequencies of G being p taking on values from Y being θ, whose range was the set The specifics of our simulation data generation scenarios are as follows. For simplicity, the dimension of the covariate Y was related to the genotype G and covariate G under different genetic models would remain the same as that under the ND mechanism, regardless of whether the HWE held. In this case, Y was generated with five levels i.e., the lvm, probit, and logit models. When Under the PO mechanism, the ordinal phenotype https://www.r-project.org/). The empirical Type I error rates and power estimates were calculated using the percentage of rejection in each scenario. The results are presented side-by-side in Tables G amounting to 1 is three, which can easily lead to samples with all the G values being 0, such that none of the three considered models can be applied.As previously described, we considered G does not satisfy the HWE conditions. Specifically, the power gain can be as high as 0.07 when G is The results of the three methods under the ND mechanism when the HWE does not hold are presented in The corresponding results when the data are generated under the PO mechanism and the HWE is assumed are displayed in The simulation results under the PO mechanism when the HWE does not hold are presented in From all of the four tables, it can be seen that the proposed method might have potential limitations in controlling Type I error rates in a few situations, while the power gains in almost all of simulation scenarios indeed indicate its efficiency for practical applications.It is well known that rheumatoid arthritis (RA) is significantly associated with some genetic variants . The aimNote that there are a total of 45 SNPs in the region of 6p21.33 according to the Genetic Analysis Workshop 16 Data, all of which meet the quality control rule of the MAF being more than 5%, the missing rate being smaller than 15%, and the least genotype frequency being no less than five. The anti-CCP measure takes four values, 1, 2, 3, and 4, and the number of subjects who have these four values were 1195, 103, 66, and 698, respectively. The total number of subjects was 2062. Five principal components coordinated by applying the multi-dimensional scaling method  to the 1In this work, we have shown that the idea of treating a genotype variable as ordinal without assuming linearity can result in a more powerful and robust test, via introducing a joint multivariate normal distribution for the group of genotypes, traits, and covariates. Meanwhile, we have also demonstrated that the proposed lvm test can provide appropriate Type I error rates. The important strength of our method is that it does not make an assumption on the type of relationship between a phenotype and genotype; nor does it treat the genotype as a continuous variable. Rather, our approach only introduces a latent multivariate normal variable to characterize the relationship between the two, which is very reasonable, and generally considerably more useful.Besides the simulations with respect to significance level of 0.05, we also conducted simulation studies with a lower significance level 0.005. The results are given in Supplementary Table S1. We found that the proposed method can reasonably control Type I error rates and achieve power gains at this lower significance level, similar to those results in In population-based genetic association studies, hundreds of thousands of subjects are often enrolled to achieve optimal power. It is inevitable that there exists a population stratification effect in such large-scale studies. Not considering the effect of population stratification could lead to many false positive findings, and therefore adjusting for its effect represents the basis for conducting a genetic association analysis . In this


Several reports have suggested a role for epigenetic mechanisms in ASD etiology. Epigenome-wide association studies (EWAS) in autism spectrum disorder (ASD) may shed light on particular biological mechanisms. However, studies of ASD cases versus controls have been limited by post-mortem timing and severely small sample sizes. Reports from in-life sampling of blood or saliva have also been very limited in sample size and/or genomic coverage. We present the largest case-control EWAS for ASD to date, combining data from population-based case-control and case-sibling pair studies.DNA from 968 blood samples from children in the Study to Explore Early Development (SEED 1) was used to generate epigenome-wide array DNA methylation (DNAm) data at 485,512 CpG sites for 453 cases and 515 controls, using the Illumina 450K Beadchip. The Simons Simplex Collection (SSC) provided 450K array DNAm data on an additional 343 cases and their unaffected siblings. We performed EWAS meta-analysis across results from the two data sets, with adjustment for sex and surrogate variables that reflect major sources of biological variation and technical confounding such as cell type, batch, and ancestry. We compared top EWAS results to those from a previous brain-based analysis. We also tested for enrichment of ASD EWAS CpGs for being targets of meQTL associations using available SNP genotype data in the SEED sample.p < 1.12 × 10− 7. Seven CpGs showed differences at p < 1 × 10− 5 and 48 at 1 × 10− 4. Of the top 7, 5 showed brain-based ASD associations as well, often with larger effect sizes, and the top 48 overall showed modest concordance (r = 0.31) in direction of effect with cerebellum samples. Finally, we observed suggestive evidence for enrichment of CpG sites controlled by SNPs (meQTL targets) among the EWAS CpG