arXiv subjects

Qing Lu

Publications and source records attributed to Qing Lu.

66 records · Page 4Linked to original sources

arXiv2018

Generalized Similarity U: A Non-parametric Test of Association Based on Similarity

Second generation sequencing technologies are being increasingly used for genetic association studies, where the main research interest is to identify sets of genetic variants that contribute to various phenotype. The phenotype can be univariate disease status, multivariate responses and even high-dimensional outcomes. Considering the genotype and phenotype as two complex objects, this also poses a general statistical problem of testing association between complex objects. We here proposed a similarity-based test, generalized similarity U (GSU), that can test the association between complex objects. We first studied the theoretical properties of the test in a general setting and then focused on the application of the test to sequencing association studies. Based on theoretical analysis, we proposed to use Laplacian kernel based similarity for GSU to boost power and enhance robustness. Through simulation, we found that GSU did have advantages over existing methods in terms of power and robustness. We further performed a whole genome sequencing (WGS) scan for Alzherimer Disease Neuroimaging Initiative (ADNI) data, identifying three genes, APOE, APOC1 and TOMM40, associated with imaging phenotype. We developed a C++ package for analysis of whole genome sequencing data using GSU. The source codes can be downloaded at https://github.com/changshuaiwei/gsu.

stat.ME↗

arXiv2016

Coherence and incoherence collective behavior in financial market

Financial markets have been extensively studied as highly complex evolving systems. In this paper, we quantify financial price fluctuations through a coupled dynamical system composed of phase oscillators. We find a Financial Coherence and Incoherence (FCI) coexistence collective behavior emerges as the system evolves into the stable state, in which the stocks split into two groups: one is represented by coherent, phase-locked oscillators, the other is composed of incoherent, drifting oscillators. It is demonstrated that the size of the coherent stock groups fluctuates during the economic periods according to real-world financial instabilities or shocks. Further, we introduce the coherent characteristic matrix to characterize the involvement dynamics of stocks in the coherent groups. Clustering results on the matrix provides a novel manifestation of the correlations among stocks in the economic periods. Our analysis for components of the groups is consistent with the Global Industry Classification Standard (GICS) classification and can also figure out features for newly developed industries. These results can provide potentially implications on characterizing inner dynamical structure of financial markets and making optimal investment tragedies.

q-fin.ST↗

arXiv2016

On the distribution of Jacobi sums

Let $\mathbf{F}_q$ be a finite field of $q$ elements. For multiplicative characters $χ_1,\dots, χ_m$ of $\mathbf{F}_q^\times$, we let $J(χ_1,\dots, χ_m)$ denote the Jacobi sum. Nicholas Katz and Zhiyong Zheng showed that for $m=2$, the normalized Jacobi sum $q^{-1/2}J(χ_1,χ_2)$ ($χ_1χ_2$ nontrivial) is asymptotically equidistributed on the unit circle as $q\to \infty$, when $χ_1$ and $χ_2$ run through all nontrivial multiplicative characters of $\mathbf{F}_q^\times$. In this paper, we show a similar property for $m\ge 2$. More generally, we show that the normalized Jacobi sum $q^{-(m-1)/2}J(χ_1,\dots,χ_m)$ ($χ_1\dotsm χ_m$ nontrivial) is asymptotically equidistributed on the unit circle, when $χ_1,\dots, χ_m$ run through arbitrary sets of nontrivial multiplicative characters of $\mathbf{F}_q^\times$ with two of the sets being sufficiently large. The case $m=2$ answers a question of Shparlinski.

math.NT↗

arXiv2015

A Generalized Similarity U Test for Multivariate Analysis of Sequencing Data

Sequencing-based studies are emerging as a major tool for genetic association studies of complex diseases. These studies pose great challenges to the traditional statistical methods (e.g., single-locus analyses based on regression methods) because of the high-dimensionality of data and the low frequency of genetic variants. In addition, there is a great interest in biology and epidemiology to identify genetic risk factors contributed to multiple disease phenotypes. The multiple phenotypes can often follow different distributions, which violates the assumptions of most current methods. In this paper, we propose a generalized similarity U test, referred to as GSU. GSU is a similarity-based test and can handle high-dimensional genotypes and phenotypes. We studied the theoretical properties of GSU, and provided the efficient p-value calculation for association test as well as the sample size and power calculation for the study design. Through simulation, we found that GSU had advantages over existing methods in terms of power and robustness to phenotype distributions. Finally, we used GSU to perform a multivariate analysis of sequencing data in the Dallas Heart Study and identified a joint association of 4 genes with 5 metabolic related phenotypes.

stat.ME↗

arXiv2015

A weighted U statistic for association analysis considering genetic heterogeneity

