Weighted Score Tests Implementing Model-Averaging Schemes in Detection of Rare Variants in Case-Control Studies

Multi-locus effect modeling is a powerful approach for detection of genes influencing a complex disease. Especially for rare variants, we need to analyze multiple variants together to achieve adequate power for detection. In this paper, we propose several parsimonious branching model techniques to assess the joint effect of a group of rare variants in a case-control study. These models implement a data reduction strategy within a likelihood framework and use a weighted score test to assess the statistical significance of the effect of the group of variants on the disease. The primary advantage of the proposed approach is that it performs model-averaging over a substantially smaller set of models supported by the data and thus gains power to detect multi-locus effects. We illustrate these proposed approaches on simulated and real data and study their performance compared to several existing rare variant detection approaches. The primary goal of this paper is to assess if there is any gain in power to detect association by averaging over a number of models instead of selecting the best model. Extensive simulations and real data application demonstrate the advantage the proposed approach in presence of causal variants with opposite directional effects along with a moderate number of null variants in linkage disequilibrium.     

A test for genetic association that incorporates information about deviation from Hardy-Weinberg proportions in cases

For assessment of genetic association between single-nucleotide polymorphisms (SNPs) and disease status, the logistic-regression model or generalized linear model is typically employed. However, testing for deviation from Hardy-Weinberg proportion in a patient group could be another approach for genetic-association studies. The Hardy-Weinberg proportion is one of the most important principles in population genetics. Deviation from Hardy-Weinberg proportion among cases (patients) could provide additional evidence for the association between SNPs and diseases. To develop a more powerful statistical test for genetic-association studies, we combined evidence about deviation from Hardy-Weinberg proportion in case subjects and standard regression approaches that use case and control subjects. In this paper, we propose two approaches for combining such information: the mean-based tail-strength measure and the median-based tail-strength measure. These measures integrate logistic regression and Hardy-Weinberg-proportion tests for the study of the association between a binary disease outcome and an SNP on the basis of case- and control-subject data. For both mean-based and median-based tail-strength measures, we derived exact formulas to compute p values. We also developed an approach for obtaining empirical p values with the use of a resampling procedure. Results from simulation studies and real-disease studies demonstrate that the proposed approach is more powerful than the traditional logistic-regression model. The type I error probabilities of our approach were also well controlled.     

Underestimated effect sizes in GWAS: fundamental limitations of single SNP analysis for dichotomous phenotypes

Complex diseases are often highly heritable. However, for many complex traits only a small proportion of the heritability can be explained by observed genetic variants in traditional genome-wide association (GWA) studies. Moreover, for some of those traits few significant SNPs have been identified. Single SNP association methods test for association at a single SNP, ignoring the effect of other SNPs. We show using a simple multi-locus odds model of complex disease that moderate to large effect sizes of causal variants may be estimated as relatively small effect sizes in single SNP association testing. This underestimation effect is most severe for diseases influenced by numerous risk variants. We relate the underestimation effect to the concept of non-collapsibility found in the statistics literature. As described, continuous phenotypes generated with linear genetic models are not affected by this underestimation effect. Since many GWA studies apply single SNP analysis to dichotomous phenotypes, previously reported results potentially underestimate true effect sizes, thereby impeding identification of true effect SNPs. Therefore, when a multi-locus model of disease risk is assumed, a multi SNP analysis may be more appropriate.     

Genetic variants in the KIF6 region and coronary event reduction from statin therapy

