Meta-analysis of genetic association studies increases sample size and the power for mapping complex traits. Existing methods are mostly developed for datasets without missing values, i.e. the summary association statistics are measured for all variants in contributing studies. In practice, genotype imputation is not always effective. This may be the case when targeted genotyping/sequencing assays are used or when the un-typed genetic variant is rare. Therefore, contributed summary statistics often contain missing values. Existing methods for imputing missing summary association statistics and using imputed values in meta-analysis, approximate conditional analysis, or simple strategies such as complete case analysis all have theoretical limitations. Applying these approaches can bias genetic effect estimates and lead to seriously inflated type-I or type-II errors in conditional analysis, which is a critical tool for identifying independently associated variants. To address this challenge and complement imputation methods, we developed a method to combine summary statistics across participating studies and consistently estimate joint effects, even when the contributed summary statistics contain large amounts of missing values. Based on this estimator, we proposed a score statistic called PCBS  for conditional analysis of single-variant and gene-level associations. Through extensive analysis of simulated and real data, we showed that the new method produces well-calibrated type-I errors and is substantially more powerful than existing approaches. We applied the proposed approach to one of the largest meta-analyses to date for the cigarettes-per-day phenotype. Using the new method, we identified multiple novel independently associated variants at known loci for tobacco use, which were otherwise missed by alternative methods. Together, the phenotypic variance explained by these variants was 1.1%, improving that of previously reported associations by 71%. These findings illustrate the extent of locus allelic heterogeneity and can help pinpoint causal variants. It is of great interest to estimate the joint effects of multiple variants from large scale meta-analyses, in order to fine-map causal variants and understand the genetic architecture for complex traits. The summary association statistics from participating studies in a meta-analysis often contain missing values at some variant sites, as the imputation methods may not work well and the variants with low imputation quality will be filtered out. Missingness is especially likely when the underlying genetic variant is rare or the participating studies use targeted genotyping array that is not suitable for imputation. Existing methods for conditional meta-analysis do not properly handle missing data, and can incorrectly estimate correlations between score statistics. As a result, they can produce highly inflated type-I errors for conditional analysis, which will result in overestimated phenotypic variance explained and incorrect identification of causal variants. We systematically evaluated this bias and proposed a novel partial correlation based score statistic. The new statistic has valid type-I errors for conditional analysis and much higher power than the existing methods, even when the contributed summary statistics contain a large fraction of missing values. We expect this method to be highly useful in the sequencing age for complex trait genetics. Meta-analysis has become a critical tool for genetic association studies in human genetics. Meta-analysis increases sample sizes, empowers association studies, and has led to many exciting discoveries in the past decade –5. Many Existing methods for conditional meta-analysis were proposed based upon the assumptions that summary association statistics from all variant sites are measured and shared. Yet, in practice, the score statistics from contributing studies often contain missing values, possibly due to the use of different genotyping arrays, sequencing capture assays, or quality control filters by each participating cohort. While genotype imputation is an effective approach to fill in missing genotype data for participating cohorts, many scenarios may preclude accurate genotype imputation. For example, a targeted genotyping array/sequencing assay (e.g. exome array) may not provide sufficient genome-wide coverage for imputation. In addition, it is challenging to impute low frequency variants even with the highest quality reference panels. Imputed genotypes of low quality are often filtered out based upon the recommendations from the best practices , since tFirst, a commonly used method for conditional analysis, COJO, can lead to biased results when contributed summary association statistics from participating studies contain missing values . The COJSecond, the strategy of imputing missing data from contributed association statistics and using imputed association statistics in meta-analysis can also lead to inflated type I errors in conditional analysis. A simple imputation strategy for marginal  analysis is to replace missing summary statistics with zeros (REPLACE0), which are their expected value under the null hypothesis , 3. ThisIn the statistics literature, synthesis methods have previously been developed to meta-analyze joint effects from different studies, where the participating studies measure different predictors , 14. TheTo overcome these limitations of existing GWAS meta-analysis methods and improve power, we developed an improved conditional meta-analysis method called partial correlation based score statistic (PCBS) that borrows strength across multiple participating studies and consistently estimates the partial variance-covariance matrices between genotypes and phenotypes. We conducted extensive simulations, and showed that our PCBS method has valid type I error and the highest power among all the methods. On the other hand, COJO, impG+meta and REPLACE0 can lead to highly inflated type I errors in the presence of missing data. SYN+, while having valid type I errors, is consistently less powerful than PCBS, especially when the missingness is high or the conditioned variants have larger effects. We also demonstrated the clear advantage of PCBS in the meta-analysis of cigarettes per day phenotype. PCBS identified many more independently associated variants from known loci, compared to alternative approaches.https://genome.sph.umich.edu/wiki/Rare_Variant_Analysis_and_Meta-Analysis). RAREMETAL and rareMETALS use marginal score statistics and exact variance-covariance matrix as input, which is suitable for rare variant association analysis. We also implemented the same method in rareGWAMA (https://github.com/dajiangliu/rareGWAMA), which conducts meta-analysis using approximate covariance matrix from a reference panel. These methods and tools have been applied and tested in a few large scale meta-analyses. We expect these methods to play an important role in sequence-based genetic studies and lead to important genetic discoveries.We implemented the proposed methods in the open-source software tools RAREMETAL  and R paIn this section, we first review the standard meta-analysis methods for single variant and gene-level association tests when analyzing datasets without missing summary statistics from contributing studies. We then illustrated the limitations of the existing methods and described the new method PCBS for valid and powerful conditional analysis in the presence of missing summary statistics from contributing studies.i at variant site j in study k as Gijk, which can take values of 0,1 or 2, representing the number of the minor  alleles in the locus. When the genotypes are imputed or generated from low pass sequencing studies, genotype dosage can be used in association analysis. In this case, Gijk will be the expected number of minor  allele counts. We denote the non-genotype covariates as Zik, which includes a vector of 1’s to incorporate the intercept in the model. Single variant association can be analyzed in a regression model: Yk = Gjkβj + Zkγk + ek. The score statistic for single variant association takes the form:0We denote the genotype for individual Uk = . The variance-covariance matrix between scores statistics is equal toWithout the loss of generality, we assume that the phenotype residuals are standardized in each study as in commonly done in practice. So For our illustration of the method, we focus on the analysis of continuous outcomes. Yet, the meta-analysis and conditional meta-analysis methods work for both continuous outcomes and binary outcomes.U = ∑kUk and V = ∑kVk. The meta-analysis statistics can be used to estimate the joint effects for variants 1,…,J, i.e. The meta-analysis score statistics and their covariance matrices are calculated using the Mantel-Haenszel method, i.e. G and G*represent the genotypes from the candidate and conditioned variants respectively. The variance covariance matrix for U equals to We denote the score statistics at candidate and conditioned variant sites as The conditional score statistic can be calculated byG*, the residual variance equals to After conditioning on the genotypes c is equal toIt is easy to verify that the variance of the conditional score statistics under MS1 Text.The single variant and gene-level tests in conditional analysis can be calculated based upon the conditional score statistics Reviewing formulae  and 4),,4), we nGjk and Yk adjusting for variable Zk, we first regress out covariate Zk from both Gjk and Yk, and then calculate the covariance between the residuals. Specifically,In statistics, to calculate the partial covariance between random variables For a given study, it is easy to check that the partial covariances are in fact scaled score statistics, i.e.Gij, phenotype Yi after adjusting the covariate effect Zi using all available summary statistics:Therefore, in meta-analysis, we propose to estimate the partial covariance between genotype Mjk is an indicator variable that takes the value of 1 when the summary statistic at variant site j is measured in study k. For notational convenience, we define the matrices of partial covariance as k. We showed in S1 Text that Here We define partial correlation based score statistics asThe covariances for S1 Text.It