hits, which was consistent across EWAS and meQTL discovery p value thresholds.In this meta-analysis of blood-based DNA from 796 cases and 858 controls, no single CpG met a Bonferroni discovery threshold of No single CpG site showed a large enough DNAm difference between cases and controls to achieve epigenome-wide significance in this sample size. However, our results suggest the potential to observe disease associations from blood-based samples. Among the seven sites achieving suggestive statistical significance, we observed consistent, and stronger, effects at the same sites among brain samples. Discovery-oriented EWAS for ASD using blood samples will likely need even larger samples and unified genetic data to further understand DNAm differences in ASD.The online version of this article (10.1186/s13229-018-0224-6) contains supplementary material, which is available to authorized users. The etiology of autism spectrum disorder (ASD) may involve epigenetic mechanisms. Indirect evidence supporting this hypothesis comes from the observation that children with Rett, Fragile X, and Angelman syndromes often show impaired communication and exhibit repetitive behaviors –3, two cRORA gene [Examination of the affected tissue, i.e., the brain, can provide important insights into potential mechanisms of disease etiology; however, there are considerable limitations with these types of studies. They suffer from severely small sample sizes, have historically had low genomic coverage, and often lack comprehensive unified clinical, demographic, and genomic data. Importantly, they are based on autopsy-derived tissue and do not reflect epigenetic marks in a living individual, are not at optimal developmental timing, and may be influenced by life experiences and cause of death. To overcome these barriers, complementary, large population-based autism epigenetic studies using accessible tissues, such as blood, from living individuals are needed. DNAm from peripheral tissues is useful to analyze for its potential to mimic DNAm signatures from the brain. But outside of brain concordance, it can also be useful for its ability reflect consequences of ASD, provided that sample collection is performed following ASD onset. Moreover, peripheral tissue DNAm signatures related to ASD may result from environmental exposures that simultaneously contribute to ASD. To date, three genome-scale epigenetic studies of autism in accessible peripheral tissues have been performed. One study of peripheral blood from 50 monozygotic twin pairs, including 6 pairs discordant for ASD at age 15, examined DNAm at over 27,000 CpG sites in promoter regions. The authors found suggestive evidence for epigenetic alterations associated with ASD and associated traits within families . SimilarORA gene . Both ofORA gene . While sHere, we overcome previous limitations and perform the largest epigenome-scale examination of DNAm, to date, among two large US case-control studies of autism: the Study to Explore Early Development, phase I (SEED I) and the Simons Simplex Collection (SSC). Both measured DNAm at over 450,000 loci in childhood blood samples from either population-based cases and controls (SEED I) or discordant sibling pairs (SSC). Meta-analysis across both sets included 796 ASD cases and 858 controls. In addition to CpG-specific differential DNAm, we explored the set of blood-derived differentially methylated sites for their concordance in post-mortem brain tissue and their enrichment for genetically controlled CpG sites.The Study to Explore Early Development is a multi-site case-control study with population-based ascertainment. In SEED phase 1, a total of 3899 families were recruited across 6 study sites  and classified into 3 groups according to a child’s diagnosis: an autism spectrum disorder (ASD) group, a general population control group (POP), and a (non-ASD) developmental delay group. Details regarding participant recruitment, biospecimen collection, and final outcome classification have been previously described , 28. Brin = 980) with genome-wide genotyping data, a complete caregiver interview, an ASD or POP classification, and a sufficient amount of DNA available for methylation measurements.Primary caregivers completed the Social Communications Questionnaire (SCQ) , a screehttps://sfari.org/ssc-instruments. A comprehensive family medical history was obtained that included the proband’s prenatal and perinatal history, developmental milestones, immunizations, medications, dietary supplements, and common behavioral treatments. Emphasis was placed on common “comorbidities” including gastrointestinal complaints, sleep irregularities, and seizures. In addition, questions were asked about genetic, autoimmune, and psychiatric disorders in members of the extended family. Probands were excluded who were younger than 4 years of age or older than 18. Probands were also excluded for conditions that might compromise the validity of diagnostic instruments, such as nonverbal mental age below 18 months, severe neurological deficits, birth trauma, perinatal complications, or genetic evidence of fragile X or Down syndromes. A complete description of exclusion/inclusion criteria can be found at http://sfari.org. Measures of adaptive function, behavior-emotional problems, and symptoms of autism were examined in parents and siblings as well as probands.Simons Simplex Collection (SSC) A complete description of the SSC, which enrolled and collected biospecimens from children and adolescents aged 4–18 years, can be found elsewhere . BrieflyThus, the SSC represents a unique, well-described sample of able children