A single nucleotide polymorphism (SNP) in KIF6, a member of the KIF9 family of kinesins, is associated with differential coronary event reduction from statin therapy in four randomized controlled trials; this SNP (rs20455) is also associated with the risk for coronary heart disease (CHD) in multiple prospective studies. We investigated whether other common SNPs in the KIF6 region were associated with event reduction from statin therapy. Of the 170 SNPs in the KIF6 region investigated in the Cholesterol and Recurrent Events trial (CARE), 28 were associated with differential event reduction from statin therapy (P (interaction) < 01 in Caucasians, adjusted for age and sex) and were further investigated in the Pravastatin or Atorvastatin Evaluation and Infection Therapy-Thrombolysis In Myocardial Infarction 22 (PROVE IT-TIMI22) and West of Scotland Coronary Prevention Study (WOSCOPS). These analyses revealed that two SNPs (rs9462535 and rs9471077), in addition to rs20455, were associated with event reduction from statin therapy (P (interaction) < 0.1 in each of the three studies). The relative risk reduction ranged from 37 to 50% (P < 0.01) in carriers of the minor alleles of these SNPs and from -4 to 13% (P > 0.4) in non-carriers. These three SNPs are in high linkage disequilibrium with one another (r (2) > 0.84). Functional studies of these variants may help to understand the role of KIF6 in the pathogenesis of CHD and differential response to statin therapy.     

Disease-driven detection of differential inherited SNP modules from SNP network

Detection of the synergetic effects between variants, such as single-nucleotide polymorphisms (SNPs), is crucial for understanding the genetic characters of complex diseases. Here, we proposed a two-step approach to detect differentially inherited SNP modules (synergetic SNP units) from a SNP network. First, SNP-SNP interactions are identified based on prior biological knowledge, such as their adjacency on the chromosome or degree of relatedness between the functional relationships of their genes. These interactions form SNP networks. Second, disease-risk SNP modules (or sub-networks) are prioritised by their differentially inherited properties in IBD (Identity by Descent) profiles of affected and unaffected sibpairs. The search process is driven by the disease information and follows the structure of a SNP network. Simulation studies have indicated that this approach achieves high accuracy and a low false-positive rate in the identification of known disease-susceptible SNPs. Applying this method to an alcoholism dataset, we found that flexible patterns of susceptible SNP combinations do play a role in complex diseases, and some known genes were detected through these risk SNP modules. One example is GRM7, a known alcoholism gene successfully detected by a SNP module comprised of two SNPs, but neither of the two SNPs was significantly associated with the disease in single-locus analysis. These identified genes are also enriched in some pathways associated with alcoholism, including the calcium signalling pathway, axon guidance and neuroactive ligand-receptor interaction. The integration of network biology and genetic analysis provides putative functional bridges between genetic variants and candidate genes or pathways, thereby providing new insight into the aetiology of complex diseases.     

Bayesian epistasis association mapping via SNP imputation

Genetic mutations may interact to increase the risk of human complex diseases. Mapping of multiple interacting disease loci in the human genome has recently shown promise in detecting genes with little main effects. The power of interaction association mapping, however, can be greatly influenced by the set of single nucleotide polymorphism (SNP) genotyped in a case-control study. Previous imputation methods only focus on imputation of individual SNPs without considering their joint distribution of possible interactions. We present a new method that simultaneously detects multilocus interaction associations and imputes missing SNPs from a full Bayesian model. Our method treats both the case-control sample and the reference data as random observations. The output of our method is the posterior probabilities of SNPs for their marginal and interacting associations with the disease. Using simulations, we show that the method produces accurate and robust imputation with little overfitting problems. We further show that, with the type I error rate maintained at a common level, SNP imputation can consistently and sometimes substantially improve the power of detecting disease interaction associations. We use a data set of inflammatory bowel disease to demonstrate the application of our method.     

Gene-centric characteristics of genome-wide association studies

Background

The high-throughput genotyping chips have contributed greatly to genome-wide association (GWA) studies to identify novel disease susceptibility single nucleotide polymorphisms (SNPs). The high-density chips are designed using two different SNP selection approaches, the direct gene-centric approach, and the indirect quasi-random SNPs or linkage disequilibrium (LD)-based tagSNPs approaches. Although all these approaches can provide high genome coverage and ascertain variants in genes, it is not clear to which extent these approaches could capture the common genic variants. It is also important to characterize and compare the differences between these approaches.

