Testing High Dimensional Covariance Matrices, with Application to Detecting Schizophrenia Risk Genes

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene "relationship" matrices that are of practical interest, such as the weighted adjacency matrices.Comment: 25 pages, 5 figures, 3 table

GemTools: A fast and efficient approach to estimating genetic ancestry

To uncover the genetic basis of complex disease, individuals are often measured at a large number of genetic variants (usually SNPs) across the genome. GemTools provides computationally efficient tools for modeling genetic ancestry based on SNP genotypes. The main algorithm creates an eigenmap based on genetic similarities, and then clusters subjects based on their map position. This process is continued iteratively until each cluster is relatively homogeneous. For genetic association studies, GemTools matches cases and controls based on genetic similarity.Comment: 5 pages, 1 figur

Genetics in psychiatry: common variant association studies.

Many psychiatric conditions and traits are associated with significant heritability. Genetic risk for psychiatric conditions encompass rare variants, identified due to major effect, as well as common variants, the latter analyzed by association analyses. We review guidelines for common variant association analyses, undertaking after assessing evidence of heritability. We highlight the importance of: suitably large sample sizes; an experimental design that controls for ancestry; careful data cleaning; correction for multiple testing; small P values for positive findings; assessment of effect size for positive findings; and, inclusion of an independent replication sample. We also note the importance of a critical discussion of any prior findings, biological follow-up where possible, and a means of accessing the raw data.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Heart failure patients' experiences of telerehabilitation

In the UK, almost 1 million people are living with heart failure, with heart and circulatory diseases accounting for 27% of all deaths, according to the British Heart Foundation. Current heart failure guidelines support cardiac rehabilitation as an intervention to reduce cardiovascular events, increase exercise tolerance and enhance patients' quality of life. Research indicates that telerehabilitation is an effective component of heart failure management, which helps overcome perceived barriers to cardiac rehabilitation including travel to appointments, long waiting times and accessibility. Understanding patient experiences and increasing telerehabilitation among heart failure patients is pertinent to implementing person-centred care, reducing risk and optimising quality of life

Shedding new light on genetic dark matter

Discoveries from genome-wide association studies have contributed to our knowledge of the genetic etiology of many complex diseases. However, these account for only a small fraction of each disease's heritability. Here, we comment on approaches currently available to uncover more of the genetic 'dark matter,' including an approach introduced recently by Naukkarinen and colleagues. These authors propose a method for distinguishing between gene expression driven by genetic variation and that driven by non-genetic factors. This dichotomy allows investigators to focus statistical tests and further molecular analyses on a smaller set of genes, thereby discovering new genetic variation affecting risk for disease. We need more methods like this one if we are to shed a powerful light on dark matter. By enhancing our understanding of molecular genetic etiology, such methods will help us to understand disease processes better and will advance the promise of personalized medicine

Amino Acid Position 11 of HLA-DRβ1 is a Major Determinant of Chromosome 6p Association with Ulcerative Colitis

The major histocompatibility complex (MHC) on chromosome 6p is an established risk locus for ulcerative colitis (UC) and Crohn’s disease (CD). We aimed to better define MHC association signals in UC and CD by combining data from dense single nucleotide polymorphism (SNP) genotyping and from imputation of classical HLA types, their constituent SNPs and corresponding amino acids in 562 UC, 611 CD, and 1,428 control subjects. Univariate and multivariate association analyses were performed, controlling for ancestry. In univariate analyses, absence of the rs9269955 C allele was strongly associated with risk for UC (P = 2.67×$10^{-13}$). rs9269955 is a SNP in the codon for amino acid position 11 of HLA-DRβ1, located in the P6 pocket of the HLA-DR antigen binding cleft. This amino acid position was also the most significantly UC-associated amino acid in omnibus tests (P = 2.68×$10^{-13}$). Multivariate modeling identified rs9269955-C and 13 other variants in best predicting UC versus control status. In contrast, there was only suggestive association evidence between the MHC and CD. Taken together, these data demonstrate that variation at HLA-DRβ1, amino acid 11 in the P6 pocket of the HLA-DR complex antigen binding cleft is a major determinant of chromosome 6p association with ulcerative colitis

Refining genetically inferred relationships using treelet covariance smoothing

Recent technological advances coupled with large sample sets have uncovered many factors underlying the genetic basis of traits and the predisposition to complex disease, but much is left to discover. A common thread to most genetic investigations is familial relationships. Close relatives can be identified from family records, and more distant relatives can be inferred from large panels of genetic markers. Unfortunately these empirical estimates can be noisy, especially regarding distant relatives. We propose a new method for denoising genetically - inferred relationship matrices by exploiting the underlying structure due to hierarchical groupings of correlated individuals. The approach, which we call Treelet Covariance Smoothing, employs a multiscale decomposition of covariance matrices to improve estimates of pairwise relationships. On both simulated and real data, we show that smoothing leads to better estimates of the relatedness amongst distantly related individuals. We illustrate our method with a large genome-wide association study and estimate the "heritability" of body mass index quite accurately. Traditionally heritability, defined as the fraction of the total trait variance attributable to additive genetic effects, is estimated from samples of closely related individuals using random effects models. We show that by using smoothed relationship matrices we can estimate heritability using population-based samples. Finally, while our methods have been developed for refining genetic relationship matrices and improving estimates of heritability, they have much broader potential application in statistics. Most notably, for error-in-variables random effects models and settings that require regularization of matrices with block or hierarchical structure.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS598 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing for an Unusual Distribution of Rare Variants

Technological advances make it possible to use high-throughput sequencing as a primary discovery tool of medical genetics, specifically for assaying rare variation. Still this approach faces the analytic challenge that the influence of very rare variants can only be evaluated effectively as a group. A further complication is that any given rare variant could have no effect, could increase risk, or could be protective. We propose here the C-alpha test statistic as a novel approach for testing for the presence of this mixture of effects across a set of rare variants. Unlike existing burden tests, C-alpha, by testing the variance rather than the mean, maintains consistent power when the target set contains both risk and protective variants. Through simulations and analysis of case/control data, we demonstrate good power relative to existing methods that assess the burden of rare variants in individuals