and adolescents with relatively severe ASD, as indicated by ADI-R and ADOS Calibrated Severity Scores .To maximize the consistency of clinical observations across sites, each clinician was trained in administration of the ADOS and ADI-R to achieve research reliability as judged by expert clinicians. Most clinicians who had not previously received research training required 4–6 months of practice. Videotapes of interviews were exchanged to ensure that reliability requirements were met and maintained throughout the study. Error rates were very low, averaging less than 0.50 errors/1000 data points. Most errors could be corrected immediately, resulting in an unusually clean data set for a multisite study of this size. During each visit, a blood sample was collected from each study participant and DNA was extracted from blood cells, while plasma was stored for future use.preprocessNoob [minfi R package [p value > 0.01 in more than 1% of probes (N = 7), or if reported sex did not match predicted sex generated via the minfi function getSex (N = 3). Probes were removed if they had a detection p value > 0.01 in more than 10% of samples (n = 702) and then if they had been previously identified as being ambiguously mapped [n = 29,146). Following QC, the analytic data included DNAm for 455,664 sites on 970 samples. We further removed two samples who were missing a final outcome classification, leaving a total of 453 cases and 515 controls used for association analyses.For the SEED samples, genomic DNA was isolated from 980 whole blood samples using the QIAsymphony midi kit (Qiagen). For each sample, 500 ng of DNA was bisulfite treated using the 96-well EZ DNA methylation kit (Zymo Research). Samples were randomized within and across plates, and across two main processing dates to minimize batch effects, and run on the Illumina HumanMethylation450 BeadChip. Background correction and dye-bias equalization was performed using the function ssNoob , 40 in t package . We incly mapped  . Probes were removed if they had a detection p value > 0.01 in more than 10% of samples (n = 483) and then if they had been previously identified as being ambiguously mapped . These steps resulted in an analytic data set with 455,816 sites on 686 samples, consisting of 343 proband-sibling pairs.For the SSC samples, 500 ng of human genomic DNA was sodium bisulfite-treated for cytosine to thymine conversion using the EZ DNA Methylation Gold kit (Zymo Research). A total of 728 samples (from 364 families) were randomized within and across plates to minimize batch effects and run on the Illumina HumanMethylation450 BeadChip. Additional details have been previously described . SimilarestimateCellCounts function in the minfi R package. Estimation incorporated reference data from 60 samples generated from 6 healthy adult men [Finally, for all SEED and SSC samples, we estimated cell type proportions for six different cell types  using the dult men .Whole genome genotyping data was available for 943 of the 970 SEED 1 samples which passed DNAm quality control steps. After genotype measurement using the Illumina HumanOmni1-Quad BeadChip, standard quality control measures were applied, including removal of samples with < 95% SNP call rate, sex discrepancies, relatedness (Pi-hat > 0.2), or excess hetero- or homozygosity, and removal of markers with < 98.5% call rate, or that were monomorphic. Phasing was performed using SHAPEIT  followedlmFit function in the limma R package [gee function in the gee R package [For the SEED data, we used linear regression modeling of the M value   as a dep package , separat package  to accouTo account for sources of technical and biological variability in our association analyses, we estimated surrogate variables (SVs)  in the cFirst, to examine the relationship between each SV and known sources of technical and biological variation, we estimated the association between each estimated SV and cell type composition, principal components of genetic ancestry, and processing batch. We then generated a visual representation of the degree of association with these variables using a heat map  in the meta-analysis, we computed mean differences between cases and controls in each of these three brain regions. We then computed Pearson correlations and quadrant count ratios between the blood effect sizes and three lists of brain effect sizes. We computed quadrant count ratios as the sum of concordant effect sizes (both positive or both negative) minus the sum of discordant effect sizes, all divided by the total number of effect sizes being compared.We sought to compare the consistency of top EWAS results from the blood-based meta-analysis to our previous analysis of post-mortem brain samples from ASD cases and controls . These dWe were interested in exploring the propensity of CpG sites that reached a level of suggestive significance in the EWAS meta-analysis to be significantly associated with nearby SNPs. We used joint DNAm and genotype data to define SNPs associated DNAm, sometimes referred to as “methylation quantitative trait loci (meQTLs)”, and the CpG sites under genetic control, or “meQTL targets”. We then tested for enrichment of meQTL targets in the top ranked CpG sites from the meta-analysis.NBatch1 = 606; NBatch2 = 362). In each batch, we first used a data-driven procedure we have described in detail previously [MatrixEQTL R package, adjusting for sex, the first five principal components to account for genetic ancestry, and the first two principal components derived from the cell composition estimates. We then defined SNP-CpG association pairs based on results