Methodology/Principal Findings

In our study, by using both the Phase II HapMap data and the disease variants extracted from OMIM, a gene-centric evaluation was first performed to evaluate the ability of the approaches in capturing the disease variants in Caucasian population. Then the distribution patterns of SNPs were also characterized in genic regions, evolutionarily conserved introns and nongenic regions, ontologies and pathways. The results show that, no mater which SNP selection approach is used, the current high-density SNP chips provide very high coverage in genic regions and can capture most of known common disease variants under HapMap frame. The results also show that the differences between the direct and the indirect approaches are relatively small. Both have similar SNP distribution patterns in these gene-centric characteristics.

Conclusions/Significance

This study suggests that the indirect approaches not only have the advantage of high coverage but also are useful for studies focusing on various functional SNPs either in genes or in the conserved regions that the direct approach supports. The study and the annotation of characteristics will be helpful for designing and analyzing GWA studies that aim to identify genetic risk factors involved in common diseases, especially variants in genes and conserved regions.     

Selecting tagging SNPs for association studies using power calculations from genotype data

Recent studies have indicated that linkage disequilibrium (LD) between single nucleotide polymorphism (SNP) markers can be used to derive a reduced set of tagging SNPs (tSNPs) for genetic association studies. Previous strategies for identifying tSNPs have focused on LD measures or haplotype diversity, but the statistical power to detect disease-associated variants using tSNPs in genetic studies has not been fully characterized. We propose a new approach of selecting tSNPs based on determining the set of SNPs with the highest power to detect association. Two-locus genotype frequencies are used in the power calculations. To show utility, we applied this power method to a large number of SNPs that had been genotyped in Caucasian samples. We demonstrate that a significant reduction in genotyping efforts can be achieved although the reduction depends on genotypic relative risk, inheritance mode and the prevalence of disease in the human population. The tSNP sets identified by our method are remarkably robust to changes in the disease model when small relative risk and additive mode of inheritance are employed. We have also evaluated the ability of the method to detect unidentified SNPs. Our findings have important implications in applying tSNPs from different data sources in association studies.     

Performance of random forest when SNPs are in linkage disequilibrium

Background  

Single nucleotide polymorphisms (SNPs) may be correlated due to linkage disequilibrium (LD). Association studies look for both direct and indirect associations with disease loci. In a Random Forest (RF) analysis, correlation between a true risk SNP and SNPs in LD may lead to diminished variable importance for the true risk SNP. One approach to address this problem is to select SNPs in linkage equilibrium (LE) for analysis. Here, we explore alternative methods for dealing with SNPs in LD: change the tree-building algorithm by building each tree in an RF only with SNPs in LE, modify the importance measure (IM), and use haplotypes instead of SNPs to build a RF.     

Particle swarm optimization algorithm for analyzing SNP–SNP interaction of renin-angiotensin system genes against hypertension

Most non-significant individual single nucleotide polymorphisms (SNPs) were undiscovered in hypertension association studies. Their possible SNP–SNP interactions were usually ignored and leaded to missing heritability. In present study, we proposed a particle swarm optimization (PSO) algorithm to analyze the SNP–SNP interaction associated with hypertension. Genotype dataset of eight SNPs of renin-angiotensin system genes for 130 non-hypertension and 313 hypertension subjects were included. Without SNP–SNP interaction, most individual SNPs were non-significant difference between the hypertension and non-hypertension groups. For SNP–SNP interaction, PSO can select the SNP combinations involving different SNP numbers, namely the best SNP barcodes, to show the maximum frequency difference between non-hypertension and hypertension groups. After computation, the best PSO-generated SNP barcodes were dominant in non-hypertension in terms of the occurrences of frequency differences between non-hypertension and hypertension groups. The OR values of the best SNP barcodes involving 2–8 SNPs were 0.705–0.334, suggesting that these SNP barcodes were protective against hypertension. In conclusion, this study demonstrated that non-significant SNPs may generate the joint effect in association study. Our proposed PSO algorithm is effective to identify the best protective SNP barcodes against hypertension.     

