Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss f ( x ) + ρ 2 dist ( x , C ) 2 and following the solution x _ρ to its limit as ρ tends to ∞. At each iteration the squared Euclidean distance dist(x,C)² is majorized by the spherical quadratic ‖x- P _C (x _k )‖², where P _C (x _k ) denotes the projection of the current iterate x _k onto C. The minimum of the surrogate function f ( x ) + ρ 2 ‖ x - P C ( x k ) ‖ 2 is given by the proximal map prox _ρ -_1f [P _C (x _k )]. The next iterate x _k+1 automatically decreases the original penalized loss for fixed ρ. Since many explicit projections and proximal maps are known, it is straightforward to derive and implement novel optimization algorithms in this setting. These algorithms can take hundreds if not thousands of iterations to converge, but the simple nature of each iteration makes proximal distance algorithms competitive with traditional algorithms. For convex problems, proximal distance algorithms reduce to proximal gradient algorithms and therefore enjoy well understood convergence properties. For nonconvex problems, one can attack convergence by invoking Zangwill's theorem. Our numerical examples demonstrate the utility of proximal distance algorithms in various high-dimensional settings, including a) linear programming, b) constrained least squares, c) projection to the closest kinship matrix, d) projection onto a second-order cone constraint, e) calculation of Horn's copositive matrix index, f) linear complementarity programming, and g) sparse principal components analysis. The proximal distance algorithm in each case is competitive or superior in speed to traditional methods such as the interior point method and the alternating direction method of multipliers (ADMM). Source code for the numerical examples can be found at https://github.com/klkeys/proxdist.

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Background

Consecutive testing of single nucleotide polymorphisms (SNPs) is usually employed to identify genetic variants associated with complex traits. Ideally one should model all covariates in unison, but most existing analysis methods for genome-wide association studies (GWAS) perform only univariate regression.

Results

We extend and efficiently implement iterative hard thresholding (IHT) for multiple regression, treating all SNPs simultaneously. Our extensions accommodate generalized linear models (GLMs), prior information on genetic variants, and grouping of variants. In our simulations, IHT recovers up to 30% more true predictors than SNP-by-SNP association testing, and exhibits a 2 to 3 orders of magnitude decrease in false positive rates compared to lasso regression. We also test IHT on the UK Biobank hypertension phenotypes and the Northern Finland Birth Cohort of 1966 cardiovascular phenotypes. We find that IHT scales to the large datasets of contemporary human genetics and recovers the plausible genetic variants identified by previous studies.

Conclusions

Our real data analysis and simulation studies suggest that IHT can (a) recover highly correlated predictors, (b) avoid over-fitting, (c) deliver better true positive and false positive rates than either marginal testing or lasso regression, (d) recover unbiased regression coefficients, (e) exploit prior information and group-sparsity and (f) be used with biobank sized data sets. Although these advances are studied for GWAS inference, our extensions are pertinent to other regression problems with large numbers of predictors.

Background and objectives

Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, BioSimulator.jl, for implementing the Gillespie algorithm, τ-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools.

Methods

We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time.

Results

BioSimulator.jl's interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics.

Conclusion

The user-friendly nature of BioSimulator.jl encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification.

Background

Consecutive testing of single nucleotide polymorphisms (SNPs) is usually employed to identify genetic variants associated with complex traits. Ideally one should model all covariates in unison, but most existing analysis methods for genome-wide association studies (GWAS) perform only univariate regression.

Results

We extend and efficiently implement iterative hard thresholding (IHT) for multiple regression, treating all SNPs simultaneously. Our extensions accommodate generalized linear models, prior information on genetic variants, and grouping of variants. In our simulations, IHT recovers up to 30% more true predictors than SNP-by-SNP association testing and exhibits a 2-3 orders of magnitude decrease in false-positive rates compared with lasso regression. We also test IHT on the UK Biobank hypertension phenotypes and the Northern Finland Birth Cohort of 1966 cardiovascular phenotypes. We find that IHT scales to the large datasets of contemporary human genetics and recovers the plausible genetic variants identified by previous studies.

