Permutation Testing in the Presence of Polygenic Variation
This article discusses problems with and solutions to performing valid permutation tests for quantitative trait loci in the presence of polygenic effects. Although permutation testing is a popular approach for determining statistical significance of a test statistic with an unknown distribution–for instance, the maximum of multiple correlated statistics or some omnibus test statistic for a gene, gene-set or pathway–naive application of permutations may result in an invalid test. The risk of performing an invalid permutation test is particularly acute in complex trait mapping where polygenicity may combine with a structured population resulting from the presence of families, cryptic relatedness, admixture or population stratification. I give both analytical derivations and a conceptual understanding of why typical permutation procedures fail and suggest an alternative permutation based algorithm, MVNpermute, that succeeds. In particular, I examine the case where a linear mixed model is used to analyze a quantitative trait and show that both phenotype and genotype permutations may result in an invalid permutation test. I provide a formula that predicts the amount of inflation of the type 1 error rate depending on the degree of misspecification of the covariance structure of the polygenic effect and the heritability of the trait. I validate this formula by doing simulations, showing that the permutation distribution matches the theoretical expectation, and that my suggested permutation based test obtains the correct null distribution. Finally, I discuss situations where naive permutations of the phenotype or genotype are valid and the applicability of the results to other test statistics.
Mediated pleiotropy between psychiatric disorders and autoimmune disorders revealed by integrative analysis of multiple GWAS
Qian Wang, Can Yang, Joel Gelernter, Hongyu Zhao
Epidemiological observations and molecular-level experiments have indicated that brain disorders in the realm of psychiatry may be influenced by immune dysregulation. However, the degree of genetic overlap between immune disorders and psychiatric disorders has not been well established. We investigated this issue by integrative analysis of genome-wide association studies (GWAS) of 18 complex human traits/diseases (five psychiatric disorders, seven autoimmune disorders, and others) and multiple genome-wide annotation resources (Central nervous system genes, immune-related expression-quantitative trait loci (eQTL) and DNase I hypertensive sites from 98 cell-lines). We detected pleiotropy in 24 of the 35 psychiatric-autoimmune disorder pairs, with statistical significance as strong as p=3.9e-285 (schizophrenia-rheumatoid arthritis). Strong enrichment (>1.4 fold) of immune-related eQTL was observed in four psychiatric disorders. Genomic regions responsible for pleiotropy between psychiatric disorders and autoimmune disorders were detected. The MHC region on chromosome 6 appears to be the most important (and it was indeed previously noted (1-3) as a confluence between schizophrenia and immune disorder risk regions), with many other regions, such as cytoband 1p13.2. We also found that most alleles shared between schizophrenia and Crohn’s disease have the same effect direction, with similar trend found for other disorder pairs, such as bipolar-Crohn’s disease. Our results offer a novel bird’s-eye view of the genetic relationship and demonstrate strong evidence for mediated pleiotropy between psychiatric disorders and autoimmune disorders. Our findings might open new routes for prevention and treatment strategies for these disorders based on a new appreciation of the importance of immunological mechanisms in mediating risk.
An Atlas of Genetic Correlations across Human Diseases and Traits
Brendan Bulik-Sullivan, Hilary K Finucane, Verneri Anttila, Alexander Gusev, Felix R Day, ReproGen Consortium, Psychiatric Genomics Consortium, Genetic Consortium for Anorexia Nervosa of the Wellcome Trust Consortium 3, John R.B. Perry, Nick Patterson, Elise Robinson, Mark J Daly, Alkes L Price, Benjamin M Neale
Identifying genetic correlations between complex traits and diseases can provide useful etiological insights and help prioritize likely causal relationships. The major challenges preventing estimation of genetic correlation from genome-wide association study (GWAS) data with current methods are the lack of availability of individual genotype data and widespread sample overlap among meta-analyses. We circumvent these difficulties by introducing a technique for estimating genetic correlation that requires only GWAS summary statistics and is not biased by sample overlap. We use our method to estimate 300 genetic correlations among 25 traits, totaling more than 1.5 million unique phenotype measurements. Our results include genetic correlations between anorexia nervosa and schizophrenia/ body mass index and associations between educational attainment and several diseases. These results highlight the power of a polygenic modeling framework, since there currently are no genome-wide significant SNPs for anorexia nervosa and only three for educational attainment.