A composite likelihood approach to latent multivariate Gaussian modeling of SNP data with application to genetic association testing

Many statistical tests have been proposed for case-control data to detect disease association with multiple single nucleotide polymorphisms (SNPs) in linkage disequilibrium. The main reason for the existence of so many tests is that each test aims to detect one or two aspects of many possible distributional differences between cases and controls, largely due to the lack of a general and yet simple model for discrete genotype data. Here we propose a latent variable model to represent SNP data: the observed SNP data are assumed to be obtained by discretizing a latent multivariate Gaussian variate. Because the latent variate is multivariate Gaussian, its distribution is completely characterized by its mean vector and covariance matrix, in contrast to much more complex forms of a general distribution for discrete multivariate SNP data. We propose a composite likelihood approach for parameter estimation. A direct application of this latent variable model is to association testing with multiple SNPs in a candidate gene or region. In contrast to many existing tests that aim to detect only one or two aspects of many possible distributional differences of discrete SNP data, we can exclusively focus on testing the mean and covariance parameters of the latent Gaussian distributions for cases and controls. Our simulation results demonstrate potential power gains of the proposed approach over some existing methods.     

Allelic Spectra of Risk SNPs Are Different for Environment/Lifestyle Dependent versus Independent Diseases

Genome-wide association studies (GWAS) have generated sufficient data to assess the role of selection in shaping allelic diversity of disease-associated SNPs. Negative selection against disease risk variants is expected to reduce their frequencies making them overrepresented in the group of minor (<50%) alleles. Indeed, we found that the overall proportion of risk alleles was higher among alleles with frequency <50% (minor alleles) compared to that in the group of major alleles. We hypothesized that negative selection may have different effects on environment (or lifestyle)-dependent versus environment (or lifestyle)-independent diseases. We used an environment/lifestyle index (ELI) to assess influence of environmental/lifestyle factors on disease etiology. ELI was defined as the number of publications mentioning “environment” or “lifestyle” AND disease per 1,000 disease-mentioning publications. We found that the frequency distributions of the risk alleles for the diseases with strong environmental/lifestyle components follow the distribution expected under a selectively neutral model, while frequency distributions of the risk alleles for the diseases with weak environmental/lifestyle influences is shifted to the lower values indicating effects of negative selection. We hypothesized that previously selectively neutral variants become risk alleles when environment changes. The hypothesis of ancestrally neutral, currently disadvantageous risk-associated alleles predicts that the distribution of risk alleles for the environment/lifestyle dependent diseases will follow a neutral model since natural selection has not had enough time to influence allele frequencies. The results of our analysis suggest that prediction of SNP functionality based on the level of evolutionary conservation may not be useful for SNPs associated with environment/lifestyle dependent diseases.     

Identification of SNP interactions using logic regression

Interactions of single nucleotide polymorphisms (SNPs) are assumed to be responsible for complex diseases such as sporadic breast cancer. Important goals of studies concerned with such genetic data are thus to identify combinations of SNPs that lead to a higher risk of developing a disease and to measure the importance of these interactions. There are many approaches based on classification methods such as CART and random forests that allow measuring the importance of single variables. But none of these methods enable the importance of combinations of variables to be quantified directly. In this paper, we show how logic regression can be employed to identify SNP interactions explanatory for the disease status in a case-control study and propose 2 measures for quantifying the importance of these interactions for classification. These approaches are then applied on the one hand to simulated data sets and on the other hand to the SNP data of the GENICA study, a study dedicated to the identification of genetic and gene-environment interactions associated with sporadic breast cancer.     

A One-Degree-of-Freedom Test for Supra-Multiplicativity of SNP Effects

Deviation from multiplicativity of genetic risk factors is biologically plausible and might explain why Genome-wide association studies (GWAS) so far could unravel only a portion of disease heritability. Still, evidence for SNP-SNP epistasis has rarely been reported, suggesting that 2-SNP models are overly simplistic. In this context, it was recently proposed that the genetic architecture of complex diseases could follow limiting pathway models. These models are defined by a critical risk allele load and imply multiple high-dimensional interactions. Here, we present a computationally efficient one-degree-of-freedom “supra-multiplicativity-test” (SMT) for SNP sets of size 2 to 500 that is designed to detect risk alleles whose joint effect is fortified when they occur together in the same individual. Via a simulation study we show that the SMT is powerful in the presence of threshold models, even when only about 30–45% of the model SNPs are available. In addition, we demonstrate that the SMT outperforms standard interaction analysis under recessive models involving just a few SNPs. We apply our test to 10 consensus Alzheimer’s disease (AD) susceptibility SNPs that were previously identified by GWAS and obtain evidence for supra-multiplicativity () that is not attributable to either two-way or three-way interaction.     