Conclusions

Our real data analysis and simulation studies suggest that IHT can (i) recover highly correlated predictors, (ii) avoid over-fitting, (iii) deliver better true-positive and false-positive rates than either marginal testing or lasso regression, (iv) recover unbiased regression coefficients, (v) exploit prior information and group-sparsity, and (vi) be used with biobank-sized datasets. Although these advances are studied for genome-wide association studies inference, our extensions are pertinent to other regression problems with large numbers of predictors.

A key aim for current genome-wide association studies (GWAS) is to interrogate the full spectrum of genetic variation underlying human traits, including rare variants, across populations. Deep whole-genome sequencing is the gold standard to fully capture genetic variation, but remains prohibitively expensive for large sample sizes. Array genotyping interrogates a sparser set of variants, which can be used as a scaffold for genotype imputation to capture a wider set of variants. However, imputation quality depends crucially on reference panel size and genetic distance from the target population. Here, we consider sequencing a subset of GWAS participants and imputing the rest using a reference panel that includes both sequenced GWAS participants and an external reference panel. We investigate how imputation quality and GWAS power are affected by the number of participants sequenced for admixed populations (African and Latino Americans) and European population isolates (Sardinians and Finns), and identify powerful, cost-effective GWAS designs given current sequencing and array costs. For populations that are well-represented in existing reference panels, we find that array genotyping alone is cost-effective and well-powered to detect common- and rare-variant associations. For poorly represented populations, sequencing a subset of participants is often most cost-effective, and can substantially increase imputation quality and GWAS power.

Background

Severe asthma exacerbations are a major cause of asthma morbidity and increased healthcare costs. Several studies have shown racial and ethnic differences in asthma exacerbation rates. We aimed to identify genetic variants associated with severe exacerbations in two high-risk populations for asthma.

Methods

A genome-wide association study of asthma in children and youth with severe exacerbations was performed in 1283 exacerbators and 2027 controls without asthma of Latino ancestry. Independent suggestive variants (P ≤ 5 × 10^-6 ) were selected for replication in 448 African Americans exacerbators and 595 controls. Case-only analyses were performed comparing the exacerbators with additional 898 Latinos and 524 African Americans asthma patients without exacerbations, while adjusting by treatment category as a proxy of asthma severity. We analyzed the functionality of associated variants with in silico methods and by correlating genotypes with methylation levels in whole blood in a subset of 473 Latinos.

Results

We identified two genome-wide significant associations for susceptibility to asthma with severe exacerbations, including a novel locus located at chromosome 2p21 (rs4952375, odds ratio = 1.39, P = 3.8 × 10^-8 ), which was also associated with asthma exacerbations in a case-only analysis (odds ratio = 1.25, P = 1.95 × 10^-3 ). This polymorphism is an expression quantitative trait locus of the long intergenic non-protein coding RNA 1913 (LINC01913) in lung tissues (P = 1.3 × 10^-7 ) and influences methylation levels of the protein kinase domain-containing cytoplasmic (PKDCC) gene in whole-blood cells (P = 9.8 × 10^-5 ).

Conclusion

We identified a novel susceptibility locus for severe asthma exacerbations in Hispanic/Latino and African American youths with functional effects in gene expression and methylation status of neighboring genes.

Statistical methods for genome-wide association studies (GWAS) continue to improve. However, the increasing volume and variety of genetic and genomic data make computational speed and ease of data manipulation mandatory in future software. In our view, a collaborative effort of statistical geneticists is required to develop open source software targeted to genetic epidemiology. Our attempt to meet this need is called the OPENMENDEL project (https://openmendel.github.io). It aims to (1) enable interactive and reproducible analyses with informative intermediate results, (2) scale to big data analytics, (3) embrace parallel and distributed computing, (4) adapt to rapid hardware evolution, (5) allow cloud computing, (6) allow integration of varied genetic data types, and (7) foster easy communication between clinicians, geneticists, statisticians, and computer scientists. This article reviews and makes recommendations to the genetic epidemiology community in the context of the OPENMENDEL project.