is easy to verify that the conditional analysis using the estimator j1 and j2 estimated from a reference panel So the approximate covariance matrix for the kth study can be written asFor rare variant association meta-analysis, it is recommended to use exact covariance matrix for conditional analysis and for gene-level association analysis. Using a reference panel to approximate the covariance between association statistics may lead to biases, as shown in Hu et al . NonetheThe PCBS method can be implemented using the approximate covariance matrices as in  and 11)11).U0 and V0. To mathematically describe this method, we define an indicator variable Mjk, which takes value 1 if the summary statistics at site j in study k is measured and 0 if missing. The meta-analysis score statistic is calculated byWhen the contributed summary association statistics from participating studies contain missing values, a natural strategy is to replace the missing values using imputation. Several imputation methods were previously developed. One method is REPLACE0, which is to replace the missing values by 0. We denote the resulting statistics as S1 Text that replacing missing summary association statistics with zero will bias the genetic effect estimate, i.e. We proved in Zimp and Ztag are Z-score statistics at the missing and tagSNP sites, Σimp,tag and Σtag are genotype correlation matrices. A special case for this condition is that both the tagSNP and missing variants have null effects. Similar to REPLACE0, applying impG+meta method can lead to inflated type I errors.A more sophisticated set of methods is to impute missing summary statistics based upon LD information. Yet, the genetic effect estimates based upon the imputed Z-score statistics are often biased, unless the following condition holdsAn alternative approach we call DISCARD, is to remove studies with missing summary statistics and only use studies with complete data. The meta-analysis score statistics under this analysis strategy are given by:An obvious limitation of the DISCARD method is that it may result in the removal of a large number of studies and a significant loss of power.Synthesis methods have been developed in the statistics literature for combining the joint effects of multiple predictors in a meta-analysis . The metOur extension, the SYN+ method includes the following steps:Derive estimating equations using marginal SNP effectsThe joint effect needed by the synthesis method can be obtained using the shared score statistics and their covariance matrices. To facilitate the presentation of the method, we re-write the full model, separating the measured  impG+meta; 2) COJO; 3) REPLACE0; 4) DISCARD and 5) SYN+ using simulated data. We simulated genetic data following a coalescent model that we previously used for evaluating rare variant association analysis methods [Gij and βj and γj are their effects respectively. The model assumes that the genetic variants have additive effects on the phenotype.For quantitative traits, phenotype data from each cohort were simulated according to the linear model:c) or non-causal (with probability 1 − c): The genetic effects for candidate variants follow a mixture normal distribution, which accommodates the possibility that a genetic variant can be causal  of the sites from each study and masked them as missing. We then applied the new method PCBS, along with impG+meta, COJO, DISCARD, REPLACE0 and SYN+ to the data. In our evaluations, we used the exact LD with COJO and impG+meta, in order to remove the influence of approximate LD and focus on the impact of missing summary statistics on the power and type I error. We evaluated the type I errors and power for each approach under a variety of scenarios with different genetic effect sizes, fractions of causal variants in the gene region, and the fractions of missing data.METabolic Syndrome In Men (METSIM)[S1 Text section 4, including the methods for association analyses and the adjusted covariates.To evaluate the effectiveness of methods in real datasets, we applied our methods to a meta-analysis of seven cohorts with a cigarettes-per-day (CPD) phenotype, a key measurement for studying nicotine dependence. Participating studies were the Minnesota Center for Twin and Family Research (MCTFR) –19, Sard (METSIM), Genes f (METSIM), COPDGen (METSIM), Center  (METSIM), and ful (METSIM) and the  (METSIM) (with th (METSIM), and metR2 < .7, and sites that showed large differences in allele frequencies from the imputation reference panel. Imputation dosages were used in the association analysis.To ensure the validity of our association analysis results, we conducted extensive quality control for the imputed genotype data. We filtered out variant sites with the imputation quality metric −8), we defined the locus as the 1 MB window surrounding it. We applied iterative single variant conditional analysis to identify independently associated variants in each locus. We started by conditioning on the most significant variant from marginal association analysis. After each round of the association analysis, if the top variant remained statistically significant, we added the top variant to the set of conditioned variants, and performed an additional round of association testing. We applied the six methods to analyze the data, including the PCBS statistic, SYN+, impG+meta, REPLACE0, DISCARD and COJO. In order to examine if the low frequency variants in aggregate can be explained by the identified independently associated variants, we also performed gene-level association analysis for rare variants with MAF<1%, conditional on the identified independently associated variants.For each sentinel SNP with genome-wide significance , impG+meta, REPLACE0, and DISCARD. Scenarios were considered for different combinations of the fractions of missing data, the genetic effects of the variants in the candidate gene, and the genetic effects of the conditioned variants.Table 1). The type I error rate for the other three methods, i.e. impG+meta, REPLACE0 and COJO are inflated in a number of scenarios. The inflation tends to increase with the effect of the conditioned variant(s) and the rate of missingness. In many scenarios, the type I error can be >100X inflated over the significance threshold (α = 5×10−8). For example, when the conditioned variant effect is .04, and the association statistics from 30% of the variant sites are missing, type I errors for impG+meta, COJO and REPLACE0 are .015, .57 and .74 under the significance threshold of α = 0.005. When the missing rate is 50%, and the conditioned variant effects is .08, the type I errors for the three methods become .25, .65, and .60.First, we noted that PCBS, SYN+ and DISCARD are the only three methods that have controlled type I errors across all scenarios, consistent with our theoretical expectation (Table 1). The power advantage of PCBS over the other two approaches increases when 1) the conditioned variant(s) have larger effects or 2) the fraction of missing summary association statistics is larger. For example, when candidate variant effect is .04, the conditioned variant effect is .08, and the missing rate of score statistics is 30%, the power for PCBS is .21, which is 75% higher than the power for SYN+ (.12). When the candidate variant effect is.08, the conditioned variant effect is .08, and score statistics from 50% of the variant sites in each participating study are missing, the power for PCBS and SYN+ are respectively .83 and .74.Second, among the methods with the controlled type I error rates , PCBS is consistently the most powerful method (Table 1). The power for DISCARD is substantially lower than PCBS and SYN+. In some scenarios where the missingness is high, the power is barely larger than the significance threshold.Due to the obvious limitations of complete case analysis, the DISCARD method of discarding the studies with missing data can lead to considerable loss of power (Table 2). When missingness is higher, the power of gene-level tests is lower, but the power loss is small. For instance, when a causal variant in the candidate gene has effects sampled from N, the conditioned variant has effect .1, and 30% of the contributed summary statistics in each study have missing values, the power for burden/SKAT/VT tests are 58%/58%/56%, which are only slightly reduced compared to the power of analyzing the complete datasets (60%/61%/60%). On the other hand, the method that discards studies with missing data has much reduced power (0.011/0.011/8.8×10−3).Interestingly, gene-level association tests are affected by two types of missing data with opposite consequences: Missing values at causal variant sites reduce power but missing values at non-causal variant sites tend to reduce noise and thus improve power (S2 Table). In our simulations, the genetic effects for a given variant in different studies were simulated from a normal distribution Our method was developed for the fixed effect meta-analysis, where the genetic effects are assumed to be constant across different studies. But since PCBS first aggregates association statistics from across studies and then performs conditional analysis, the impact of genetic effects heterogeneities does not invalidate the test and the type I error remains well controlled. The power is slightly reduced, but the advantages over other methods remain. To confirm this, we performed simulation analysis assuming that the genetic effects across studies are heterogeneous . Compared to common variants, rare variants were considerably more likely to be missing: 95.3% of the variants with MAF<1% were missing from at least one cohort, compared to the fraction of 20.1% for the common variants with MAF>1%.It is important to note that even with high quality imputation panels, such as the haplotype reference consortium panel , there w10 is well calibrated . The genomic control value is 1.14 for common variants with MAF>0.01, and 1.00 for rare variants with MAF<0.01. The genomic control value is consistent with that of large scale GWAS for highly polygenic traits [S2 Fig), including the well-known CPD associated loci, the nicotine receptor genes CHRNB2, CHRNB3-CHRNA6, CHRNA5-CHRNB4-CHRNA3, the gene CYP2A6 that encodes cytochrome P450 protein, the gene PDE1C that encodes