Kernel‐Machine Testing Coupled with a Rank‐Truncation Method for Genetic Pathway Analysis

Traditional genome‐wide association studies (GWASs) usually focus on single‐marker analysis, which only accesses marginal effects. Pathway analysis, on the other hand, considers biological pathway gene marker hierarchical structure and therefore provides additional insights into the genetic architecture underlining complex diseases. Recently, a number of methods for pathway analysis have been proposed to assess the significance of a biological pathway from a collection of single‐nucleotide polymorphisms. In this study, we propose a novel approach for pathway analysis that assesses the effects of genes using the sequence kernel association test and the effects of pathways using an extended adaptive rank truncated product statistic. It has been increasingly recognized that complex diseases are caused by both common and rare variants. We propose a new weighting scheme for genetic variants across the whole allelic frequency spectrum to be analyzed together without any form of frequency cutoff for defining rare variants. The proposed approach is flexible. It is applicable to both binary and continuous traits, and incorporating covariates is easy. Furthermore, it can be readily applied to GWAS data, exome‐sequencing data, and deep resequencing data. We evaluate the new approach on data simulated under comprehensive scenarios and show that it has the highest power in most of the scenarios while maintaining the correct type I error rate. We also apply our proposed methodology to data from a study of the association between bipolar disorder and candidate pathways from Wellcome Trust Case Control Consortium (WTCCC) to show its utility.     

Truncated tests for combining evidence of summary statistics

To date, thousands of genetic variants to be associated with numerous human traits and diseases have been identified by genome-wide association studies (GWASs). The GWASs focus on testing the association between single trait and genetic variants. However, the analysis of multiple traits and single nucleotide polymorphisms (SNPs) might reflect physiological process of complex diseases and the corresponding study is called pleiotropy association analysis. Modern day GWASs report only summary statistics instead of individual-level phenotype and genotype data to avoid logistical and privacy issues. Existing methods for combining multiple phenotypes GWAS summary statistics mainly focus on low-dimensional phenotypes while lose power in high-dimensional cases. To overcome this defect, we propose two kinds of truncated tests to combine multiple phenotypes summary statistics. Extensive simulations show that the proposed methods are robust and powerful when the dimension of the phenotypes is high and only part of the phenotypes are associated with the SNPs. We apply the proposed methods to blood cytokines data collected from Finnish population. Results show that the proposed tests can identify additional genetic markers that are missed by single trait analysis.     

Stratification-score matching improves correction for confounding by population stratification in case-control association studies

Proper control of confounding due to population stratification is crucial for valid analysis of case-control association studies. Fine matching of cases and controls based on genetic ancestry is an increasingly popular strategy to correct for such confounding, both in genome-wide association studies (GWASs) as well as studies that employ next-generation sequencing, where matching can be used when selecting a subset of participants from a GWAS for rare-variant analysis. Existing matching methods match on measures of genetic ancestry that combine multiple components of ancestry into a scalar quantity. However, we show that including nonconfounding ancestry components in a matching criterion can lead to inaccurate matches, and hence to an improper control of confounding. To resolve this issue, we propose a novel method that assigns cases and controls to matched strata based on the stratification score (Epstein et al. [2007] Am J Hum Genet 80:921-930), which is the probability of disease given genomic variables. Matching on the stratification score leads to more accurate matches because case participants are matched to control participants who have a similar risk of disease given ancestry information. We illustrate our matching method using the African-American arm of the GAIN GWAS of schizophrenia. In this study, we observe that confounding due to stratification can be resolved by our matching approach but not by other existing matching procedures. We also use simulated data to show our novel matching approach can provide a more appropriate correction for population stratification than existing matching approaches.     

Incorporating Functional Genomic Information in Genetic Association Studies Using an Empirical Bayes Approach

There is a large amount of functional genetic data available, which can be used to inform fine‐mapping association studies (in diseases with well‐characterised disease pathways). Single nucleotide polymorphism (SNP) prioritization via Bayes factors is attractive because prior information can inform the effect size or the prior probability of causal association. This approach requires the specification of the effect size. If the information needed to estimate a priori the probability density for the effect sizes for causal SNPs in a genomic region isn't consistent or isn't available, then specifying a prior variance for the effect sizes is challenging. We propose both an empirical method to estimate this prior variance, and a coherent approach to using SNP‐level functional data, to inform the prior probability of causal association. Through simulation we show that when ranking SNPs by our empirical Bayes factor in a fine‐mapping study, the causal SNP rank is generally as high or higher than the rank using Bayes factors with other plausible values of the prior variance. Importantly, we also show that assigning SNP‐specific prior probabilities of association based on expert prior functional knowledge of the disease mechanism can lead to improved causal SNPs ranks compared to ranking with identical prior probabilities of association. We demonstrate the use of our methods by applying the methods to the fine mapping of the CASP8 region of chromosome 2 using genotype data from the Collaborative Oncological Gene‐Environment Study (COGS) Consortium. The data we analysed included approximately 46,000 breast cancer case and 43,000 healthy control samples.     