Identification of an Interaction between VWF rs7965413 and Platelet Count as a Novel Risk Marker for Metabolic Syndrome: An Extensive Search of Candidate Polymorphisms in a Case-Control Study

Although many single nucleotide polymorphisms (SNPs) have been identified to be associated with metabolic syndrome (MetS), there was only a slight improvement in the ability to predict future MetS by the simply addition of SNPs to clinical risk markers. To improve the ability to predict future MetS, combinational effects, such as SNP—SNP interaction, SNP—environment interaction, and SNP—clinical parameter (SNP × CP) interaction should be also considered. We performed a case-control study to explore novel SNP × CP interactions as risk markers for MetS based on health check-up data of Japanese male employees. We selected 99 SNPs that were previously reported to be associated with MetS and components of MetS; subsequently, we genotyped these SNPs from 360 cases and 1983 control subjects. First, we performed logistic regression analyses to assess the association of each SNP with MetS. Of these SNPs, five SNPs were significantly associated with MetS (P < 0.05): LRP2 rs2544390, rs1800592 between UCP1 and TBC1D9, APOA5 rs662799, VWF rs7965413, and rs1411766 between MYO16 and IRS2. Furthermore, we performed multiple logistic regression analyses, including an SNP term, a CP term, and an SNP × CP interaction term for each CP and SNP that was significantly associated with MetS. We identified a novel SNP × CP interaction between rs7965413 and platelet count that was significantly associated with MetS [SNP term: odds ratio (OR) = 0.78, P = 0.004; SNP × CP interaction term: OR = 1.33, P = 0.001]. This association of the SNP × CP interaction with MetS remained nominally significant in multiple logistic regression analysis after adjustment for either the number of MetS components or MetS components excluding obesity. Our results reveal new insight into platelet count as a risk marker for MetS.     

Selection of single-nucleotide polymorphisms in disease association data

We studied several methods for selecting single-nucleotide polymorphisms (SNPs) in a disease association study. Two major categories for analytical strategy are the univariate and the set selection approaches. The univariate approach evaluates each SNP marker one at a time, while the set selection approach tests disease association of a set of SNP markers simultaneously. We examined various test statistics that can be utilized in testing disease association and also reviewed several multiple testing procedures that can properly control the family-wise error rates when the univariate approach is applied to multiple markers. The set association methods were then briefly reviewed. Finally, we applied these methods to the data from Collaborative Study on the Genetics of Alcoholism (COGA).     

Log-linear model-based multifactor dimensionality reduction method to detect gene gene interactions

MOTIVATION: The identification and characterization of susceptibility genes that influence the risk of common and complex diseases remains a statistical and computational challenge in genetic association studies. This is partly because the effect of any single genetic variant for a common and complex disease may be dependent on other genetic variants (gene-gene interaction) and environmental factors (gene-environment interaction). To address this problem, the multifactor dimensionality reduction (MDR) method has been proposed by Ritchie et al. to detect gene-gene interactions or gene-environment interactions. The MDR method identifies polymorphism combinations associated with the common and complex multifactorial diseases by collapsing high-dimensional genetic factors into a single dimension. That is, the MDR method classifies the combination of multilocus genotypes into high-risk and low-risk groups based on a comparison of the ratios of the numbers of cases and controls. When a high-order interaction model is considered with multi-dimensional factors, however, there may be many sparse or empty cells in the contingency tables. The MDR method cannot classify an empty cell as high risk or low risk and leaves it as undetermined. RESULTS: In this article, we propose the log-linear model-based multifactor dimensionality reduction (LM MDR) method to improve the MDR in classifying sparse or empty cells. The LM MDR method estimates frequencies for empty cells from a parsimonious log-linear model so that they can be assigned to high-and low-risk groups. In addition, LM MDR includes MDR as a special case when the saturated log-linear model is fitted. Simulation studies show that the LM MDR method has greater power and smaller error rates than the MDR method. The LM MDR method is also compared with the MDR method using as an example sporadic Alzheimer's disease.     