Converging evidence suggests that common complex diseases with the same or similar clinical manifestations could have different underlying genetic etiologies. While current research interests have shifted toward uncovering rare variants and structural variations predisposing to human diseases, the impact of heterogeneity in genetic studies of complex diseases has been largely overlooked. Most of the existing statistical methods assume the disease under investigation has a homogeneous genetic effect and could, therefore, have low power if the disease undergoes heterogeneous pathophysiological and etiological processes. In this paper, we propose a heterogeneity weighted U (HWU) method for association analyses considering genetic heterogeneity. HWU can be applied to various types of phenotypes (e.g., binary and continuous) and is computationally effcient for high- dimensional genetic data. Through simulations, we showed the advantage of HWU when the underlying genetic etiology of a disease was heterogeneous, as well as the robustness of HWU against different model assumptions (e.g., phenotype distributions). Using HWU, we conducted a genome-wide analysis of nicotine dependence from the Study of Addiction: Genetics and Environments (SAGE) dataset. The genome-wide analysis of nearly one million genetic markers took 7 hours, identifying heterogeneous effects of two new genes (i.e., CYP3A5 and IKBKB) on nicotine dependence.

stat.ME↗

arXiv2015

Trees Assembling Mann Whitney Approach for Detecting Genome-wide Joint Association among Low Marginal Effect loci

Common complex diseases are likely influenced by the interplay of hundreds, or even thousands, of genetic variants. Converging evidence shows that genetic variants with low marginal effects (LME) play an important role in disease development. Despite their potential significance, discovering LME genetic variants and assessing their joint association on high dimensional data (e.g., genome wide association studies) remain a great challenge. To facilitate joint association analysis among a large ensemble of LME genetic variants, we proposed a computationally efficient and powerful approach, which we call Trees Assembling Mann whitney (TAMW). Through simulation studies and an empirical data application, we found that TAMW outperformed multifactor dimensionality reduction (MDR) and the likelihood ratio based Mann whitney approach (LRMW) when the underlying complex disease involves multiple LME loci and their interactions. For instance, in a simulation with 20 interacting LME loci, TAMW attained a higher power (power=0.931) than both MDR (power=0.599) and LRMW (power=0.704). In an empirical study of 29 known Crohn's disease (CD) loci, TAMW also identified a stronger joint association with CD than those detected by MDR and LRMW. Finally, we applied TAMW to Wellcome Trust CD GWAS to conduct a genome wide analysis. The analysis of 459K single nucleotide polymorphisms was completed in 40 hours using parallel computing, and revealed a joint association predisposing to CD (p-value=2.763e-19). Further analysis of the newly discovered association suggested that 13 genes, such as ATG16L1 and LACC1, may play an important role in CD pathophysiological and etiological processes.

q-bio.QM↗

arXiv2015

A Weighted U Statistic for Genetic Association Analyses of Sequencing Data

With advancements in next generation sequencing technology, a massive amount of sequencing data are generated, offering a great opportunity to comprehensively investigate the role of rare variants in the genetic etiology of complex diseases. Nevertheless, this poses a great challenge for the statistical analysis of high-dimensional sequencing data. The association analyses based on traditional statistical methods suffer substantial power loss because of the low frequency of genetic variants and the extremely high dimensionality of the data. We developed a weighted U statistic, referred to as WU-seq, for the high-dimensional association analysis of sequencing data. Based on a non-parametric U statistic, WU-SEQ makes no assumption of the underlying disease model and phenotype distribution, and can be applied to a variety of phenotypes. Through simulation studies and an empirical study, we showed that WU-SEQ outperformed a commonly used SKAT method when the underlying assumptions were violated (e.g., the phenotype followed a heavy-tailed distribution). Even when the assumptions were satisfied, WU-SEQ still attained comparable performance to SKAT. Finally, we applied WU-seq to sequencing data from the Dallas Heart Study (DHS), and detected an association between ANGPTL 4 and very low density lipoprotein cholesterol.

stat.ME↗

arXiv2015

GWGGI: software for genome-wide gene-gene interaction analysis

Background: While the importance of gene-gene interactions in human diseases has been well recognized, identifying them has been a great challenge, especially through association studies with millions of genetic markers and thousands of individuals. Computationally efficient and powerful tools are in great need for the identification of new gene-gene interactions in high-dimensional association studies. Result: We develop C++ software for genome-wide gene-gene interaction analyses (GWGGI). GWGGI utilizes tree-based algorithms to search a large number of genetic markers for a disease-associated joint association with the consideration of high-order interactions, and then uses non-parametric statistics to test the joint association. The package includes two functions, likelihood ratio Mann-whitney (LRMW) and Tree Assembling Mann-whitney (TAMW).We optimize the data storage and computational efficiency of the software, making it feasible to run the genome-wide analysis on a personal computer. The use of GWGGI was demonstrated by using two real data-sets with nearly 500 k genetic markers. Conclusion: Through the empirical study, we demonstrated that the genome-wide gene-gene interaction analysis using GWGGI could be accomplished within a reasonable time on a personal computer (i.e., ~3.5 hours for LRMW and ~10 hours for TAMW). We also showed that LRMW was suitable to detect interaction among a small number of genetic variants with moderate-to-strong marginal effect, while TAMW was useful to detect interaction among a larger number of low-marginal-effect genetic variants.