Multikernel linear mixed model with adaptive lasso for complex phenotype prediction

Linear mixed models (LMMs) and their extensions have been widely used for high-dimensional genomic data analyses. While LMMs hold great promise for risk prediction research, the high dimensionality of the data and different effect sizes of genomic regions bring great analytical and computational challenges. In this work, we present a multikernel linear mixed model with adaptive lasso (KLMM-AL) to predict phenotypes using high-dimensional genomic data. We develop two algorithms for estimating parameters from our model and also establish the asymptotic properties of LMM with adaptive lasso when only one dependent observation is available. The proposed KLMM-AL can account for heterogeneous effect sizes from different genomic regions, capture both additive and nonadditive genetic effects, and adaptively and efficiently select predictive genomic regions and their corresponding effects. Through simulation studies, we demonstrate that KLMM-AL outperforms most of existing methods. Moreover, KLMM-AL achieves high sensitivity and specificity of selecting predictive genomic regions. KLMM-AL is further illustrated by an application to the sequencing dataset obtained from the Alzheimer's disease neuroimaging initiative.     

eQuIPS: eQTL Analysis Using Informed Partitioning of SNPs – A Fully Bayesian Approach

We develop a Bayesian multi‐SNP Markov chain Monte Carlo approach that allows published functional significance scores to objectively inform single nucleotide polymorphism (SNP) prior effect sizes in expression quantitative trait locus (eQTL) studies. We developed the Normal Gamma prior to allow the inclusion of functional information. We partition SNPs into predefined functional groups and select prior distributions that fit the group‐specific observed functional significance scores. We test our method on two simulated datasets and previously analysed human eQTL data containing validated causal SNPs. In our simulations the modified Normal Gamma always performs at least as well, and generally outperforms, the other methods considered. When analysing the human eQTL data, we placed all SNPs into their actual functional group. The ranks of the four validated causal SNPs analysed using the modified Normal Gamma increase dramatically compared to those of the other methods considered. Using our new method, three of the four validated SNPs are ranked in the top 1% of SNPs and the other is in the top 2%. For the standard Normal Gamma, the best of the other methods, the four validated SNPs had ranks in the top 1%, 4%, 20% and 59%. Crucially these substantive improvements in the ranks make it highly likely that most, if not all, of these validated SNPs would have been flagged for follow‐up using our new method, whereas at least two of them would certainly not have been using the current approaches.     

Risk prediction using genome‐wide association studies

Over the last few years, many new genetic associations have been identified by genome‐wide association studies (GWAS). There are potentially many uses of these identified variants: a better understanding of disease etiology, personalized medicine, new leads for studying underlying biology, and risk prediction. Recently, there has been some skepticism regarding the prospects of risk prediction using GWAS, primarily motivated by the fact that individual effect sizes of variants associated with the phenotype are mostly small. However, there have also been arguments that many disease‐associated variants have not yet been identified; hence, prospects for risk prediction may improve if more variants are included. From a risk prediction perspective, it is reasonable to average a larger number of predictors, of which some may have (limited) predictive power, and some actually may be noise. The idea being that when added together, the combined small signals results in a signal that is stronger than the noise from the unrelated predictors. We examine various aspects of the construction of models for the estimation of disease probability. We compare different methods to construct such models, to examine how implementation of cross‐validation may influence results, and to examine which single nucleotide polymorphisms (SNPs) are most useful for prediction. We carry out our investigation on GWAS of the Welcome Trust Case Control Consortium. For Crohn's disease, we confirm our results on another GWAS. Our results suggest that utilizing a larger number of SNPs than those which reach genome‐wide significance, for example using the lasso, improves the construction of risk prediction models. Genet. Epidemiol. 34: 643‐652, 2010. © 2010 Wiley‐Liss, Inc.     