that can gain 100% power in the parameter survey (“permissive”), 90% power (“intermediate”), and 80% power (“stringent”). If a SNP-CpG association pair was significant at a designated threshold in each batch, the CpG site was labeled a meQTL target under that threshold for the downstream enrichment analysis.In lieu of applying our SV selection method see “” to evereviously  to selecp value thresholds (p < 1 × 10− 3 and p < 1 × 10− 4) and the three meQTL p value thresholds. In each enrichment test, we accounted for the two main features of CpG sites likely to affect results: the degree of variability in DNAm at that CpG and the number of SNPs in the boundary considered. To do this, we binned each CpG site by decile according to these factors. For each EWAS/meQTL threshold scenario, we compared the proportion of meQTL targets among ASD-related CpGs to a null distribution of randomly selected CpGs, equal in count to the number of ASD-associated sites, matched on the same variability and nearby SNP decile. We defined a fold enrichment statistic as the count of meQTL targets in the ASD-associated CpGs divided by the mean proportion of meQTL targets from the null set, and an enrichment p value as the number of null CpG sets with a count of meQTL targets that was equal to or exceeded the count in the ASD-associated CpG list.We tested for enrichment of meQTL targets in ASD-associated CpG sites. We examined this using two ASD EWAS meta-analysis p values and effect sizes detected in our meta-analysis. No CpG sites reached a Bonferroni level of significance, and effect sizes were modest  was 1.03, with a slight separation from expectation at the tail , among results from three different brain regions with data available from our previous analysis of post-mortem brain samples and ASD [r = 0.31; QCR = 0.33), although prefrontal cortex  and temporal cortex  showed only minimal concordance , but not at a significance threshold corrected for the six tests performed overall  and a consistent direction of effect towards enrichment. Also, tests conducted for CpGs meeting the more stringent EWAS p value threshold (1 × 10− 4) displayed a consistently greater effect size than their corresponding tests from the more liberal EWAS threshold.When considering all CpGs associated with ASD at a liberal p < 1 × 10− 4, including 7 CpGs at p < 1 × 10− 5. Associations with ASD at these sites display moderate concordance with post-mortem brain sample results from a previous study and display suggestive evidence for enrichment of SNP-controlled CpG sites, or meQTL targets.We report results from a large study investigating the relationship between ASD and DNAm. A case-control meta-analysis of peripheral blood samples from the Study to Explore Early Development and the Simons Simplex Collection revealed that none of the 455,068 CpG sites investigated were associated with ASD at a genome-wide significant threshold. However, 48 CpG sites reached suggestive significance levels at Blood-based DNAm signatures of ASD may reflect causal mechanisms that mimic signatures seen in the brain. However, case-control sampling, by design occurring after disease onset, can also reflect consequences of ASD or of environmental exposures. Nonetheless, given the potential involvement of epigenetic mechanisms in ASD –12, and Ideally, tissue-relevant samples from earliest in utero development would provide the greatest mechanistic insights. However, this is not typically available and our study is based instead on a case-control design using blood-based samples. Recent examples of blood-based epigenetic work in brain-based disorders have shown utility, particularly when focused on integration of genetic and epigenetic variation or when inferring biological pathways rather than discovery of specific CpGs , 59–63. In summary, our results suggest a potential role of genetic factors in contributing to DNAm differences in ASD. This is consistent with a recently reported meta-analysis combining these results with an additional European case control sample. In that report, while ASD itself was not associated with DNAm at a genome-wide significance threshold, polygenic risk scores for ASD were associated with DNAm at particular CpGs . In contAdditional file 1Figures S1-S2. Depiction of surrogate variable selection process for SEED (S1) and SSC (S2). Panel A: Heatmap indicating degree of association with known potential technical variables or confounders with estimated surrogate variables. Panel B: Inflation factor (lambda) calculated for progressively including surrogate variables in association models. The number of surrogate variables to include in the ultimate association testing model was to determine to be that which properly controlled the inflation factor and adequately captured known technical variables or confounders. See “Additional file 2Table S1. Demographic characteristics for samples in the SSC (S2) dataset. (XLSX 11 kb)Additional file 3Table S2. Full summary statistics and meta-analysis results for all 445,608 CpG sites that were present in both the cleaned SEED and SSC datasets. (CSV 40707 kb)Additional file 4Table S3. Concordance between suggestively associated (p < 1 × 10− 4) CpG sites in peripheral blood and their corresponding effect sizes in three brain regions. (CSV 3 kb)Additional file 5Figures S3. Quadrant plots depicting concordance in effect sizes between suggestively associated (p < 1 × 10− 4) CpG sites in peripheral blood and three brain regions. A) Prefrontal cortex B) Temporal Cortex C) Cerebellum. Points in red indicate those sites with p < 1 × 10− 5 in peripheral blood. (PNG 21 kb)