Genetic Architecture Of Complex Diseases Research Articles

A Novel Detection Method for High-Order SNP Epistatic Interactions Based on Explicit-Encoding-Based Multitasking Harmony Search.

To elucidate the genetic basis of complex diseases, it is crucial to discover the single-nucleotide polymorphisms (SNPs) contributing to disease susceptibility. This is particularly challenging for high-order SNP epistatic interactions (HEIs), which exhibit small individual effects but potentially large joint effects. These interactions are difficult to detect due to the vast search space, encompassing billions of possible combinations, and the computational complexity of evaluating them. This study proposes a novel explicit-encoding-based multitasking harmony search algorithm (MTHS-EE-DHEI) specifically designed to address this challenge. The algorithm operates in three stages. First, a harmony search algorithm is employed, utilizing four lightweight evaluation functions, such as Bayesian network and entropy, to efficiently explore potential SNP combinations related to disease status. Second, a G-test statistical method is applied to filter out insignificant SNP combinations. Finally, two machine learning-based methods, multifactor dimensionality reduction (MDR) as well as random forest (RF), are employed to validate the classification performance of the remaining significant SNP combinations. This research aims to demonstrate the effectiveness of MTHS-EE-DHEI in identifying HEIs compared to existing methods, potentially providing valuable insights into the genetic architecture of complex diseases. The performance of MTHS-EE-DHEI was evaluated on twenty simulated disease datasets and three real-world datasets encompassing age-related macular degeneration (AMD), rheumatoid arthritis (RA), and breast cancer (BC). The results demonstrably indicate that MTHS-EE-DHEI outperforms four state-of-the-art algorithms in terms of both detection power and computational efficiency. The source code is available at https://github.com/shouhengtuo/MTHS-EE-DHEI.git .

Genetic associations with disease in populations with Indigenous American ancestries.

The genetic architecture of complex diseases affecting populations with Indigenous American ancestries is poorly understood due to their underrepresentation in genomics studies. While most of the genetic diversity associated with disease trait variation is shared among worldwide populations, a fraction of this component is expected to be unique to each continental group, including Indigenous Americans. Here, I describe the current state of knowledge from genome-wide association studies on Indigenous populations, as well as non-Indigenous populations with partial Indigenous ancestries from the American continent, focusing on disease susceptibility and anthropometric traits. While some studies identified risk alleles unique to Indigenous populations, their effects on trait variation are mostly small. I suggest that the associations rendered by many inter-population studies are probably inflated due to the absence of socio-cultural-economic covariates in the association models. I encourage the inclusion of admixed individuals in future GWAS studies to control for inter-ancestry differences in environmental factors. I suggest that some complex diseases might have arisen as trade-off costs of adaptations to past evolutionary selective pressures. Finally, I discuss how expanding panels with Indigenous ancestries in GWAS studies is key to accurately assess genetic risk in populations from the American continent, thus decreasing global health disparities.

Genome-wide association study of heart failure in a multiethnic south-east asian cohort

Abstract NMRC Heart failure (HF) is a leading cause of morbidity and mortality worldwide (1). While existing genome-wide association studies (GWAS) have yielded many different loci and causal genes, most of such studies has been conducted in European populations (2). There has been little insight into the genetic architecture of complex diseases, especially HF among Asians, despite up to 60% of the world population consisting of Asians. Through this study, we aim to uncover the genomic basis of heart failure in a South-East Asian cohort, with deep phenotyping of cardiovascular, metabolic, immune, and inflammatory traits. We conducted the largest multi-ancestry South-east Asian all-cause HF GWAS (n=2310, 1305 cases and 1005 controls), utilizing whole genome sequencing (WGS) data. Eleven independent loci were found to be associated with HF (P-value = 5e10-8). In-silico and functional studies were interrogated, allowing us to map most of the loci (n=9) to various genes implicated in various metabolic diseases - hypertension (HTN), diabetes mellitus (DM), and coronary artery disease (CAD). We further conducted a phenome-wide association study (PWAS) of significant loci, which revealed that they augment signals related to CAD, atrial fibrillation, DM and HTN, suggesting a shared genetic etiology between these metabolic risk factors and Asian HF. Of note, this the first HF GWAS to implicate the PDE9A gene, which was previously discovered as a potential biomarker for HF with preserved ejection fraction (HFpEF) through its involvement in the cGMP signaling pathways, and is currently being explored as a therapeutic target in the treatment of HFpEF (3). Polygenic risk scores (PRS) were calculated for heart failure in this Asian cohort, which identified that the most optimized model (HF PRS), included 19,431 of the most significant genetic variants (p=0.073). The prediction power of the HF PRS on HF risk was tested in UKB Asian subjects (N=10,016; 413 cases and 9,603 controls). Our results showed that the highest 10% percentile HF PRS risk subjects in UKB Asian were at 1.56-fold risks (95% CI: 1.16-2.08) for HF. This study provides a comprehensive understanding of the genetic architecture, and sheds light on novel biological pathways underlying HF in a south-east Asian population, indicating a highly metabolic underpinnings of this disease. It provides a step towards developing a precision-medicine based approach for risk stratification, prevention, and management of HF among Asians. Furthermore, this study provides evidence for the use of WGS in GWAS, to expand the discovery of novel targets for downstream interrogation, biomarker and drug development for complex diseases.