Comparative assessment of the association information captured by SNP tagging

Exploiting the association between single nucleotide polymorphisms (SNP) can potentially reduce the costs of association mapping of common disease genes. Different methods have been proposed for defining subsets of SNPs as proxies (or tagSNPs) for other SNPs, some of which rely upon a model of haplotype blocks. Other approaches only consider the pair-wise correlation between markers as a basis for selecting tagSNPs. Yet another, recently proposed model-based method takes marker heterozygosity and genetic distance into account in order to maximize the expected utility of a marker set to map frequent, but unobserved genetic variants. We compared these tagging approaches with regard to their ability to correlate tagSNPs and bi-allelic, potentially disease-causing genetic variants. We used the CEU sample of chromosome 19 from the HapMap project for an initial comparison, and demonstrated a comparable performance of both approaches but a difference in terms of tagSNPs selected and variants captured. In any case, we conclude that a considerable loss of information appears to be inherent to any type of SNP tagging, even when dense marker sets are available for SNP selection.     

Conditional likelihood methods for haplotype-based association analysis using matched case-control data

Genetic epidemiologists routinely assess disease susceptibility in relation to haplotypes, that is, combinations of alleles on a single chromosome. We study statistical methods for inferring haplotype-related disease risk using single nucleotide polymorphism (SNP) genotype data from matched case-control studies, where controls are individually matched to cases on some selected factors. Assuming a logistic regression model for haplotype-disease association, we propose two conditional likelihood approaches that address the issue that haplotypes cannot be inferred with certainty from SNP genotype data (phase ambiguity). One approach is based on the likelihood of disease status conditioned on the total number of cases, genotypes, and other covariates within each matching stratum, and the other is based on the joint likelihood of disease status and genotypes conditioned only on the total number of cases and other covariates. The joint-likelihood approach is generally more efficient, particularly for assessing haplotype-environment interactions. Simulation studies demonstrated that the first approach was more robust to model assumptions on the diplotype distribution conditioned on environmental risk variables and matching factors in the control population. We applied the two methods to analyze a matched case-control study of prostate cancer.     

Regulatory polymorphisms in the cyclophilin A gene, PPIA, accelerate progression to AIDS

Human cyclophilin A, or CypA, encoded by the gene peptidyl prolyl isomerase A (PPIA), is incorporated into the HIV type 1 (HIV-1) virion and promotes HIV-1 infectivity by facilitating virus uncoating. We examined the effect of single nucleotide polymorphisms (SNPs) and haplotypes within the PPIA gene on HIV-1 infection and disease progression in five HIV-1 longitudinal history cohorts. Kaplan-Meier survival statistics and Cox proportional hazards model were used to assess time to AIDS outcomes. Among eight SNPs tested, two promoter SNPs (SNP3 and SNP4) in perfect linkage disequilibrium were associated with more rapid CD4(+) T-cell loss (relative hazard = 3.7, p = 0.003) in African Americans. Among European Americans, these alleles were also associated with a significant trend to more rapid progression to AIDS in a multi-point categorical analysis (p = 0.005). Both SNPs showed differential nuclear protein-binding efficiencies in a gel shift assay. In addition, one SNP (SNP5) located in the 5' UTR previously shown to be associated with higher ex vivo HIV-1 replication was found to be more frequent in HIV-1-positive individuals than in those highly exposed uninfected individuals. These results implicate regulatory PPIA polymorphisms as a component of genetic susceptibility to HIV-1 infection or disease progression, affirming the important role of PPIA in HIV-1 pathogenesis.