Phosphodiesterase 1C, FAM163B-DBH, YTHDF3 and GRM4. Among these loci, CHRNB2 and FAM163B-DBH are associated with CPD at the genome-wide significance threshold for the first time.The Quantile-Quantile plot for–logc traits , 30. Thec traits  was 1.01CHRNA5-CHRNB4-CHRNA3 and CYP2A6 loci have been consistently implicated in human GWAS to date. The other nicotine receptor gene CHRNB3-CHRNA6 was first identified with genome-wide significance in an isolated population for associations with nicotine dependence and nicotine use [CHRNB2 was implicated in the nicotine dependence trait, but not at genome-wide significance. To our knowledge, there is no report that this gene is associated with CPD at genome-wide significance [While smoking behaviors are known to be heritable, only the tine use . CHRNB2 ificance .CHRNA5-CHRNB4-CHRNA3 locus and 4 independently associated variants for the CYP2A6 locus at genome-wide significance threshold  (Table 3). The other loci do not have additional independently associated variants besides the sentinel variant.In order to understand the allelic architecture of the CPD phenotype and compare different methods on real data, we performed sequential forward selection with the new PCBS method, and identified 5 independently associated variants for the S3 Table). Using the SYN+ method, fewer independently associated variants are identified. At the CHRNA5-CHRNB4-CHRNA3 locus, 3 independently associated variants are identified, and also at the CYP2A6 locus, only 3 independently associated variants are identified. DISCARD also identifies fewer number of independently associated SNPs. The results from real data analysis is consistent with our simulation study that PCBS has higher power than alternative approaches.As a comparison, we also performed sequential forward selection using the five alternative approaches (Table 3 and S3 Table). Together, the analysis of real data confirmed our simulation experiments.Among the approaches that have inflated type I errors in simulations, impG+meta identifies a lot of SNPs with very significant p-values. Many of these identified SNPs have substantial missingness among the participating cohorts . Given the inflated type I errors that we observed in simulations, as well as the small available sample sizes for the top variants, the validity of the results using impG+meta is of concern. Most of the top variants identified by COJO and REPLACE0 have low missingness, so there are not many false positive results. Yet, COJO and REPLACE0 identified fewer independently associated SNPs compared to PCBS and SYN+ (S4 Table). We first analyzed these 11 variants conditional on our independently associated variants. All of these variants became insignificant, which indicated that our newly identified independently associated variants can explain previously known association signals. We also performed conditional analysis in the opposite direction to examine if our identified association signal may be explained by the known variants. We found that variants within the CPY2A6 locus remained highly significant and variants within the CHRNA5-CHRNB4-CHRNA3 locus remained marginally significant. Together, our independently associated variants explained 1.1% of the phenotypic variance, which substantially improves the phenotypic variance (.64%) explained by the 11 known signals.We examined if our independently associated variants explained previously known association signals. To do this, we looked up GWAS catalog  using keS5 Table). 27 genes were analyzed using simple burden, SKAT and VT tests under a MAF threshold of 0.01. Only one gene (CHRNA5) has gene-level p-values less than 0.05/27, which is the Bonferroni threshold. None of the genes have exome-wide significant gene-level association p-values.Finally, in addition to single variant association, we investigated if rare variants within each of the 9 loci were independently associated with the CPD phenotype  nor monomorphic sites contribute to the single variant meta-analysis statistic. Yet they should be treated differently in joint and conditional meta-analysis. Summary statistics from monomorphic variants should be replaced by zeros. On the other hand, summary statistics from un-called variants should be treated as missing data, and the conditional association analysis can be performed using our partial correlation based score statistics.While not the focus of this article, the proposed method is also helpful for downstream analyses that make use of the joint effects of multiple variants, e.g. estimating the phenotypic variance explained by variants in LD or fine mapping causal variants  and sequence-based meta-analysis. Correct inference on the joint and conditional effects using these methods will pave the way for a more accurate characterization and a more complete understanding of the genetic architecture of complex traits.S1 Text(DOCX)Click here for additional data file.S1 FigGenomic control values were separately reported for variants with MAF>0.01 and with MAF<0.01.(TIFF)Click here for additional data file.S2 Fig(TIFF)Click here for additional data file.S1 TableWe evaluated the impact of large heterogeneity in the genetic effects on the power and type I errors for the PCBS statistics. The effects of the conditioned variants in each cohort are sampled from the distribution (DOCX)Click here for additional data file.S2 TableWe evaluated the impact of large heterogeneity in the genetic effects on the power and type I errors for the PCBS statistics. The genetic effects for the conditioned variants in each cohort are sampled from the distribution (DOCX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 TableWe analyzed independently associated variants from the meta-analysis conditional on the previously known GWAS signals (Panel A). We also performed the conditional analyses in the opposite direction, where we analyzed the previously reported GWAS variants conditional on the identified independently associated variants (Panel B).(XLSX)Click here for additional data file.S5 TableWe analyzed gene-level association conditional on the independently associated variants in the same loci, which were identified using sequential forward selection. Three gene level association tests were performed, including simple burden tests, SKAT and VT. No significant gene-level associations were identified (with p<0.05/27).(XLSX)Click here for additional data file.


The genetic risk scores for the other psychiatric and cognitive traits were not related to depressive symptom severity or change over time. Our preliminary results indicated, as expected, that the genomics of the response of patients with major depression to cognitive behavior therapy were complex and that future efforts should aim to maximize sample size and limit subject heterogeneity in order to gain a better understanding of the use of genetic risk factors to predict treatment outcome.Major depressive disorder is heritable and a leading cause of disability. Cognitive behavior therapy is an effective treatment for major depression. By quantifying genetic risk scores based on common genetic variants, the aim of this report was to explore the utility of psychiatric and cognitive trait genetic risk scores, for predicting the response of 894 adults with major depressive disorder to cognitive behavior therapy. The participants were recruited in a psychiatric setting, and the primary outcome score was measured using the Montgomery Åsberg Depression Rating Scale-Self Rated. Single-nucleotide polymorphism genotyping arrays were used to calculate the genomic risk scores based on large genetic studies of six phenotypes: major depressive disorder, bipolar disorder, attention-deficit/hyperactivity disorder, autism spectrum disorder, intelligence, and educational attainment. Linear mixed-effect models were used to test the relationships between the six genetic risk scores and cognitive behavior therapy outcome. Our analyses yielded one significant interaction effect (B = 0.09,  Major depressive disorder (MDD) is a common and heritable illness with a lifetime prevalence of around 14–15% . Twin stSeveral studies have suggested clinical predictors of CBT outcome, such as baseline symptom severity , psychopHowever, the results have been mixed . TherefoThe study of genetic predictors of psychological treatment outcome, sometimes called therapygenetics , is a fap-value threshold.However, experience from pharmacogenetic studies implicates the unlikeliness of finding strongly replicated single-nucleotide polymorphisms (SNPs) with a large contribution to a complex trait, such as treatment response, and that large samples and well-defined homogeneous phenotypes are needed . AttemptThe present study explored the utility of GRSs for predicting treatment response in a sample of 894 subjects with MDD who underwent a standardized iCBT protocol. We tested the hypothesis that a GRS for MDD and five other psychiatric  and cognitive traits  are associated with the effects of iCBT treatment over time. We chose these traits because cause often informs cure , greatern = 49), quality control issues (n = 11), and missing phenotypes (n = 10).Between 2008 and 2016, adult patients with MDD who started iCBT at the Internet Psychiatry Clinic in Stockholm , a goverAfter an online screening, the patients came to the clinic for psychiatric assessments, including a structured diagnostic interview  . A psychThe core interventions of iCBT are the same as those administered face-to-face in conventional CBT. The iCBT program consisted of 10 text modules with components covering standard CBT interventions for patients with MDD, such as psychoeducation, cognitive restructuring, behavioral activation, and relapse prevention, that were to be completed in 12 weeks. Each module had a set of tasks and homework assignments to be completed each week that were monitored by the therapist via the secure online platform. In general, the patient and therapist interactions were limited to email contact, and there were no live meetings. A thorough description of the program has been published previously .The primary outcome measure was assessed using the Montgomery Åsberg Depression Rating Scale-Self report (MADRS-S) . The MADGenotyping was performed at LIFE & BRAIN GmbH  using