Disentangling the complexity of psoriasis in the post-genome-wide association era.

In recent years, genome-wide association studies (GWAS) have been instrumental in unraveling the genetic architecture of complex diseases, including psoriasis. The application of large-scale GWA studies in psoriasis has illustrated several associated loci that participate in the cutaneous inflammation, however explaining a fraction of the disease heritability. With the advent of high-throughput sequencing technologies and functional genomics approaches, the post-GWAS era aims to unravel the functional mechanisms underlying the inter-individual variability in psoriasis patients. In this review, we present the key advances of psoriasis GWAS in under-represented populations, rare, non-coding and structural variants and epistatic phenomena that orchestrate the interplay between different cell types. We further review the gene-gene and gene-environment interactions contributing to the disease predisposition and development of comorbidities through Mendelian randomization studies and pleiotropic effects of psoriasis-associated loci. We finally examine the holistic approaches conducted in psoriasis through system genetics and state-of-the-art transcriptomic analyses, discussing their potential implication in the expanding field of precision medicine and characterization of comorbidities.

Gene Interactions in Human Disease Studies-Evidence Is Mounting.

Despite monumental advances in molecular technology to generate genome sequence data at scale, there is still a considerable proportion of heritability in most complex diseases that remains unexplained. Because many of the discoveries have been single-nucleotide variants with small to moderate effects on disease, the functional implication of many of the variants is still unknown and, thus, we have limited new drug targets and therapeutics. We, and many others, posit that one primary factor that has limited our ability to identify novel drug targets from genome-wide association studies may be due to gene interactions (epistasis), gene-environment interactions, network/pathway effects, or multiomic relationships. We propose that many of these complex models explain much of the underlying genetic architecture of complex disease. In this review, we discuss the evidence from multiple research avenues, ranging from pairs of alleles to multiomic integration studies and pharmacogenomics, that supports the need for further investigation of gene interactions (or epistasis) in genetic and genomic studies of human disease. Our goal is to catalog the mounting evidence for epistasis in genetic studies and the connections between genetic interactions and human health and disease that could enable precision medicine of the future. Expected final online publication date for the Annual Review of Biomedical Data Science, Volume 6 is August 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Ravages: An R package for the simulation and analysis of rare variants in multicategory phenotypes.

Current software packages for the analysis and the simulations of rare variants are only available for binary and continuous traits. Ravages provides solutions in a single R package to perform rare variant association tests for multicategory, binary and continuous phenotypes, to simulate datasets under different scenarios and to compute statistical power. Association tests can be run in the whole genome thanks to C++ implementation of most of the functions, using either RAVA-FIRST, a recently developed strategy to filter and analyse genome-wide rare variants, or user-defined candidate regions. Ravages also includes a simulation module that generates genetic data for cases who can be stratified into several subgroups and for controls. Through comparisons with existing programmes, we show that Ravages complements existing tools and will be useful to study the genetic architecture of complex diseases. Ravages is available on the CRAN at https://cran.r-project.org/web/packages/Ravages/ and maintained on Github at https://github.com/genostats/Ravages.

NSPA: characterizing the disease association of multiple genetic interactions at single-subject resolution.