Identification of Grouped Rare and Common Variants via Penalized Logistic Regression

In spite of the success of genome‐wide association studies in finding many common variants associated with disease, these variants seem to explain only a small proportion of the estimated heritability. Data collection has turned toward exome and whole genome sequencing, but it is well known that single marker methods frequently used for common variants have low power to detect rare variants associated with disease, even with very large sample sizes. In response, a variety of methods have been developed that attempt to cluster rare variants so that they may gather strength from one another under the premise that there may be multiple causal variants within a gene. Most of these methods group variants by gene or proximity, and test one gene or marker window at a time. We propose a penalized regression method (PeRC) that analyzes all genes at once, allowing grouping of all (rare and common) variants within a gene, along with subgrouping of the rare variants, thus borrowing strength from both rare and common variants within the same gene. The method can incorporate either a burden‐based weighting of the rare variants or one in which the weights are data driven. In simulations, our method performs favorably when compared to many previously proposed approaches, including its predecessor, the sparse group lasso [Friedman et al., 2010].     

A frequentist design for basket trials using adaptive lasso

A basket trial aims to expedite the drug development process by evaluating a new therapy in multiple populations within the same clinical trial. Each population, referred to as a “basket”, can be defined by disease type, biomarkers, or other patient characteristics. The objective of a basket trial is to identify the subset of baskets for which the new therapy shows promise. The conventional approach would be to analyze each of the baskets independently. Alternatively, several Bayesian dynamic borrowing methods have been proposed that share data across baskets when responses appear similar. These methods can achieve higher power than independent testing in exchange for a risk of some inflation in the type 1 error rate. In this paper we propose a frequentist approach to dynamic borrowing for basket trials using adaptive lasso. Through simulation studies we demonstrate adaptive lasso can achieve similar power and type 1 error to the existing Bayesian methods. The proposed approach has the benefit of being easier to implement and faster than existing methods. In addition, the adaptive lasso approach is very flexible: it can be extended to basket trials with any number of treatment arms and any type of endpoint.     

Incorporating biological information into association studies of sequencing data

We summarize the methodological contributions from Group 3 of Genetic Analysis Workshop 17 (GAW17). The overarching goal of these methods was the evaluation and enhancement of state-of-the-art approaches in integration of biological knowledge into association studies of rare variants. We found that methods loosely fell into three major categories: (1) hypothesis testing of index scores based on aggregating rare variants at the gene level, (2) variable selection techniques that incorporate biological prior information, and (3) novel approaches that integrate external (i.e., not provided by GAW17) prior information, such as pathway and single-nucleotide polymorphism (SNP) annotations. Commonalities among the findings from these contributions are that gene-based analysis of rare variants is advantageous to single-SNP analysis and that the minor allele frequency threshold to identify rare variants may influence power and thus needs to be carefully considered. A consistent increase in power was also identified by considering only nonsynonymous SNPs in the analyses. Overall, we found that no single method had an appreciable advantage over the other methods. However, methods that carried out sensitivity analyses by comparing biologically informative to noninformative prior probabilities demonstrated that integrating biological knowledge into statistical analyses always, at the least, enabled subtle improvements in the performance of any statistical method applied to these simulated data. Although these statistical improvements reflect the simulation model assumed for GAW17, our hope is that the simulation models provide a reasonable representation of the underlying biology and that these methods can thus be of utility in real data.     

A novel chi‐square statistic for detecting group differences between pathways in systems epidemiology

Traditional epidemiology often pays more attention to the identification of a single factor rather than to the pathway that is related to a disease, and therefore, it is difficult to explore the disease mechanism. Systems epidemiology aims to integrate putative lifestyle exposures and biomarkers extracted from multiple omics platforms to offer new insights into the pathway mechanisms that underlie disease at the human population level. One key but inadequately addressed question is how to develop powerful statistics to identify whether one candidate pathway is associated with a disease. Bearing in mind that a pathway difference can result from not only changes in the nodes but also changes in the edges, we propose a novel statistic for detecting group differences between pathways, which in principle, captures the nodes changes and edge changes, as well as simultaneously accounting for the pathway structure simultaneously. The proposed test has been proven to follow the chi‐square distribution, and various simulations have shown it has better performance than other existing methods. Integrating genome‐wide DNA methylation data, we analyzed one real data set from the Bogalusa cohort study and significantly identified a potential pathway, Smoking → SOCS3 → PIK3R1, which was strongly associated with abdominal obesity. The proposed test was powerful and efficient at identifying pathway differences between two groups, and it can be extended to other disciplines that involve statistical comparisons between pathways. The source code in R is available on our website. Copyright © 2016 John Wiley & Sons, Ltd.     

A flexible quantile regression model for medical costs with application to Medical Expenditure Panel Survey Study

Medical costs are often skewed to the right and heteroscedastic, having a sophisticated relation with covariates. Mean function regression models with low‐dimensional covariates have been extensively considered in the literature. However, it is important to develop a robust alternative to find the underlying relationship between medical costs and high‐dimensional covariates. In this paper, we propose a new quantile regression model to analyze medical costs. We also consider variable selection, using an adaptive lasso penalized variable selection method to identify significant factors of the covariates. Simulation studies are conducted to illustrate the performance of the estimation method. We apply our method to the analysis of the Medical Expenditure Panel Survey dataset.     