the Infinium Global Screening Array 1.0 BeadArray  and automated workflow according to the manufacturer's instructions. The raw data were analyzed using GenomeStudio 2.0  using the Infinium cluster file (GSA-24v1-0_A1_ClusterFile.egt). A reclustering step was performed using the GenTrain 3 algorithm in Genome Studio 2.0.https://www.med.unc.edu/pgc/results-and-downloads) and the GWAS results for IQ and EDU from published GWAS meta-analyses [GRSs were generated for the following six phenotypes: MDD, bipolar disorder (BIP), attention-deficit/hyperactivity disorder (ADHD), autism spectrum disorder (ASD), intelligence (IQ), and educational attainment (EDU). We obtained the corresponding GWAS results for MDD, BIP , ADHD 4, and ASDanalyses , 50. TheThe GWAS data from the 964 iCBT samples were processed using the PGC Ricopili pipeline for quality control and genotype imputation with reference genomes from the 1000 Genomes Project (phase 1 version 3) . Eleven 2 < 0.1 in 1-Mb window) on the overlapping SNPs using the European samples from the 1000 Genomes Project as a linkage disequilibrium reference. We computed eight sets of GRS for each phenotype under the p-value cutoffs of ≤ 1x10-5, ≤ 1x10-4, ≤ 0.001, ≤ 0.01, ≤ 0.05, ≤ 0.1, ≤ 0.5, ≤ 1. The GRS calculations were performed using PLINK (version 1.9) [The GRS values were derived for the target set iCBT samples as the sum of the scores based on the risk alleles weighted by the effect size from the discovery sample. To select an independent set of SNPs for calculating the GRS, we conducted linkage disequilibrium clumping (rion 1.9) .R [p-value cutoff were investigated in separate models while controlling for the top five ancestry PC scores. (2) Age and sex were added to the models in step 1. (3) A full model was created in which all six GRSs were entered while controlling for ancestry PCs, age, and sex. As stated above, all covariates  were entered as both main effects and interaction effects with linear time in these analyses. To reduce multiple testing, we tested each of the six GRS at predetermined p < 0.05 in main analyses. In addition, we presented the results on GRS at all p-value thresholds as sensitivity analyses  with which significant or near-significant (p < 0.10) main or interaction effects were obtained. For this, we used the influence.ME package [We performed outlier analyses to detect influential cases that may have biased the regression models. These analyses were performed on the GRS  package  to calcup < 2 × 10−16) and a significant positive effect of quadratic time  on MADRS-S ratings. See Supplementary Table We observed a significant negative effect of time  yielded one significant result. Namely, the ASD GRS was associated with MADRS-S changes over treatment time. This was reflected in the significant interaction effect  between ASD GRS and time (GRS × time): meaning that the higher the ASD genetic load, the less iCBT treatment response over time , thus producing a large body of treatment outcome data. The limitations of the study include that this study was likely still too small to detect robust and reliable associations with treatment response on both the aggregate (GRS) and individual locus (SNP) levels. In addition, the therapeutic mechanisms of iCBT can differ from traditional CBT and hereby limit the generalization of the results.Our finding of an association of ASD GRS with CBT outcome is the first significant finding using a genome-wide approach in the field of therapygenetics. These preliminary findings need to be replicated before firm conclusions can be drawn and the possibility of the finding being a false positive must be considered.Supplementary Figure 1Supplementary Figure 2Supplementary Figure 1 LegendSupplementary Figure 2 LegendSupplemental tables


A further integration of DNA methylation (n = 1980) and epigenomic annotation data highlight 3 genes  with plausible regulatory mechanisms, whereby a genetic variant exerts an effect on T2D through epigenetic regulation of gene expression. Our study uncovers additional loci, proposes putative genetic regulatory mechanisms for T2D, and provides evidence of purifying selection for T2D-associated variants.Type 2 diabetes (T2D) is a very common disease in humans. Here we conduct a meta-analysis of genome-wide association studies (GWAS) with ~16 million genetic variants in 62,892 T2D cases and 596,424 controls of European ancestry. We identify 139 common and 4 rare variants associated with T2D, 42 of which (39 common and 3 rare variants) are independent of the known variants. Integration of the gene expression data from blood ( GWAS have so far identified 129 loci associated with type 2 diabetes (T2D). Here, the authors meta-analyse three large T2D GWA studies which uncovers 42 additional loci, further prioritize 33 functional genes using eQTL and mQTL data and propose regulatory mechanisms for three putative T2D genes. It is primarily caused by insulin resistance  and/or insufficient insulin production by beta cells2. Genetic studies using linkage analysis and candidate gene approaches have led to the discovery of an initial set of T2D-associated loci 4. Over the past decade, genome-wide association studies (GWAS) with increasing sample sizes have identified 144 genetic variants (not completely independent) at 129 loci associated with T2D6.Type 2 diabetes (T2D) is a common disease with a worldwide prevalence that increased rapidly from 4.7% in 1980 to 8.5% in 20147. This well-known “missing heritability” problem is likely due to the presence of common variants  that have small effects and have not yet been detected and/or rare variants that are not well tagged by common single nucleotide polymorphisms (SNPs)7. The contribution of rare variants to genetic variation in the occurrence of common diseases is under debate8, and a recent study suggested that the contribution of rare variants to the heritability of T2D is likely to be limited9. If most T2D-associated genetic variants are common in the population, continual discoveries of variants with small effects are expected from large-scale GWAS using the current experimental design. Furthermore, limited progress has been made in understanding the regulatory mechanisms of the genetic loci identified by GWAS. Thus, the etiology and the genetic basis underlying the development of this disease remain largely unknown. Recent methodological advances have provided us with an opportunity to identify functional genes and their regulatory elements by combining GWAS summary statistics with data from molecular quantitative trait loci studies with large sample sizes11.Despite a large number of variants discovered using GWAS, the associated variants in total, explains only a small proportion (~10%) of the heritability of T2D5, Genetic Epidemiology Research on Aging (GERA)12, and the full cohort release of the UK Biobank (UKB)13. We then integrate the GWAS meta-analysis results with gene expression and DNA methylation data to identify genes that might be functionally relevant to T2D and to infer plausible mechanisms, whereby genetic variants affect T2D risk through gene regulation by DNA methylation11. We further estimate the genetic architecture of T2D using whole-genome estimation approaches. Our study identifies additional T2D-risk variants, prioritizes functional genes, and proposes putative genetic regulatory mechanisms for T2D.In this study, we perform a meta-analysis of GWAS in a very large sample of T2D , by combining 3 GWAS data sets of European ancestry: DIAbetes Genetics Replication and Meta-analysis (DIAGRAM)14 (1KGP) phase 1 using a summary data-based imputation approach, ImpG15 , there were 139 near-independent variants at P < 5 × 10−8 (Supplementary Data P = 1.3 × 10−347) at the known TCF7L2 locus19. Among the 139 variants, 39 are not in LD with the known variants  in 62,892 T2D cases and 596,424 controls from the DIAGRAM , GERA  and UKB  data sets after quality controls  after correcting for multiple tests , with only 1 locus showing significant associations with both insulin secretion and sensitivity. The limited number of overlapping associations observed might be due to the relatively small sample sizes in the insulin studies. We further estimated the genetic correlation (rg) between insulin secretion (or sensitivity) and T2D by the bivariate LD score regression approach18 using summary-level data. The estimate of rg between T2D and insulin secretion was −0.15 (s.e. = 0.10), and that between T2D and insulin sensitivity was −0.57 (s.e. = 0.10). Gene set enrichment test also showed that T2D-associated loci were enriched in “glucose homeostasis” and “insulin secretion” pathways  in the association analysis in UKB and detected 11 rare variants at P < 5 × 10−8 and 4 of them were at P < 5 × 10−9  = 1.33, P = 4.4 × 10−14) is a missense variant that encodes a p.Ser539Trp alteration in PAM and was reported to be associated with decreased insulin release from pancreatic beta cells27. Variant rs146886108 , which showed a protective effect against T2D, is a novel locus and a missense variant that encodes p.Arg187Gln in ANKH29. Variant rs117229942  is an intron variant in TCF7L24. Variant rs527320094 , located in LOC105378797, is also a novel rare-variant association, with no other significant SNP (either common or rare) within a ±1 Mb window. We did not observe any substantial difference in association signals for these 4 variants between the results from BOLT-LMM30 and logistic regression31 considering the difference in sample size  analysis33 using the top-associated expression quantitative trait locus (eQTL) as an instrumental variable to test for association between the expression level of each gene and T2D (Methods). We used GWAS summary data from our meta-analysis and eQTL summary data from the eQTLGen  and CAGE consortia (n = 2765)34 for the SMR analysis (Methods). We identified 40 genes in eQTLGen and 24 genes in CAGE at an experimental-wise significance level . Therefore, genes not rejected by HEIDI  were those associated with T2D through pleiotropy at a shared genetic variant. Of the genes that passed the SMR test, 27 genes in eQTLGen and 15 genes in CAGE were not rejected by the HEIDI test , SSSCA1 (rs1194076), and P2RX4 (rs2071271) in eQTLGen were not significant in the T2D