The interaction between genetic variables is one of the major barriers to characterizing the genetic architecture of complex traits. To consider epistasis, network science approaches are increasingly being used in research to elucidate the genetic architecture of complex diseases. Network science approaches associate genetic variables' disease susceptibility to their topological importance in the network. However, this network only represents genetic interactions and does not describe how these interactions attribute to disease association at the subject-scale. We propose the Network-based Subject Portrait Approach (NSPA) and an accompanying feature transformation method to determine the collective risk impact of multiple genetic interactions for each subject. The feature transformation method converts genetic variants of subjects into new values that capture how genetic variables interact with others to attribute to a subject's disease association. We apply this approach to synthetic and genetic datasets and learn that (1) the disease association can be captured using multiple disjoint sets of genetic interactions and (2) the feature transformation method based on NSPA improves predictive performance comparing with using the original genetic variables. Our findings confirm the role of genetic interaction in complex disease and provide a novel approach for gene-disease association studies to identify genetic architecture in the context of epistasis. The codes of NSPA are now available in: https://github.com/MIB-Lab/Network-based-Subject-Portrait-Approach. ting.hu@queensu.ca. Supplementary data are available at Bioinformatics Advances online.

Genome-Wide Causation Studies of Complex Diseases.

Despite significant progress in dissecting the genetic architecture of complex diseases by genome-wide association studies (GWAS), the signals identified by association analysis may not have specific pathological relevance to diseases so that a large fraction of disease-causing genetic variants is still hidden. Association is used to measure dependence between two variables or two sets of variables. GWAS test association between a disease and single-nucleotide polymorphisms (SNPs) (or other genetic variants) across the genome. Association analysis may detect superficial patterns between disease and genetic variants. Association signals provide limited information on the causal mechanism of diseases. The use of association analysis as a major analytical platform for genetic studies of complex diseases is a key issue that may hamper discovery of disease mechanisms, calling into the questions the ability of GWAS to identify loci-underlying diseases. It is time to move beyond association analysis toward techniques, which enables the discovery of the underlying causal genetic structures of complex diseases. To achieve this, we propose the concept of genome-wide causation studies (GWCS) as an alternative to GWAS and develop additive noise models (ANMs) for genetic causation analysis. Type 1 error rates and power of the ANMs in testing causation are presented. We conducted GWCS of schizophrenia. Both simulation and real data analysis show that the proportion of the overlapped association and causation signals is small. Thus, we anticipate that our analysis will stimulate serious discussion of the applicability of GWAS and GWCS.

Protein interaction networks define the genetic architecture of preterm birth

The likely genetic architecture of complex diseases is that subgroups of patients share variants in genes in specific networks sufficient to express a shared phenotype. We combined high throughput sequencing with advanced bioinformatic approaches to identify such subgroups of patients with variants in shared networks. We performed targeted sequencing of patients with 2 or 3 generations of preterm birth on genes, gene sets and haplotype blocks that were highly associated with preterm birth. We analyzed the data using a multi-sample, protein–protein interaction (PPI) tool to identify significant clusters of patients associated with preterm birth. We identified shared protein interaction networks among preterm cases in two statistically significant clusters, p < 0.001. We also found two small control-dominated clusters. We replicated these data on an independent, large birth cohort. Separation testing showed significant similarity scores between the clusters from the two independent cohorts of patients. Canonical pathway analysis of the unique genes defining these clusters demonstrated enrichment in inflammatory signaling pathways, the glucocorticoid receptor, the insulin receptor, EGF and B-cell signaling, These results support a genetic architecture defined by subgroups of patients that share variants in genes in specific networks and pathways which are sufficient to give rise to the disease phenotype.

LYRUS: a machine learning model for predicting the pathogenicity of missense variants.

SummarySingle amino acid variations (SAVs) are a primary contributor to variations in the human genome. Identifying pathogenic SAVs can provide insights to the genetic architecture of complex diseases. Most approaches for predicting the functional effects or pathogenicity of SAVs rely on either sequence or structural information. This study presents 〈Lai Yang Rubenstein Uzun Sarkar〉 (LYRUS), a machine learning method that uses an XGBoost classifier to predict the pathogenicity of SAVs. LYRUS incorporates five sequence-based, six structure-based and four dynamics-based features. Uniquely, LYRUS includes a newly proposed sequence co-evolution feature called the variation number. LYRUS was trained using a dataset that contains 4363 protein structures corresponding to 22 639 SAVs from the ClinVar database, and tested using the VariBench testing dataset. Performance analysis showed that LYRUS achieved comparable performance to current variant effect predictors. LYRUS’s performance was also benchmarked against six Deep Mutational Scanning datasets for PTEN and TP53.Availability and implementationLYRUS is freely available and the source code can be found at https://github.com/jiaying2508/LYRUS.Supplementary information Supplementary data are available at Bioinformatics Advances online.

CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations.

MotivationGene–environment interaction (GEI) studies are a general framework that can be used to identify genetic variants that modify the effects of environmental, physiological, lifestyle or treatment effects on complex traits. Moreover, accounting for GEIs can enhance our understanding of the genetic architecture of complex diseases and traits. However, commonly used statistical software programs for GEI studies are either not applicable to testing certain types of GEI hypotheses or have not been optimized for use in large samples.ResultsHere, we develop a new software program, GEM (Gene–Environment interaction analysis in Millions of samples), which supports the inclusion of multiple GEI terms, adjustment for GEI covariates and robust inference, while allowing multi-threading to reduce computation time. GEM can conduct GEI tests as well as joint tests of genetic main and interaction effects for both continuous and binary phenotypes. Through simulations, we demonstrate that GEM scales to millions of samples while addressing limitations of existing software programs. We additionally conduct a gene-sex interaction analysis on waist-hip ratio in 352 768 unrelated individuals from the UK Biobank, identifying 24 novel loci in the joint test that have not previously been reported in combined or sex-specific analyses. Our results demonstrate that GEM can facilitate the next generation of large-scale GEI studies and help advance our understanding of the genetic architecture of complex diseases and traits.Availability and implementationGEM is freely available as an open source project at https://github.com/large-scale-gxe-methods/GEM.Supplementary information Supplementary data are available at Bioinformatics online.

The impact of non-additive genetic associations on age-related complex diseases

Genome-wide association studies (GWAS) are not fully comprehensive, as current strategies typically test only the additive model, exclude the X chromosome, and use only one reference panel for genotype imputation. We implement an extensive GWAS strategy, GUIDANCE, which improves genotype imputation by using multiple reference panels and includes the analysis of the X chromosome and non-additive models to test for association. We apply this methodology to 62,281 subjects across 22 age-related diseases and identify 94 genome-wide associated loci, including 26 previously unreported. Moreover, we observe that 27.7% of the 94 loci are missed if we use standard imputation strategies with a single reference panel, such as HRC, and only test the additive model. Among the new findings, we identify three novel low-frequency recessive variants with odds ratios larger than 4, which need at least a three-fold larger sample size to be detected under the additive model. This study highlights the benefits of applying innovative strategies to better uncover the genetic architecture of complex diseases.

Multi-Set Testing Strategies Show Good Behavior When Applied to Very Large Sets of Rare Variants.

Gene-based tests of association (e.g., variance components and burden tests) are now common practice for analyses attempting to elucidate the contribution of rare genetic variants on common disease. As sequencing datasets continue to grow in size, the number of variants within each set (e.g., gene) being tested is also continuing to grow. Pathway-based methods have been used to allow for the initial aggregation of gene-based statistical evidence and then the subsequent aggregation of evidence across the pathway. This “multi-set” approach (first gene-based test, followed by pathway-based) lacks thorough exploration in regard to evaluating genotype–phenotype associations in the age of large, sequenced datasets. In particular, we wonder whether there are statistical and biological characteristics that make the multi-set approach optimal vs. simply doing all gene-based tests? In this paper, we provide an intuitive framework for evaluating these questions and use simulated data to affirm us this intuition. A real data application is provided demonstrating how our insights manifest themselves in practice. Ultimately, we find that when initial subsets are biologically informative (e.g., tending to aggregate causal genetic variants within one or more subsets, often genes), multi-set strategies can improve statistical power, with particular gains in cases where causal variants are aggregated in subsets with less variants overall (high proportion of causal variants in the subset). However, we find that there is little advantage when the sets are non-informative (similar proportion of causal variants in the subsets). Our application to real data further demonstrates this intuition. In practice, we recommend wider use of pathway-based methods and further exploration of optimal ways of aggregating variants into subsets based on emerging biological evidence of the genetic architecture of complex disease.