Detecting rare and common variants for complex traits: sibpair and odds ratio weighted sum statistics (SPWSS, ORWSS)

It is generally known that risk variants segregate together with a disease within families, but this information has not been used in the existing statistical methods for detecting rare variants. Here we introduce two weighted sum statistics that can apply to either genome-wide association data or resequencing data for identifying rare disease variants: weights calculated based on sibpairs and odd ratios, respectively. We evaluated the two methods via extensive simulations under different disease models. We compared the proposed methods with the weighted sum statistic (WSS) proposed by Madsen and Browning, keeping the same genotyping or resequencing cost. Our methods clearly demonstrate more statistical power than the WSS. In addition, we found that using sibpair information can increase power over using only unrelated samples by more than 40%. We applied our methods to the Framingham Heart Study (FHS) and Wellcome Trust Case Control Consortium (WTCCC) hypertension datasets. Although we did not identify any genes as reaching a genome-wide significance level, we found variants in the candidate gene angiotensinogen significantly associated with hypertension at P = 6.9 × 10(-4), whereas the most significant single SNP association evidence is P = 0.063. We further applied the odds ratio weighted method to the IFIH1 gene for type-1 diabetes in the WTCCC data. Our method yielded a P-value of 4.82 × 10(-4), much more significant than that obtained by haplotype-based methods. We demonstrated that family data are extremely informative in searching for rare variants underlying complex traits, and the odds ratio weighted sum statistic is more efficient than currently existing methods.     

Performance and Robustness of Penalized and Unpenalized Methods for Genetic Prediction of Complex Human Disease

A central goal of medical genetics is to accurately predict complex disease from genotypes. Here, we present a comprehensive analysis of simulated and real data using lasso and elastic‐net penalized support‐vector machine models, a mixed‐effects linear model, a polygenic score, and unpenalized logistic regression. In simulation, the sparse penalized models achieved lower false‐positive rates and higher precision than the other methods for detecting causal SNPs. The common practice of prefiltering SNP lists for subsequent penalized modeling was examined and shown to substantially reduce the ability to recover the causal SNPs. Using genome‐wide SNP profiles across eight complex diseases within cross‐validation, lasso and elastic‐net models achieved substantially better predictive ability in celiac disease, type 1 diabetes, and Crohn's disease, and had equivalent predictive ability in the rest, with the results in celiac disease strongly replicating between independent datasets. We investigated the effect of linkage disequilibrium on the predictive models, showing that the penalized methods leverage this information to their advantage, compared with methods that assume SNP independence. Our findings show that sparse penalized approaches are robust across different disease architectures, producing as good as or better phenotype predictions and variance explained. This has fundamental ramifications for the selection and future development of methods to genetically predict human disease.     

Discovery of complex pathways from observational data

Unraveling complex interactions has been a challenge in epidemiologic research. We introduce a pathway modeling framework that discovers plausible pathways from observational data, and allows estimation of both the net effect of the pathway and the types of interactions occurring among genetic or environmental risk factors. Each discovered pathway structure links combinations of observed variables through intermediate latent nodes to a final node, the outcome. Biologic knowledge can be readily applied in this framework as a prior on pathway structure to give preference to more biologically plausible models, thereby providing more precise estimation of Bayes factors for pathways of greatest interest by Markov Chain Monte Carlo (MCMC) methods. Data were simulated for binary inputs of which only a subset was involved in different pathway topologies. Our algorithm was then used to recover the pathway from the simulated data. The posterior distributions of inputs, pairwise and higher‐order interactions, and topologies were obtained by MCMC methods. The evidence in favor of a particular pathway or interaction was summarized using Bayes factors. Our method can correctly identify the risk factors and interactions involved in the simulated pathway. We apply our framework to an asthma case–control data set with polymorphisms in 12 genes. Copyright © 2010 John Wiley & Sons, Ltd.     

Learning from disasters to improve patient safety: applying the generic disaster pathway to health system errors

In a previous paper we developed a generic disaster pathway model drawing from disaster inquiries in the space, shipping, aviation, mining, rail and nuclear industries. To test our hypothesis that our generic disaster model can be applied to healthcare errors, we ustilised three exemplar cases featuring different types and sources of errors. We found that it is possible to apply our generic disaster pathway to healthcare errors, and to identify the combination of human, organisational and design risk factors which contribute to the severity and speed at which errors occur. We conclude that error pathways provide a useful tool from which healthcare services can learn to appreciate and potentially circumvent or ameliorate errors, prior to their reaching the no-return threshold.     