meta-analysis, likely due to the lack of power; these SNPs were expected to be detected in future studies with larger sample sizes.Most previous studies have reported the gene in closest physical proximity to the most significant SNP at a GWAS locus. However, gene regulation can be influenced by genetic variants that are physically distal to the genes35 (n = 1980) to identify DNA methylation (DNAm) sites associated with T2D through pleiotropy at a shared genetic variant. In total, 235 DNAm sites were associated with T2D, with PSMR < 6.3 × 10−7PHEIDI > 1.6 × 10−4Penrichment = 1.6 × 10−7) and weak enhancers   data from McRae et al.35 n = 190 to idenmentclasspt{minima36 . We denoted these 4 tissues as GTEx-AALP. Of the 27 putative T2D genes identified by SMR and HEIDI using the eQTLGen data, 10 had a cis-eQTL at PeQTL < 5 × 10−8 in at least one of the 4 GTEx-AALP tissues (Supplementary Data n = 153–385) compared to that of eQTLGen , as demonstrated by simulation (Supplementary Note PeQTL < 5 × 10−8 in GTEx-blood (n = 369). We first performed the SMR analysis in GTEx-blood and found that 12 of the 17 genes were replicated at PSMR < 2.9 × 10−3   in at least one of the 4 GTEx-AALP tissues, a replication rate comparable to that found in GTEx-blood. Among the 8 genes, CWF19L1, for which the cis-eQTL effects are highly consistent across different tissues, was significant in all the data sets , comparable to and not significantly different from the value of 0.64 (s.e. = 0.16) between eQTLGen and GTEx-blood. We also found that the estimated SMR effects of 18 genes, which passed the SMR test and were not rejected by the HEIDI test in either eQTLGen or GTEx, were highly correlated (Pearson’s correlation r = 0.80)  correlate with those estimated in the GTEx tissues, accounting for sampling variation in estimated SNP effects37. In addition, tissue-specific effects that are not detected in blood will affect the power of the SMR and HEIDI analysis rather than generating false positive associations.These results support the validity of using eQTL data from blood for the SMR and HEIDI analysis; using this method, we can make use of eQTL data from very large samples to increase the statistical power, consistent with the conclusions of a recent studyCAMK1D, TP53INP1, and ATP5G1 as examples to hypothesize possible mechanisms of how genetic variants affect T2D risk by controlling DNAm for gene regulation11. Functional gene annotation information was acquired from the Roadmap Epigenomics Mapping Consortium (REMC)39.Here, we used the genes CAMK1D with T2D was identified in both eQTL data sets . It was previously shown that rs11257655 is located in the binding motif for FOXA1/FOXA2 and that the T allele of this SNP is a risk allele that increases the expression level of CAMK1D through allelic-specific binding of FOXA1 and FOXA240. Another functional study demonstrated that increasing the expression of FOXA1 and its subsequent binding to enhancers was associated with DNA demethylation41. Our analysis was consistent with previous studies in showing that the T allele of rs11257655 increases both CAMK1D transcription  by SMR  to the promoter. When the DNAm level of the promoter region is high, the binding of repressor(s) is disrupted, allowing the binding of transcription factors that recruit RNA polymerase and resulting in up-regulation of gene expression. Increased expression of this gene has been shown to increase T2D risk by decreasing the survival rate of pancreatic beta cells through a TCF7L2-p53-p53INP1-dependent pathway.The second example is is Table . This waATP5G1 and UBE2Z, the expression levels of which were significantly associated with T2D according to the SMR analysis  are the targets of several approved drugs (drugs that have been approved in at least one jurisdiction). ARG1 (UniProt ID: P05089), whose expression level was negatively associated with T2D risk, is targeted by three approved drugs: ornithine (DrugBank ID: DB00129), urea (DrugBank ID: DB03904), and manganese (DrugBank ID: DB06757), but the pharmacological mechanism of action of these drugs remains unknown. Arginase (ARG1 is an isoform of arginase in liver) is a manganese-containing enzyme that catalyzes the hydrolysis of arginine to ornithine and urea. Arginase in vascular tissue might be a potential therapeutic target for the treatment of vascular dysfunction in diabetes46. Metformin, an oral antidiabetic drug that is used in the treatment of diabetes, was reported to increase ARG1 expression in a murine macrophage cell line47, consistent with our SMR result that increased expression of ARG1 was associated with decreased T2D risk . The likely mechanism is that metformin activates AMP-activated protein kinase (AMPK), resulting in increased expression of ARG148, again consistent with our SMR result. LTA (UniProt ID: P08637), whose expression level was negatively associated with T2D risk, is targeted by the approved drug etanercept (DrugBank ID: DB00005) for rheumatoid arthritis (RA) treatment. P2RX4 (UniProt ID: Q99571), the expression level of which was positively associated with T2D risk, is targeted by eslicarbazepine acetate . Eslicarbazepine acetate is an anticonvulsant that inhibits repeated neuronal firing and stabilizes the inactivated state of voltage-gated sodium channels; its pharmacological action makes it useful as an adjunctive therapy for partial-onset seizures49. Antagonists of P2RX4 inhibit high glucose and are useful in the treatment of diabetic nephropathy50. We also explored whether any of these three genes have potential adverse effects by checking the associations of the lead variants at the three loci with lipid- and insulin-related traits from previous studies  and found that 3 genes (51 (Methods) in a subset of unrelated individuals in UKB  to estimate the variance explained by SNPs in different MAF ranges . We partitioned the SNPs into 7 MAF bins with high- and low-LD bins within each MAF bin to avoid MAF- and/or LD-mediated bias in 52, the explained variance is uniformly distributed as a function of MAF, which means that the variance explained by variants with MAF ≤ 0.1 equals that explained by variants with MAF > 0.4. However, in our results, the MAF bin containing low-MAF and rare variants (MAF ≤ 0.1) showed a larger estimate than any other MAF bin , we performed an additional analysis using a recently developed method, BayesS54  to estimate the relationship between variance in effect size and MAF (Methods). The method also allowed us to estimate π) on each chromosome. The results . The mean estimate of π, i.e., the proportion of SNPs with non-zero effects, was 1.75% across all chromosomes  or from an LD score regression analysis  using all the UKB individuals  , were not affected by BMI or dyslipidemia . Unfortunately, we did not have access to mQTL data from whole-genome bisulfite sequencing (WGBS) in a large sample. Nevertheless, it is noteworthy that there are three T2D-associated variants at the CAMK1D/CDC123, ADCY5, and KLHDC5 loci that show hypomethylation and allelic imbalance as identified by Thurner et al.42 using WGBS data (n = 10), all of which were genome-wide significant in our mQTL-based SMR analysis. In addition, a previous study showed that T2D-associated loci were enriched in islet stretch enhancers63, ~54.1% of which were tagged by at least one of the DNAm probe in the 450 K array (annotation data from ref. 64). Despite these limitations, our study highlights the benefits of integrating multiple omics data to identify functional genes and putative regulatory mechanisms driven by local genetic variation. Future applications of integrative omics data analyses are expected to improve our understanding of the biological mechanisms underlying T2D and other common diseases.This study has a number of limitations. First, the SNP-T2D associations identified by the meta-analysis might be biased by misdiagnosis of T1D (type 1 diabetes) and latent autoimmune diabetes in adults5, Genetic Epidemiology Research on Adult Health and Aging (GERA)12 and UKB13.The data used in this study were derived from 659,316 individuals of European ancestry and a small cohort from Pakistan, and were obtained from three data sets: DIAbetes Genetics Replication And Meta-analysis (DIAGRAM)65 . In stage 2, there were 22,669 cases and 58,119 controls genotyped on Metabochips , including 1178 cases and 2472 controls of Pakistani descent. There was limited evidence of genetic heterogeneity between individuals of European and those of Pakistani descent for T2D5. The sample prevalence was 23.3% (17.6% in stage 1 and 28.1% in stage 2). We imputed the stage 1 summary statistics by ImpG15 and combined the imputed data with stage 2 summary statistics (Supplementary Note DIAGRAM: The DIAGRAM data were obtained from publicly available databases (see URLs section) and included 2 stages of summary statistics. In stage 1, there were 12,171 cases and 56,862 controls from 12 GWAS cohorts of European descent, and the genotype data were imputed to the HapMap2 ProjectP value ≤ 1 × 10–6 or minor allele count ≤ 1 and removing individuals with missing rate ≥ 0.02) and imputed the genotype data to the 1000 Genomes Projects (1KGP) reference panels14 using IMPUTE266. We used GCTA67 (see URLs section) to compute the genetic relationship matrix (GRM) of all the individuals based on a subset of imputed SNPs (HapMap3 SNPs with MAF ≥ 0.01 and imputation info score ≥ 0.3), removed the related individuals at a genetic relatedness threshold of 0.05, and retained 53,888 individuals  for further analysis. We computed the first 20 principal components (PCs) from the GRM. The summary statistics in GERA were obtained from a GWAS analysis using PLINK231 with sex, age, and the first 20 PCs fitted as covariates. To examine the influence of imputation panel on the meta-analysis result, we further imputed GERA to the HRC68 using the Sanger imputation service (see URLs section).GERA: There were 6905 cases and 46,983 controls in GERA, and the sample prevalence was 12.4%. We cleaned the GERA genotype data using standard quality control (QC) filters  by projecting the UKB participants onto the 1KGP PCs. Genotype probabilities were converted to hard-call genotypes using PLINK231 , and we excluded SNPs with minor allele count < 