Learning gene networks underlying clinical phenotypes using SNP perturbation.

Availability of genome sequence, molecular, and clinical phenotype data for large patient cohorts generated by recent technological advances provides an opportunity to dissect the genetic architecture of complex diseases at system level. However, previous analyses of such data have largely focused on the co-localization of SNPs associated with clinical and expression traits, each identified from genome-wide association studies and expression quantitative trait locus mapping. Thus, their description of the molecular mechanisms behind the SNPs influencing clinical phenotypes was limited to the single gene linked to the co-localized SNP. Here we introduce PerturbNet, a statistical framework for learning gene networks that modulate the influence of genetic variants on phenotypes, using genetic variants as naturally occurring perturbation of a biological system. PerturbNet uses a probabilistic graphical model to directly model the cascade of perturbation from genetic variants to the gene network to the phenotype network along with the networks at each layer of the biological system. PerturbNet learns the entire model by solving a single optimization problem with an efficient algorithm that can analyze human genome-wide data within a few hours. PerturbNet inference procedures extract a detailed description of how the gene network modulates the genetic effects on phenotypes. Using simulated and asthma data, we demonstrate that PerturbNet improves statistical power for detecting disease-linked SNPs and identifies gene networks and network modules mediating the SNP effects on traits, providing deeper insights into the underlying molecular mechanisms.

Detecting rare haplotypes associated with complex diseases using both population and family data: Combined logistic Bayesian Lasso.

Haplotype-based association methods have been developed to understand the genetic architecture of complex diseases. Compared to single-variant-based methods, haplotype methods are thought to be more biologically relevant, since there are typically multiple non-independent genetic variants involved in complex diseases, and the use of haplotypes implicitly accounts for non-independence caused by linkage disequilibrium. In recent years, with the focus moving from common to rare variants, haplotype-based methods have also evolved accordingly to uncover the roles of rare haplotypes. One particular approach is regularization-based, with the use of Bayesian least absolute shrinkage and selection operator (Lasso) as an example. This type of methods has been developed for either case-control population data (the logistic Bayesian Lasso (LBL)) or family data (family-triad-based logistic Bayesian Lasso (famLBL)). In some situations, both family data and case-control data are available; therefore, it would be a waste of resources if only one of them could be analyzed. To make full usage of available data to increase power, we propose a unified approach that can combine both case-control and family data (combined logistic Bayesian Lasso (cLBL)). Through simulations, we characterized the performance of cLBL and showed the advantage of cLBL over existing methods. We further applied cLBL to the Framingham Heart Study data to demonstrate its utility in real data applications.

Ancestry-Dependent Enrichment of Deleterious Homozygotes in Runs of Homozygosity

Runs of homozygosity (ROH) are important genomic features that manifest when an individual inherits two haplotypes that are identical by descent. Their length distributions are informative about population history, and their genomic locations are useful for mapping recessive loci contributing to both Mendelian and complex disease risk. We have previously shown that ROH, and especially long ROH that are likely the result of recent parental relatedness, are enriched for homozygous deleterious coding variation in a worldwide sample of outbred individuals. However, the distribution of ROH in admixed populations and their relationship to deleterious homozygous genotypes is understudied. Here we analyze whole-genome sequencing data from 1,441 unrelated individuals from self-identified African American, Puerto Rican, and Mexican American populations. These populations are three-way admixed between European, African, and Native American ancestries and provide an opportunity to study the distribution of deleterious alleles partitioned by local ancestry and ROH. We re-capitulate previous findings that long ROH are enriched for deleterious variation genome-wide. We then partition by local ancestry and show that deleterious homozygotes arise at a higher rate when ROH overlap African ancestry segments than when they overlap European or Native American ancestry segments of the genome. These results suggest that, while ROH on any haplotype background are associated with an inflation of deleterious homozygous variation, African haplotype backgrounds may play a particularly important role in the genetic architecture of complex diseases for admixed individuals, highlighting the need for further study of these populations.