A Single Gene Causes an Interspecific Difference in Pigmentation in Drosophila
Yasir H. Ahmed-Braimah, Andrea L. Sweigart
The genetic basis of species differences remains understudied. Studies in insects have contributed significantly to our understanding of morphological evolution. Pigmentation traits in particular have received a great deal of attention and several genes in the insect pigmentation pathway have been implicated in inter- and intraspecific differences. Nonetheless, much remains unknown about many of the genes in this pathway and their potential role in understudied taxa. Here we genetically analyze the puparium color difference between members of the Virilis group of Drosophila. The puparium of Drosophila virilis is black, while those of D. americana, D. novamexicana, and D. lummei are brown. We used a series of backcross hybrid populations between D. americana and D. virilis to map the genomic interval responsible for the difference between this species pair. First, we show that the pupal case color difference is caused by a single Mendelizing factor, which we ultimately map to an ~11kb region on chromosome 5. The mapped interval includes only the first exon and regulatory region(s) of the dopamine N-acetyltransferase gene (Dat). This gene encodes an enzyme that is known to play a part in the insect pigmentation pathway. Second, we show that this gene is highly expressed at the onset of pupation in light-brown taxa (D. americana and D. novamexicana) relative to D. virilis, but not in the dark-brown D. lummei. Finally, we examine the role of Dat in adult pigmentation between D. americana (heavily melanized) and D. novamexicana (lightly melanized) and find no discernible effect of this gene in adults. Our results demonstrate that a single gene is entirely or almost entirely responsible for a morphological difference between species.
A consistency lemma in statistical phylogenetics
(Submitted on 26 Jan 2015)
This short note provides a simple formal proof of a folklore result in statistical phylogenetics concerning the convergence of bootstrap support for a tree and its edges.
Ebola virus is evolving but not changing: no evidence for functional change in EBOV from 1976 to the 2014 outbreak
Abayomi S Olabode, Xiaowei Jiang, David L Robertson, Simon C Lovell
The Ebola epidemic is having a devastating impact in West Africa. Sequencing of Ebola viruses from infected individuals has revealed extensive genetic variation, leading to speculation that the virus may be adapting to the human host and accounting for the scale of the 2014 outbreak. We show that so far there is no evidence for adaptation of EBOV to humans. We analyze the putatively functional changes associated with the current and previous Ebola outbreaks, and find no significant molecular changes. Observed amino acid replacements have minimal effect on protein structure, being neither stabilizing nor destabilizing. Replacements are not found in regions of the proteins associated with known functions and tend to occur in disordered regions. This observation indicates that the difference between the current and previous outbreaks is not due to the observed evolutionary change of the virus. Instead, epidemiological factors must be responsible for the unprecedented spread of EBOV.
Exploring the genetic patterns of complex diseases via the integrative genome-wide approach
Ben Teng, Can Yang, Jiming Liu, Zhipeng Cai, Xiang Wan
(Submitted on 26 Jan 2015)
Motivation: Genome-wide association studies (GWASs), which assay more than a million single nucleotide polymorphisms (SNPs) in thousands of individuals, have been widely used to identify genetic risk variants for complex diseases. However, most of the variants that have been identified contribute relatively small increments of risk and only explain a small portion of the genetic variation in complex diseases. This is the so-called missing heritability problem. Evidence has indicated that many complex diseases are genetically related, meaning these diseases share common genetic risk variants. Therefore, exploring the genetic correlations across multiple related studies could be a promising strategy for removing spurious associations and identifying underlying genetic risk variants, and thereby uncovering the mystery of missing heritability in complex diseases. Results: We present a general and robust method to identify genetic patterns from multiple large-scale genomic datasets. We treat the summary statistics as a matrix and demonstrate that genetic patterns will form a low-rank matrix plus a sparse component. Hence, we formulate the problem as a matrix recovering problem, where we aim to discover risk variants shared by multiple diseases/traits and those for each individual disease/trait. We propose a convex formulation for matrix recovery and an efficient algorithm to solve the problem. We demonstrate the advantages of our method using both synthesized datasets and real datasets. The experimental results show that our method can successfully reconstruct both the shared and the individual genetic patterns from summary statistics and achieve better performance compared with alternative methods under a wide range of scenarios.