5, Hardy-Weinberg equilibrium test P value < 1 × 10–6, missing genotype rate > 0.05, or imputation info score < 0.3. The UKB phenotype was acquired from self-report, ICD10 main diagnoses and ICD10 secondary diagnoses . The GWAS analysis in UKB was conducted in BOLT-LMM30 with sex and age fitted as covariates. In the BOLT-LMM analysis, we used 711,933 SNPs acquired by LD pruning (r2 < 0.9) from Hapmap3 SNPs to control for relatedness, population stratification and polygenic effects. We transformed the effect size from BOLT-LMM on the observed 0–1 scale to the OR using LMOR69.UKB: Genotype data from UKB were cleaned and imputed to HRC by the UKB team16. The stage 2 meta-analysis data were used in the follow-up analyses.Before conducting the meta-analysis, we performed several analyses in which we examined genetic heterogeneity and sample overlap among data sets . There are at least two models consistent with an observed SMR association, i.e., pleiotropy (a genetic variant having effects on both trait and gene expression) and linkage . The HEIDI test10 uses multiple SNPs in a cis-eQTL region to distinguish pleiotropy from linkage by testing whether there is heterogeneity in SMR effects estimated at different SNPs in LD with the top associated cis-eQTL. We used the SMR and HEIDI methods to test for pleiotropic associations between gene expression and T2D, between DNAm and T2D, and between T2D-associated gene expression and T2D-associted DNAm. In the SMR analysis, we used eQTL summary data from the eQTLGen Consortium , the CAGE 34 and the GTEx v7 release 36. In CAGE and eQTLGen, gene expression levels were measured using Illumina gene expression arrays; in GTEx, gene expression levels were measured by RNA-seq. The SNP genotypes in all cohorts were imputed to 1KGP. The cis-eQTL within 2 Mb of the gene expression probes with PeQTL < 5 × 10−8 were selected as the instrumental variables in the SMR test. The mQTL summary data were obtained from genetic analyses of DNA methylation measured on Illumina HumanMethylation450 arrays 35. We used mQTL data generated by the 450 K methylation arrays rather than whole-genome bisulfite sequencing (WGBS) because WGBS-based mQTL data of large sample size (at least 100 s) are not available yet. We demonstrated the statistical power of SMR test in our study by simulation under a pleiotropy model ; in this subset, we kept all 15,767 cases among the unrelated individuals to maximize the sample size of cases and randomly selected 104,233 individuals from 332,813 unrelated controls. We first estimated the segment-based LD score, stratified ~18 million SNPs into 2 groups based on the segment-based LD scores (high vs. low LD groups separated by the median), and then stratified the SNPs in each LD group into 7 MAF bins . We computed the GRMs using the stratified SNPs and performed GREML analysis fitting 14 GRMs  in one model to estimate the SNP-based heritability in each MAF bin. We used 10% as the population prevalence to convert the estimate to that on the liability scale.The MAF- and LD-stratified GREML (GREML-LDMS) is a method for estimating SNP-based heritability that is robust to model misspecification54 to estimate the joint distribution of SNP effect size and allele frequency. This analysis is based on 348,580 unrelated individuals  and HapMap3 SNPs (~1.23 million) with sex, age, and the first 10 PCs fitted as covariates. Each SNP effect has a mixture prior of a normal distribution and a point mass at zero, with an unknown mixing probability, π, representing the degree of polygenicity. The variance in effect size is modeled to be dependent on MAF through a parameter S. Under an evolutionarily neutral model, SNP effect sizes are independent of MAF, i.e., S = 0. A negative (positive) value of S indicates that variants with lower MAF are prone to having larger  effects, consistent with a model of negative (positive) selection. A Markov-chain Monte Carlo (MCMC) algorithm was used to draw posterior samples for statistical inference. The posterior mean was used as the point estimate, and the posterior standard error was approximated by the standard deviation of the MCMC samples. We conducted the analysis chromosome-wise for ease of computation.We used GCTB-BayesShttps://www.magicinvestigators.org/. For DrugBank, see https://www.drugbank.ca/. For DrugBank documentation, see https://www.drugbank.ca/documentation. For GWAS catalog, see http://www.ebi.ac.uk/gwas/. For DIAGRAM summary data, see http://www.diagram-consortium.org/. For Sanger imputation service, see https://imputation.sanger.ac.uk/. For GCTA, see http://cnsgenomics.com/software/gcta/. For GCTB, see http://cnsgenomics.com/software/gctb/.For MAGIC consortium, see http://cnsgenomics.com/data.html.Summary statistics from the meta-analysis are available at Supplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10Supplementary Data 11Supplementary Data 12Supplementary Data 13Supplementary Data 14Supplementary Data 15


The development of sequencing techniques and statistical methods provides great opportunities for identifying the impact of rare genetic variation on complex traits. However, there is a lack of knowledge on the impact of sample size, case numbers, the balance of cases vs controls for both burden and dispersion based rare variant association methods. For example, Phenome-Wide Association Studies may have a wide range of case and control sample sizes across hundreds of diagnoses and traits, and with the application of statistical methods to rare variants, it is important to understand the strengths and limitations of the analyses.We conducted a large-scale simulation of randomly selected low-frequency protein-coding regions using twelve different balanced samples with an equal number of cases and controls as well as twenty-one unbalanced sample scenarios. We further explored statistical performance of different minor allele frequency thresholds and a range of genetic effect sizes. Our simulation results demonstrate that using an unbalanced study design has an overall higher type I error rate for both burden and dispersion tests compared with a balanced study design. Regression has an overall higher type I error with balanced cases and controls, while SKAT has higher type I error for unbalanced case-control scenarios. We also found that both type I error and power were driven by the number of cases in addition to the case to control ratio under large control group scenarios. Based on our power simulations, we observed that a SKAT analysis with case numbers larger than 200 for unbalanced case-control models yielded over 90% power with relatively well controlled type I error. To achieve similar power in regression, over 500 cases are needed. Moreover, SKAT showed higher power to detect associations in unbalanced case-control scenarios than regression.Our results provide important insights into rare variant association study designs by providing a landscape of type I error and statistical power for a wide range of sample sizes. These results can serve as a benchmark for making decisions about study design for rare variant analyses.The online version of this article (10.1186/s12859-018-2591-6) contains supplementary material, which is available to authorized users. During the last decade, Genome-Wide Association Studies (GWAS) have greatly advanced our understanding of the impact of common variants on complex traits. The associations of alleles with frequency more than 1–5% have provided important insights into research and clinical practice . DespiteDue to the low frequency of rare variants, single locus association tests in traditional GWAS are underpowered for rare variant association analysis  unless tNumerous association methods have been developed , 9–18, aStatistical power for both burden and dispersion tests has been assessed in many simulation settings , 19, 20,In this study, we performed extensive simulation analyses to assess the influence of sample size on the type I error and power distribution for regression (a burden test) and SKAT (a dispersion test). We designed twelve balanced sample size datasets and twenty-one unbalanced sample size scenarios. Since a large sample size has been widely known as a necessity for detecting significant rare variant associations , 8, 25, We evaluated burden-based tests using logistic regression and dispersion-based tests using SKAT. All associations are evaluated for a binary outcome on a simulated gene with an average of 143 rare variant loci. We varied the number of cases, controls, and also the balance between cases and controls. All reported results here have a MAF upper bound (UB) set at 0.01. The supplementary material . We compare four scenarios here: an upper bound on simulated rare variants with a MAF of 0.01 and 0.05; a balanced sample size with 2000 cases and 2000 controls, and an unbalanced sample size with 200 cases and 10,000 controls. We chose these sample sizes from the results of our previous simulations as we observed both regression and SKAT to have adequate power and controlled type I error with these case control numbers.As shown in Fig. Previous simulation studies have been conducted to characterize the statistical performance for burden and dispersion-based approaches using a balanced population of cases and controls , 19, 20.We found an overall higher type I error rate for unbalanced samples (mostly above 0.05) compared with balanced samples (mostly below 0.05) for both tests, suggesting that an unequal number of cases and controls has a clear statistical impact on type I error for rare variant association analysis. Previous research has reported that the type I error rate for SKAT is conservative for smaller sample sizes . Indeed,Statistical power largely depends on the number of disease loci and the odds ratio. In this paper, we evaluated both same-direction signal (i.e. 2.5 odds ratio) and mixed odds ratio models Table  on 10 diAs for models with a range of variants contributing to risk and protection for an outcome, our results suggest that SKAT has an overall higher power compared with logistic regression. The results are expected since burden tests lose power when variants contribute to a range of risk and protection for an outcome. Understandably, as the impact of the rare variants