q-bio.QM↗

arXiv2014

Modeling and Testing for Joint Association Using a Genetic Random Field Model

Substantial progress has been made in identifying single genetic variants predisposing to common complex diseases. Nonetheless, the genetic etiology of human diseases remains largely unknown. Human complex diseases are likely influenced by the joint effect of a large number of genetic variants instead of a single variant. The joint analysis of multiple genetic variants considering linkage disequilibrium (LD) and potential interactions can further enhance the discovery process, leading to the identification of new disease-susceptibility genetic variants. Motivated by the recent development in spatial statistics, we propose a new statistical model based on the random field theory, referred to as a genetic random field model (GenRF), for joint association analysis with the consideration of possible gene-gene interactions and LD. Using a pseudo-likelihood approach, a GenRF test for the joint association of multiple genetic variants is developed, which has the following advantages: 1. considering complex interactions for improved performance; 2. natural dimension reduction; 3. boosting power in the presence of LD; 4. computationally efficient. Simulation studies are conducted under various scenarios. Compared with a commonly adopted kernel machine approach, SKAT, GenRF shows overall comparable performance and better performance in the presence of complex interactions. The method is further illustrated by an application to the Dallas Heart Study.

stat.ME↗

arXiv2014

8-rank of the class group and isotropy index

Suppose $F=\mathbb{Q}(\sqrt{-p_1\dotsm p_t})$ is an imaginary quadratic number field with distinct primes $p_1,\dots,p_{t}$, where $p_i\equiv 1\pmod{4}$ ($i=1,\dots,t-1$) and $p_t\equiv 3\pmod{4}$. We express the possible values of the 8-rank $r_8$ of the class group of $F$ in terms of a quadratic form $Q$ over $\mathbb{F}_2$ which is defined by quartic symbols. In particular, we show that $r_8$ is bounded by the isotropy index of $Q$.

math.NT↗

arXiv2013

Methods for scoring the collective effect of SNPs: Minor alleles of common SNPs quantitatively affect traits/diseases and are under both positive and negative selection

Most common SNPs are popularly assumed to be neutral. We here developed novel methods to examine in animal models and humans whether extreme amount of minor alleles (MAs) carried by an individual may represent extreme trait values and common diseases. We analyzed panels of genetic reference populations and identified the MAs in each panel and the MA content (MAC) that each strain carried. We also analyzed 21 published GWAS datasets of human diseases and identified the MAC of each case or control. MAC was nearly linearly linked to quantitative variations in numerous traits in model organisms, including life span, tumor susceptibility, learning and memory, sensitivity to alcohol and anti-psychotic drugs, and two correlated traits poor reproductive fitness and strong immunity. Similarly, in Europeans or European Americans, enrichment of MAs of fast but not slow evolutionary rate was linked to autoimmune and numerous other diseases, including type 2 diabetes, Parkinson's disease, psychiatric disorders, alcohol and cocaine addictions, cancer, and less life span. Therefore, both high and low MAC correlated with extreme values in many traits, indicating stabilizing selection on most MAs. The methods here are broadly applicable and may help solve the missing heritability problem in complex traits and diseases.

q-bio.GN↗

arXiv2013

Role of genetic polymorphisms in transgenerational inheritance in budding yeast

Transgenerational inheritance of a trait is presumably affected by both genetic and environmental factors but remains poorly understood. We studied the effect of genetic polymorphisms on transgenerational inheritance of yeast segregants that were derived from a cross between a laboratory strain and a wild strain of Saccharomyces cerevisiae. For each SNP analyzed, the parental allele present in less than half of the segregants panel was called the minor allele (MA). We found a nonrandom distribution of MAs in the segregants, indicating natural selection. We compared segregants with high MA content (MAC) relative to those with less and found a more dramatic shortening of the lag phase length for the high MAC group in response to 14 days of ethanol training. Also, the short lag phase as acquired and epigenetically memorized by ethanol training was more dramatically lost after 7 days of recovery in ethanol free medium for the high MAC group. Sodium chloride treatment produced similar observations. Using public datasets, we found MAC linkage to mRNA expression of hundreds of genes. Finally, we found preferential effect of MAC on traits with high number of known additive quantitative trait loci (QTLs). These results provide evidence for the slightly deleterious nature of most MAs and a lower capacity to maintain inheritance of traits in individuals or cells with greater MAC, which have implications for disease prevention and treatment and the "missing heritability" problem in complex traits and diseases.

q-bio.GN↗