Genome-wide enhancer annotations differ significantly in genomic distribution, evolution, and function

BackgroundNon-coding gene regulatory enhancers are essential to transcription in mammalian cells. As a result, a large variety of experimental and computational strategies have been developed to identify cis-regulatory enhancer sequences. Given the differences in the biological signals assayed, some variation in the enhancers identified by different methods is expected; however, the concordance of enhancers identified by different methods has not been comprehensively evaluated. This is critically needed, since in practice, most studies consider enhancers identified by only a single method. Here, we compare enhancer sets from eleven representative strategies in four biological contexts.ResultsAll sets we evaluated overlap significantly more than expected by chance; however, there is significant dissimilarity in their genomic, evolutionary, and functional characteristics, both at the element and base-pair level, within each context. The disagreement is sufficient to influence interpretation of candidate SNPs from GWAS studies, and to lead to disparate conclusions about enhancer and disease mechanisms. Most regions identified as enhancers are supported by only one method, and we find limited evidence that regions identified by multiple methods are better candidates than those identified by a single method. As a result, we cannot recommend the use of any single enhancer identification strategy in all settings.ConclusionsOur results highlight the inherent complexity of enhancer biology and identify an important challenge to mapping the genetic architecture of complex disease. Greater appreciation of how the diverse enhancer identification strategies in use today relate to the dynamic activity of gene regulatory regions is needed to enable robust and reproducible results.

A rectified factor network based biclustering method for detecting cancer-related coding genes and miRNAs, and their interactions.

Detecting cancer-related genes and their interactions is a crucial task in cancer research. For this purpose, we proposed an efficient method, to detect coding genes, microRNAs (miRNAs), and their interactions related to a particular cancer or a cancer subtype using their expression data from the same set of samples. Firstly, biclusters specific to a particular type of cancer are detected based on rectified factor networks and ranked according to their associations with general cancers. Secondly, coding genes and miRNAs in each bicluster are prioritized by considering their differential expression and differential correlation values, protein-protein interaction data, and potential cancer markers. Finally, a rank fusion process is used to obtain the final comprehensive rank by combining multiple ranking results. We applied our proposed method on breast cancer datasets. Results show that our method outperforms other methods in detecting breast cancer-related coding genes and miRNAs. Furthermore, our method is very efficient in computing time, which can handle tens of thousands genes/miRNAs and hundreds of patients in hours on a desktop. This work may aid researchers in studying the genetic architecture of complex diseases, and improving the accuracy of diagnosis.

Genetic Study on Small Insertions and Deletions in Psoriasis Reveals a Role in Complex Human Diseases

Genetic studies based on single-nucleotide polymorphisms have provided valuable insights into the genetic architecture of complex diseases. However, a large fraction of heritability for most of these diseases remains unexplained, and the impact of small insertions and deletions (InDels) has been neglected. We performed a comprehensive screen on the exome sequence data of 1,326 genes using the SOAP-PopIndel method for InDels in 32,043 Chinese Han individuals and identified 29 unreported InDels within 25 susceptibility genes associated with psoriasis. Specifically, we identified 12 common, 9 low-frequency, and 8 rare InDels that explained approximately 1.29% of the heritability of psoriasis. Further analyses identified KIAA0319, RELN, NCAPG, ABO, AADACL2, LMAN1, FLG, HERC5, CCDC66, LEKR1, AFF3, ABCG2, ANXA7, SYTL2,GIPR, METTL1, and FYCO1 as unreported genes for psoriasis. In addition, identified InDels were associated with the following reported genes: IFIH1, ERAP1, ERAP2, LNPEP, UBLCP1, and STAT3; unreported independent associations for exonic InDels were found within GJB2 and ZNF816A. Our study enriched the genetic basis and pathogenesis of psoriasis and highlighted the non-negligible impact of InDels on complex human diseases.

Case-control studies of gene-environment interactions. When a case might not be the case.

Case-control Genome-Wide Association Studies (GWAS) provide a rich resource for studying the genetic architecture of complex diseases. A key is to elucidate how the genetic effects vary by the environment, what is traditionally defined by Gene-Environment interactions (GxE). The overlooked complication is that multiple, distinct pathophysiologic mechanisms may lead to the same clinical diagnosis and often these mechanisms have distinct genetic bases. In this paper, we first show that using the clinically diagnosed status can lead to severely biased estimates of GxE interactions in situations when the frequency of the pathologic diagnosis of interest, as compared to other diagnoses, depends on the environment. We then propose a pseudo-likelihood solution to correct the bias. Finally, we demonstrate our method in extensive simulations and in a GWAS of Alzheimer’s disease.