on outcome increases, power increases for all scenarios.Based on our type I error and power results across various unbalanced sample sizes, a clear trend exists between these statistics and the number of cases in addition to the case to control ratio . Case to control ratio was calculated as the number of cases divided by the number of controls. Details of the study design with respect to sample size are shown in Table Minor allele frequencies (MAFs) were randomly assigned to our simulated rare variants using allele frequency distribution data from actual whole exome sequencing data from 50,726 patients from the MyCode Community Health Initiative as a part of the DiscovEHR project . Due to As our primary goal is to compare the effect of case-control sample sizes, we set other parameters as constant across all the datasets Table . All simAll of the datasets were generated using the software SeqSIMLA2.8, which can be used to design simulated datasets given user-specified sample size, effect sizes for genetic traits, and genetic model . The dis1, x2, x3, …, xp represent the genotypes across p disease loci. β1, β2, β3, …, βp represent the log of the odds ratios. SeqSIMLA will search for α so that the disease prevalence is close to the specified prevalence. Here, disease prevalence was set to 5%.xEach type I error or power value was calculated from 1000 independent simulated datasets with significance assessed at α = 0.05. We replicated 1000 runs 30 times as to account for sampling variability. Running 30 replicates of 1000 datasets was optimal to reduce computational and memory burden. The simulated data did not have any missingness in either genotype or phenotype. Type I error was obtained from null datasets with no genetic association signal. For power, 10 random disease loci with an odds ratio of 2.5 per locus were simulated. In our study, power is defined as the probability of detecting a true signal (i.e. to reject the null hypothesis) when the null hypothesis is false. Power is calculated as the number of datasets that have rejected the null hypothesis at α = 0.05 level divided by the total number of datasets (i.e. 1000). We also designed three sets of mixed odds ratio models where half of the 10 disease loci had protective effects, and half had risk effects, as described more in the next section.For most of the simulations, an odds ratio of 2.5 was used for 10 disease loci, indicating consistent risk for all associated rare variants. We also designed three types of protective and risk odds ratio combinations for the 10 disease loci. The detailed odds ratio for 10 disease loci are shown in Table All of the boxplots were generated using the “geom_boxplot” function within “ggplot2” R package . The “reAdditional file 1:Figure S1 and S2. Type I error and power simulation results with MAF upper bound of 0.05. Figure S3. Type I error and power simulation results using a constant case to control ratio. Figure S4. Type I error comparison when case control sample size is reversed. Table S1. Simulation results for case sample size of 200 and control sample size of 50 k, 100 k and 200 k. (PDF 551 kb)Additional file 2:A summary of results for type I error and power simulations with MAF upper bound of 0.01. (XLS 109 kb)


GAW20 working group 5 brought together researchers who contributed 7 papers with the aim of evaluating methods to detect genetic by epigenetic interactions. GAW20 distributed real data from the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) study, including single-nucleotide polymorphism (SNP) markers, methylation (cytosine-phosphate-guanine [CpG]) markers, and phenotype information on up to 995 individuals. In addition, a simulated data set based on the real data was provided.The 7 contributed papers analyzed these data sets with a number of different statistical methods, including generalized linear mixed models, mediation analysis, machine learning, W-test, and sparsity-inducing regularized regression. These methods generally appeared to perform well. Several papers confirmed a number of causative SNPs in either the large number of simulation sets or the real data on chromosome 11. Findings were also reported for different SNPs, CpG sites, and SNP–CpG site interaction pairs.In the simulation (200 replications), power appeared generally good for large interaction effects, but smaller effects will require larger studies or consortium collaboration for realizing a sufficient power. Genes do not act in isolation: the expression of gene-coded proteins is affected by many factors, including other genes, environment, and epigenetics. These interactions can complicate the identification of genes related to a particular trait or disease because some genes with an important effect through interaction can have a small marginal effect. The usefulness of interaction models for identifying causation based on disease and risk factors is demonstrated by Ruth Othman’s 1996 seminal paper  and geneThis paper surveys the findings of the papers presented at GAW20 in group 5: Gene by Methylation Interactions. Even though there are issues common to all interaction approaches, each interaction type has its own specific features. In the case of gene by epigenetic interactions, all the mechanisms of epigenetics are not yet fully understood. However, it is generally accepted that methylation of a DNA strand causes loci on the methylated span to be turned “off.” The generally available measure of methylation is the percentage of copies of a DNA strand site that are methylated . The expectation is that individuals with higher levels of methylation at a site will have a lower level of gene expression for that site. Incorporating this expectation into a statistical analysis can simplify it, as compared to, for example, an analysis of an environmental factor for which the direction and mechanism of the effect are completely unknown. As our understanding of the relationships between epigenetics and genes, environment, and ancestral epigenetics improves, we will be able to further refine the statistical tests for gene by epigenetic interaction. The papers included in this group represent a wide range of approaches facilitated by the current understanding of gene by epigenetic interaction.The data for GAW20 was provided by the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) project , 6. GAW2pre or TGpost . One paper examined cytosine-phosphate-guanine (CpG) site variation (Hu and Li).The GAW20 group 5 applied methods to both available types of data: real and simulated . The reaMost papers examined real GOLDN  data. One paper analyzed the simulated data in addition to real data , and one paper studied simulated data only ; model 1.b included only the interaction effect on TG post–medication-treatment plus the vector of covariates; model 2.a included as the response variable the change of TG (posttreatment–pretreatment) including the main effects, SNP and the methylation difference between visits 4 and 2, their interaction and covariates ; model 2.b was a reduced version of model 2.a that included only interactions. The models 1.a and 1.b were fitted using PROC GLM and PROC MIXED. Models 2.a and 2.b were fitted using only PROC MIXED. Regression trees were applied using SAS (v. 9.4) and SAS Data Mining (v. 14.1), as well as random forest in Python from the SciKit-Learn package, to predict outcome variables by averaging the predictions of a large number of uncorrelated regression trees. The authors tested for sensitivity using causative SNP-CpG site pairs and noncausative SNP-CpG site pairs to estimate the empirical null. They identified reasonable power to detect the main causative loci, depending on sample size and strength of the effects at the SNP and CpG sites.In Daw et al. , GLMs, mp values from 7.5 × 10− 6 to 7.0 × 10− 5. None of these 15 were reported by other papers in our group.Sun et al.  worked wcoxme R package [Mediation analysis was implemented by Fisher et al. , who inv package . They coHu and Li investigated the relation between genotype and methylation levels pretreatment and posttreatment via Gaussian mixture-model clustering. First, they identified CpG sites with multimodal methylation level distributions (mmCpGs). Subsequently, they identified SNPs that segregate with mmCpG modes to identify genes that may play a role in methylation levels. The authors identified 3785 and 3847 mmCpGs in pretreatment and posttreatment data sets . Of thesCPT1A and the APOA5 regions.Romanescu et al. applied a region-based test to identify CpG site regions associated with TG levels. They applied 4 statistical models: a single-site test for CpG site association and 3 regional tests. In regions defined by GENCODE annotation, they conducted a principal component analysis for SNP genotypes and for methylation levels. Then they conducted association tests incorporating (a) the SNP-principal component, (b) the CpG sites principal component, and (c) both. The authors used chromosome 11 real data. Their mixed linear models account for family structure, while incorporating the method proposed by Gauderman  using prlmekin function from the coxme R package [APOA5, was also found in other papers of this group.Veenstra et al. employed a candidate gene and a genome-wide approach to identify genetic and epigenetic effects on baseline TG. To remove any confounding effects, they adjusted for 6 covariates: age, sex, smoking, metabolic syndrome diagnosis (msdx), fasting time at baseline, and high-density lipoprotein cholesterol. They used the  package . FurtherCPT1A.Zhou and Lo applied LASSO (least absolute shrinkage and selection operator)-type regression models to identify SNP–CpG site interactions . The metCPT1A, which was previously reported by the GOLDN study [CPT1A and the genes in the APOA5 region, are biologically involved in lipid metabolism. The other papers that analyzed real TG data ); 2 papers looked at absolute change in log(TG), with 1 paper also examining post(log(TG)) and 1 dichotomizing percent change in TG. In addition, 1 study used CpG sites as a response variable. Papers 4, 6, and 7 all analyzed baseline TG and obtained a set of overlapping results on chromosome 11 , but smaller effects appear to require larger studies or consortiums to have sufficient power.