Sequential haplotype scan methods for association analysis

Multi-locus association analyses, including haplotype-based analyses, can sometimes provide greater power than single-locus analyses for detecting disease susceptibility loci. This potential gain, however, can be compromised by the large number of degrees of freedom caused by irrelevant markers. Exhaustive search for the optimal set of markers might be possible for a small number of markers, yet it is computationally inefficient. In this paper, we present a sequential haplotype scan method to search for combinations of adjacent markers that are jointly associated with disease status. When evaluating each marker, we add markers close to it in a sequential manner: a marker is added if its contribution to the haplotype association with disease is warranted, conditional on current haplotypes. This conditional evaluation is based on the well-known Mantel-Haenszel statistic. We propose two permutation based methods to evaluate the growing haplotypes: a haplotype method for the combined markers, and a summary method that sums conditional statistics. We compared our proposed methods, the single-locus method, and a sliding window method using simulated data. We also applied our sequential haplotype scan algorithm to experimental data for CYP2D6. The results indicate that the sequential scan procedure can identify a set of adjacent markers whose haplotypes might have strong genetic effects or be in linkage disequilibrium with disease predisposing variants. As a result, our methods can achieve greater power than the single-locus method, yet is much more computationally efficient than sliding window methods.     

Empirical extensions of the lasso penalty to reduce the false discovery rate in high‐dimensional Cox regression models

Correct selection of prognostic biomarkers among multiple candidates is becoming increasingly challenging as the dimensionality of biological data becomes higher. Therefore, minimizing the false discovery rate (FDR) is of primary importance, while a low false negative rate (FNR) is a complementary measure. The lasso is a popular selection method in Cox regression, but its results depend heavily on the penalty parameter λ. Usually, λ is chosen using maximum cross‐validated log‐likelihood (max‐cvl). However, this method has often a very high FDR. We review methods for a more conservative choice of λ. We propose an empirical extension of the cvl by adding a penalization term, which trades off between the goodness‐of‐fit and the parsimony of the model, leading to the selection of fewer biomarkers and, as we show, to the reduction of the FDR without large increase in FNR. We conducted a simulation study considering null and moderately sparse alternative scenarios and compared our approach with the standard lasso and 10 other competitors: Akaike information criterion (AIC), corrected AIC, Bayesian information criterion (BIC), extended BIC, Hannan and Quinn information criterion (HQIC), risk information criterion (RIC), one‐standard‐error rule, adaptive lasso, stability selection, and percentile lasso. Our extension achieved the best compromise across all the scenarios between a reduction of the FDR and a limited raise of the FNR, followed by the AIC, the RIC, and the adaptive lasso, which performed well in some settings. We illustrate the methods using gene expression data of 523 breast cancer patients. In conclusion, we propose to apply our extension to the lasso whenever a stringent FDR with a limited FNR is targeted. Copyright © 2016 John Wiley & Sons, Ltd.     

On the analysis of sequence data: testing for disease susceptibility loci using patterns of linkage disequilibrium

Despite the numerous and successful applications of genome-wide association studies (GWASs), there has been a lot of difficulty in discovering disease susceptibility loci (DSLs). This is due to the fact that the GWAS approach is an indirect mapping technique, often identifying markers. For the identification of DSLs, which is required for the understanding of the genetic pathways for complex diseases, sequencing data that examines every genetic locus directly is necessary. Yet, there is currently a lack of methodology targeted at the identification of the DSLs in sequencing data: existing methods localize the causal variant to a region but not to a single variant, and therefore do not allow one to identify unique loci that cause the phenotype association. Here, we have developed such a method to determine if there is evidence that an individual loci affects case/control status with sequencing data. This methodology differs from other rare variant approaches: rather than testing an entire region comprised of many loci for association with the phenotype, we can identify the individual genetic locus that causes the association between the phenotype and the genetic region. For each variant, the test determines if the pattern of linkage disequilibrium (LD) across the other variants coincides with the pattern expected if that variant were a DSL. Power simulations show that the method successfully detects the causal variant, distinguishing it from other nearby variants (in high LD with the causal variant), and outperforms the standard tests. The efficiency of the method is especially apparent with small samples, which are currently realistic for studies due to sequencing data costs. The practical relevance of the approach is illustrated by an application to a sequencing dataset for nonsyndromic cleft lip with or without cleft palate. The proposed method implicated one variant (P = 0.002, 0.062 after Bonferroni correction), which was not found by standard analyses. Code for implementation is available.