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Free, publicly-accessible full text available December 15, 2024
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Abstract Background Identifying variants associated with complex traits is a challenging task in genetic association studies due to linkage disequilibrium (LD) between genetic variants and population stratification, unrelated to the disease risk. Existing methods of population structure correction use principal component analysis or linear mixed models with a random effect when modeling associations between a trait of interest and genetic markers. However, due to stringent significance thresholds and latent interactions between the markers, these methods often fail to detect genuinely associated variants.
Results To overcome this, we propose CluStrat, which corrects for complex arbitrarily structured populations while leveraging the linkage disequilibrium induced distances between genetic markers. It performs an agglomerative hierarchical clustering using the Mahalanobis distance covariance matrix of the markers. In simulation studies, we show that our method outperforms existing methods in detecting true causal variants. Applying CluStrat on WTCCC2 and UK Biobank cohorts, we found biologically relevant associations in Schizophrenia and Myocardial Infarction. CluStrat was also able to correct for population structure in polygenic adaptation of height in Europeans.
Conclusions CluStrat highlights the advantages of biologically relevant distance metrics, such as the Mahalanobis distance, which captures the cryptic interactions within populations in the presence of LD better than the Euclidean distance.
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Abstract Complex disorders are caused by a combination of genetic, environmental and lifestyle factors, and their prevalence can vary greatly across different populations. The extent to which genetic risk, as identified by Genome Wide Association Study (GWAS), correlates to disease prevalence in different populations has not been investigated systematically. Here, we studied 14 different complex disorders and explored whether polygenic risk scores (PRS) based on current GWAS correlate to disease prevalence within Europe and around the world. A clear variation in GWAS-based genetic risk was observed based on ancestry and we identified populations that have a higher genetic liability for developing certain disorders. We found that for four out of the 14 studied disorders, PRS significantly correlates to disease prevalence within Europe. We also found significant correlations between worldwide disease prevalence and PRS for eight of the studied disorders with Multiple Sclerosis genetic risk having the highest correlation to disease prevalence. Based on current GWAS results, the across population differences in genetic risk for certain disorders can potentially be used to understand differences in disease prevalence and identify populations with the highest genetic liability. The study highlights both the limitations of PRS based on current GWAS but also the fact that in some cases, PRS may already have high predictive power. This could be due to the genetic architecture of specific disorders or increased GWAS power in some cases.
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Models in which the covariance matrix has the structure of a sparse matrix plus a low rank perturbation are ubiquitous in data science applications. It is often desirable for algorithms to take advantage of such structures, avoiding costly matrix computations that often require cubic time and quadratic storage. This is often accomplished by performing operations that maintain such structures, for example, matrix inversion via the Sherman–Morrison–Woodbury formula. In this article, we consider the matrix square root and inverse square root operations. Given a low rank perturbation to a matrix, we argue that a low‐rank approximate correction to the (inverse) square root exists. We do so by establishing a geometric decay bound on the true correction's eigenvalues. We then proceed to frame the correction as the solution of an algebraic Riccati equation, and discuss how a low‐rank solution to that equation can be computed. We analyze the approximation error incurred when approximately solving the algebraic Riccati equation, providing spectral and Frobenius norm forward and backward error bounds. Finally, we describe several applications of our algorithms, and demonstrate their utility in numerical experiments.more » « less
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Introduction Autoimmune disorders (ADs) are a group of about 80 disorders that occur when self-attacking autoantibodies are produced due to failure in the self-tolerance mechanisms. ADs are polygenic disorders and associations with genes both in the human leukocyte antigen (HLA) region and outside of it have been described. Previous studies have shown that they are highly comorbid with shared genetic risk factors, while epidemiological studies revealed associations between various lifestyle and health-related phenotypes and ADs.
Methods Here, for the first time, we performed a comparative polygenic risk score (PRS) - Phenome Wide Association Study (PheWAS) for 11 different ADs (Juvenile Idiopathic Arthritis, Primary Sclerosing Cholangitis, Celiac Disease, Multiple Sclerosis, Rheumatoid Arthritis, Psoriasis, Myasthenia Gravis, Type 1 Diabetes, Systemic Lupus Erythematosus, Vitiligo Late Onset, Vitiligo Early Onset) and 3,254 phenotypes available in the UK Biobank that include a wide range of socio-demographic, lifestyle and health-related outcomes. Additionally, we investigated the genetic relationships of the studied ADs, calculating their genetic correlation and conducting cross-disorder GWAS meta-analyses for the observed AD clusters.
Results In total, we identified 508 phenotypes significantly associated with at least one AD PRS. 272 phenotypes were significantly associated after excluding variants in the HLA region from the PRS estimation. Through genetic correlation and genetic factor analyses, we identified four genetic factors that run across studied ADs. Cross-trait meta-analyses within each factor revealed pleiotropic genome-wide significant loci.
Discussion Overall, our study confirms the association of different factors with genetic susceptibility for ADs and reveals novel observations that need to be further explored.
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