An important and broadly used tool for selection purposes and to increase yield and genetic gain in plant breeding programs is genomic prediction (GP). Genomic prediction is a technique where molecular marker information and phenotypic data are used to predict the phenotype  of individuals for which only marker data are available. Higher prediction accuracy can be achieved not only by using efficient models but also by using quality molecular marker and phenotypic data. The steps of a typical quality control (QC) of marker data include the elimination of markers with certain level of minor allele frequency (MAF) and missing marker values and the imputation of missing marker values. In this article, we evaluated how the prediction accuracy is influenced by the combination of 12 MAF values, 27 different percentages of missing marker values, and 2 imputation techniques ). We constructed a response surface of prediction accuracy values for the two ITs as a function of MAF and percentage of missing marker values using soybean data from the University of Nebraska–Lincoln Soybean Breeding Program. We found that both the genetic architecture of the trait and the IT affect the prediction accuracy implying that we have to be careful how we perform QC on the marker data. For the corresponding combinations MAF-percentage of missing values we observed that implementing the RF imputation increased the number of markers by 2 to 5 times than the simple naïve imputation method that is based on the mean allele dosage of the non-missing values at each loci. We conclude that there is not a unique strategy (combination of the QCs and imputation method) that outperforms the results of the others for all traits. According to the World Agricultural Outlook Report by the United States Department of Agriculture (USDA), in 2016, the United States produced more than 100 million of tons of soybean, and in 2018, it was projected that the production would be close to 120 million of tons. Soybean provides a high-quality vegetable protein that is used primarily in animal feed and for human food uses and is the leading vegetable protein produced worldwide. Soybean oil is a high-quality vegetable oil that is used in food, feed, and industrial applications. Thus, with the increasing demand for high-quality and sustainable food production, it is necessary to improve soybean yield and increase the performance through genetic improvement. Rates of genetic gain in soybean have been estimated at about 17 to 22 kg/ha/year, but potentially can be improved.4 compared with marker-assisted selection. Genomic prediction is a procedure that combines genotypic and phenotypic information to build prediction models and performs prediction on un-phenotyped lines using only their marker profiles. The technique was first introduced by Meuwissen et al.5 Since then, a lot of effort was devoted to model development in GP,69 implementation of GP,11 and model comparison.1214With the advancements in genotyping technologies and sequencing, an important increment in the number of delivered markers at low cost can be achieved, which can open opportunities to increase genetic gain in soybean. Genomic prediction (GP) is a technique that is widely used in breeding programs for cultivar development, and it aids the selection process by taking advantage of the use of molecular markers for estimating the performance of lines based on their genomic estimated breeding value. It is more effective than traditional phenotypic or pedigree-based selection, and it has the potential to increase genetic gain by threefolds14 used response surface methodology to optimize GP models based on number of lines, number of markers, number of quantitative trait loci, degree of epistasis (gene-by-gene interaction), and degree of heritability (proportion of phenotypic variability explained by the genetic variability) in a simulated data set. There are studies that aim to improve GP models by optimizing the relationship between the training and the testing sets.15 Genomic prediction models can also be improved by optimizing the quality control (QC) of the genotypic data used for model development. Jarquín et al16 compared prediction models for a soybean population grown by the University of Nebraska—Lincoln Soybean Breeding Program with different degrees of missingness and minor allele frequency (MAF) in the genomic marker data. However, the focus of the study was not to evaluate a comprehensive set of factors considered in QC but to evaluate the genotype-by-sequencing genotyping technology in GP for soybean breeding.16Another avenue to improve GP models is to optimize them according to the data available for prediction. Howard et al17 others use information from higher density panels from reference individuals,18 or are based on classification and regression methods for unordered markers.19 A compressive review of the impacts on predictive ability of several imputation methods can be found in Rutkoski et al.20In this study, we evaluated GP accuracy based on QC of genomic data collected on soybean populations grown by the University of Nebraska—Lincoln Soybean Breeding Program. We varied the sets of markers to be included in the model by considering different percentages of missing values  and different levels for MAF (12 levels). Training and testing sets for all these combinations (27 × 12 = 324) were conformed 200 times. The evaluation of this comprehensive set of combinations offered the opportunity to construct the response surface of the prediction accuracy . As the genotyping by sequencing (GBS) technology is not perfect and a large number of missing values are delivered, 2 imputation methods were implemented to compare their effects on the predictive ability of the models -based imputation). In this context, several novelty methods have been developed for imputing missing data. Some of these consider haplotype phase information,In this article, first the phenotypic and genotypic marker data that were used for GP are introduced. Then, it is described how the QCs were implemented for the different factors and levels used for constructing the response surface of the prediction accuracy values for the 2 imputation methods. Briefly, the GP model that was implemented is also introduced. Finally, we discuss the response surface of the prediction accuracy values dependent on the level of missing marker values, the MAF, and the imputation technique (IT) used to create more comprehensive sets of genomic data, and some conclusions based on our findings are provided.16 Phenotypes of 3 traits were considered in the analysis: grain yield (GY), days to maturity (DTM), and plant height (PH). The phenotypes were adjusted accounting for the location and block effects due to the experimental design. The genomic data, the genotyping procedure, and the GBS analysis are described in detail in Jarquín et al.16 Briefly, DNA isolation was performed using the Qiagen DNeasy Plant 96 kit, and the samples were analyzed in the Institute of Genomic Diversity at Cornell University. Then, the GBS analysis pipeline implemented in Tassel Version 3.0.156 was used to call the single-nucleotide polymorphisms (SNPs). After the SNP calling, the molecular marker information consisted of 216K SNP markers.The predictions were conducted using phenotypic and genotypic data on 301 soybean lines grown by the University of Nebraska—Lincoln Breeding Program. These lines belong to 3 maturity groups (MG)  and were tested in 6 locations in Nebraska . Only in the Phillips and Mead locations were all the lines tested. A complete description of the distribution of the lines and the experimental design can be found in Jarquín et al.The GP model used to evaluate prediction accuracy for the 3 traits  was the genomic best linear unbiased prediction (G-BLUP) model including only additive effects. The model can be written asiy is the phenotype of the ith line , μ is the overall mean, ig is the additive genetic value of the ith line, and εi is the corresponding residual term.where y = μ + g + ε, where g = Xb with X being a n × p (n is the number of genotype and p is the number of markers) dimensional matrix of genotype scores. Considering that the marker effects associated with the jth marker  are distributed as g (the vector of genetic effects) are the null vector 0 and G is commonly referred to as the Genomic Relationship Matrix and its entries describe the genetic similarities among pair of lines.Using matrix notation, the model can be written as The model was evaluated based on prediction accuracy, which was defined as the first moment Pearson correlation coefficient between the observed phenotypic value and the predicted genomic-enabled breeding value. The predictions were carried out using a tenfold cross-validation scheme, which was repeated 200 times. Then, the mean and the variance of the prediction accuracy values were calculated.21 and wheat,22 a MAF of 0.05 was used for GBS and an Infinitum SNP array, respectively, while23 considered a cut-off of 0.01 in wheat for GBS data. PMMS is the percentage of missing marker scores is the percentage of marker scores in the genomic data set that are missing. A large percentage of missing values would lead to inaccurate estimations of markers’ effects delivering biased and incorrect predictions. Thus, markers with a large PMMS should be avoided in the analysis. For this factor, these previous authors considered a similar cut-off criterion and discarded those markers with more than 20%, 15%, and 20%, respectively.Quality control is a fundamental step in genomic data analysis and GP, and it might significantly influence the prediction accuracy. In our study, we focused on evaluating 3 of the most important factors in QC. These are done after the genomic data are translated to a numeric format. These 3 factors were the MAF, the percentage of missing marker scores (PMMS), and the IT used to complete the genotypic data. Minor allele frequency is the proportion of the second most common allele occurring in a population. Using genomic data, it is calculated as the frequency of the second most common allele among the genotyped lines. This value provides information about the proportion of common versus rare variants in the population. The procedure consists in discarding markers from the analysis with a MAF smaller than a given cut-off value. In genomic studies, different cut-off points have been adopted for discarding makers based on MAF. Thus, there is not a conventional value used in all species. For example, in maizeThe purpose of the study was to evaluate prediction accuracy using genomic data where MAF and PMMS are varied under 2 ITs (naïve and RF). The response of the prediction accuracy under different combinations of the levels of MAF and PMMS was visualized by a response surface plot. The response surface was evaluated at all of the pairwise combinations of 12 levels of MAF and 27 levels of PMMS. The response surface was examined for highest peak, and 4 common MAF × PMMS combinations were evaluated. Also, the number of markers at each MAF × PMMS combinations were computed, and the values were added in the bottom part of the response surface plot using a scaled surface.In this study, the response surface of GP accuracy was created as a function of the combination of MAF and PMMS, and 2 ITs used for imputing missing values in the genomic data were compared. For the predictions, genomic and yield data from the University of Nebraska—Lincoln Soybean Breeding Program were used.The 12 levels considered for MAF were 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40, while the 27 levels for PMMS were 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13%, 14%, 15%, 16%, 17%, 18%, 19%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, and 80%. For imputing the marker scores, we compared the naïve and RF ITs. Figures 1Besides the 4 common coordinates, the highest peak is also shown on the response surface plots. In only one case, the highest peak was also 1 of the 4 commonly evaluated coordinates. The black dots represent the mean prediction accuracy values for the 4 common coordinates, and the yellow dots are the mean prediction accuracy values for the highest peak. The blue dots show the standard deviation of the prediction accuracy using the 200 replicates for a 10-fold cross-validation design. The numerical values within the plots represent the number of markers used at those coordinates (combinations).For GY under the naïve IT , the hig24 this trait is controlled by a very few loci. Here, the RF imputation gave the highest predictive ability (0.524) using approximately 2.5 times more markers (9287) than the naïve imputation (3799), which produced a mean correlation of 0.515. Similar to the previous case, the response surface obtained by the RF seemed a little flatter than the surface obtained by the other imputation method. Despite the imputation method, there were sizable improvements in predictive ability with respect to conventional QCs. These improvements ranged between 27% and 48% for naïve imputation, while for RF, it was between 17% and 47%. Hence, a clear advantage was shown by considering other than conventionally used QCs.Results for PH  and 4 shDays to maturity showed a slight improvement in predictive ability by using the RF imputation compared with the naïve method. Similarly to the other 2 traits, the response surface was flatter  using the RF technique. This IT gave the highest correlation (0.704) using 2.2 times more markers (26 512) than what was necessary with the naïve method (11 917), which delivered a mean correlation of 0.691. For this trait, the improvements with respect to conventional QCs ranged between 2% and 7% for both imputation methods. Thus, no significant improvements were observed considering other values than the commonly used QCs.In this study, we showed that the improvements in predictive ability are affected by (1) the genetic architecture of the trait and (2) the imputation method as well. The highest correlations were found considering different combinations of MAF and PMMS, which also varied the number of markers necessary for the analysis. In general, RF produced flatter response surfaces showing a slight advantage by using this imputation method. Also, this method needed between 2 and 5 times more markers than the naïve imputation for producing comparable results. Finally, we saw sizable, moderate, and null improvements in predictive ability for PH, GY, and DTM, respectively, by considering QCs other than those that are commonly used.