Bronchodilator (BD) drugs are commonly prescribed for treatment and management of obstructive lung function present with diseases such as asthma. Administration of BD medication can partially or fully restore lung function as measured by pulmonary function tests. The genetics of baseline lung function measures taken before BD medication have been extensively studied, and the genetics of the BD response itself have received some attention. However, few studies have focused on the genetics of post-BD lung function. To address this gap, we analyzed lung function phenotypes in 1103 subjects from the Study of African Americans, Asthma, Genes, and Environment, a pediatric asthma case-control cohort, using an integrative genomic analysis approach that combined genotype, locus-specific genetic ancestry, and functional annotation information. We integrated genome-wide association study (GWAS) results with an admixture mapping scan of three pulmonary function tests (forced expiratory volume in 1 s [FEV₁ ], forced vital capacity [FVC], and FEV₁ /FVC) taken before and after albuterol BD administration on the same subjects, yielding six traits. We identified 18 GWAS loci, and five additional loci from admixture mapping, spanning several known and novel lung function candidate genes. Most loci identified via admixture mapping exhibited wide variation in minor allele frequency across genotyped global populations. Functional fine-mapping revealed an enrichment of epigenetic annotations from peripheral blood mononuclear cells, fetal lung tissue, and lung fibroblasts. Our results point to three novel potential genetic drivers of pre- and post-BD lung function: ADAMTS1, RAD54B, and EGLN3.

Rationale: Puerto Ricans have the highest childhood asthma prevalence in the United States (23.6%); however, the etiology is uncertain.Objectives: In this study, we sought to uncover the genetic architecture of lung function in Puerto Rican youth with and without asthma who were recruited from the island (n = 836).Methods: We used admixture-mapping and whole-genome sequencing data to discover genomic regions associated with lung function. Functional roles of the prioritized candidate SNPs were examined with chromatin immunoprecipitation sequencing, RNA sequencing, and expression quantitative trait loci data.Measurements and Main Results: We discovered a genomic region at 1q32 that was significantly associated with a 0.12-L decrease in the lung volume of exhaled air (95% confidence interval, -0.17 to -0.07; P = 6.62 × 10^-8) with each allele of African ancestry. Within this region, two SNPs were expression quantitative trait loci of TMEM9 in nasal airway epithelial cells and MROH3P in esophagus mucosa. The minor alleles of these SNPs were associated with significantly decreased lung function and decreased TMEM9 gene expression. Another admixture-mapping peak was observed on chromosome 5q35.1, indicating that each Native American ancestry allele was associated with a 0.15-L increase in lung function (95% confidence interval, 0.08-0.21; P = 5.03 × 10^-6). The region-based association tests identified four suggestive windows that harbored candidate rare variants associated with lung function.Conclusions: We identified common and rare genetic variants that may play a critical role in lung function among Puerto Rican youth. We independently validated an inflammatory pathway that could potentially be used to develop more targeted treatments and interventions for patients with asthma.

The genetic control of gene expression is a core component of human physiology. For the past several years, transcriptome-wide association studies have leveraged large datasets of linked genotype and RNA sequencing information to create a powerful gene-based test of association that has been used in dozens of studies. While numerous discoveries have been made, the populations in the training data are overwhelmingly of European descent, and little is known about the generalizability of these models to other populations. Here, we test for cross-population generalizability of gene expression prediction models using a dataset of African American individuals with RNA-Seq data in whole blood. We find that the default models trained in large datasets such as GTEx and DGN fare poorly in African Americans, with a notable reduction in prediction accuracy when compared to European Americans. We replicate these limitations in cross-population generalizability using the five populations in the GEUVADIS dataset. Via realistic simulations of both populations and gene expression, we show that accurate cross-population generalizability of transcriptome prediction only arises when eQTL architecture is substantially shared across populations. In contrast, models with non-identical eQTLs showed patterns similar to real-world data. Therefore, generating RNA-Seq data in diverse populations is a critical step towards multi-ethnic utility of gene expression prediction.