The use of hierarchical models for estimating relative risks of individual genetic variants: an application to a study of melanoma

For major genes known to influence the risk of cancer, an important task is to determine the risks conferred by individual variants, so that one can appropriately counsel carriers of these mutations. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little empirical evidence available about each individual mutation. Hierarchical modeling offers a natural strategy to leverage the collective evidence from these rare variants with sparse data. This can be accomplished when there are available higher-level covariates that characterize the variants in terms of attributes that could distinguish their association with disease. In this article, we explore the use of hierarchical modeling for this purpose using data from a large population-based study of the risks of melanoma conferred by variants in the CDKN2A gene. We employ both a pseudo-likelihood approach and a Bayesian approach using Gibbs sampling. The results indicate that relative risk estimates tend to be primarily influenced by the individual case-control frequencies when several cases and/or controls are observed with the variant under study, but that relative risk estimates for variants with very sparse data are more influenced by the higher-level covariate values, as one would expect. The analysis offers encouragement that we can draw strength from the aggregating power of hierarchical models to provide guidance to medical geneticists when they offer counseling to patients with rare or even hitherto unobserved variants. However, further research is needed to validate the application of asymptotic methods to such sparse data.     

Joint association testing of common and rare genetic variants using hierarchical modeling

New sequencing technologies provide an opportunity for assessing the impact of rare and common variants on complex diseases. Several methods have been developed for evaluating rare variants, many of which use weighted collapsing to combine rare variants. Some approaches require arbitrary frequency thresholds below which to collapse alleles, and most assume that effect sizes for each collapsed variant are either the same or a function of minor allele frequency. Some methods also further assume that all rare variants are deleterious rather than protective. We expect that such assumptions will not hold in general, and as a result performance of these tests will be adversely affected. We propose a hierarchical model, implemented in the new program CHARM, to detect the joint signal from rare and common variants within a genomic region while properly accounting for linkage disequilibrium between variants. Our model explores the scale, rather than the center of the odds ratio distribution, allowing for both causative and protective effects. We use cross-validation to assess the evidence for association in a region. We use model averaging to widen the range of disease models under which we will have good power. To assess this approach, we simulate data under a range of disease models with effects at common and/or rare variants. Overall, our method had more power than other well-known rare variant approaches; it performed well when either only rare, or only common variants were causal, and better than other approaches when both common and rare variants contributed to disease.     

Detecting association of rare and common variants based on cross‐validation prediction error

Despite the extensive discovery of disease‐associated common variants, much of the genetic contribution to complex traits remains unexplained. Rare variants may explain additional disease risk or trait variability. Although sequencing technology provides a supreme opportunity to investigate the roles of rare variants in complex diseases, detection of these variants in sequencing‐based association studies presents substantial challenges. In this article, we propose novel statistical tests to test the association between rare and common variants in a genomic region and a complex trait of interest based on cross‐validation prediction error (PE). We first propose a PE method based on Ridge regression. Based on PE, we also propose another two tests PE‐WS and PE‐TOW by testing a weighted combination of variants with two different weighting schemes. PE‐WS is the PE version of the test based on the weighted sum statistic (WS) and PE‐TOW is the PE version of the test based on the optimally weighted combination of variants (TOW). Using extensive simulation studies, we are able to show that (1) PE‐TOW and PE‐WS are consistently more powerful than TOW and WS, respectively, and (2) PE is the most powerful test when causal variants contain both common and rare variants.     

Detecting rare variants for complex traits using family and unrelated data

Large genome‐wide association studies (GWAS) have been performed to detect common genetic variants involved in common diseases, but most of the variants found this way account for only a small portion of the trait variance. Furthermore, candidate gene‐based resequencing suggests that many rare genetic variants contribute to the trait variance of common diseases. Here we propose two designs, sibpair and unrelated‐case designs, to detect rare genetic variants in either a candidate gene‐based or genome‐wide association analysis. First we show that we can detect and classify together rare risk haplotypes using a relatively small sample with either of these designs, and then have increased power to test association in a larger case‐control sample. This method can also be applied to resequencing data. Next we apply the method to the Wellcome Trust Case Control Consortium (WTCCC) coronary artery disease (CAD) and hypertension (HT) data, the latter being the only trait for which no genome‐wide association evidence was reported in the original WTCCC study, and identify one interesting gene associated with HT and four associated with CAD at a genome‐wide significance level of 5%. These results suggest that searching for rare genetic variants is feasible and can be fruitful in current GWAS, candidate gene studies or resequencing studies. Genet. Epidemiol. 34: 171–187, 2010. © 2009 Wiley‐Liss, Inc.     

Detecting association of rare and common variants by testing an optimally weighted combination of variants

Next-generation sequencing technology will soon allow sequencing the whole genome of large groups of individuals, and thus will make directly testing rare variants possible. Currently, most of existing methods for rare variant association studies are essentially testing the effect of a weighted combination of variants with different weighting schemes. Performance of these methods depends on the weights being used and no optimal weights are available. By putting large weights on rare variants and small weights on common variants, these methods target at rare variants only, although increasing evidence shows that complex diseases are caused by both common and rare variants. In this paper, we analytically derive optimal weights under a certain criterion. Based on the optimal weights, we propose a Variable Weight Test for testing the effect of an Optimally Weighted combination of variants (VW-TOW). VW-TOW aims to test the effects of both rare and common variants. VW-TOW is applicable to both quantitative and qualitative traits, allows covariates, can control for population stratification, and is robust to directions of effects of causal variants. Extensive simulation studies and application to the Genetic Analysis Workshop 17 (GAW17) data show that VW-TOW is more powerful than existing ones either for testing effects of both rare and common variants or for testing effects of rare variants only.     

Bayesian analysis of rare variants in genetic association studies

Recent advances in next-generation sequencing technologies facilitate the detection of rare variants, making it possible to uncover the roles of rare variants in complex diseases. As any single rare variants contain little variation, association analysis of rare variants requires statistical methods that can effectively combine the information across variants and estimate their overall effect. In this study, we propose a novel Bayesian generalized linear model for analyzing multiple rare variants within a gene or genomic region in genetic association studies. Our model can deal with complicated situations that have not been fully addressed by existing methods, including issues of disparate effects and nonfunctional variants. Our method jointly models the overall effect and the weights of multiple rare variants and estimates them from the data. This approach produces different weights to different variants based on their contributions to the phenotype, yielding an effective summary of the information across variants. We evaluate the proposed method and compare its performance to existing methods on extensive simulated data. The results show that the proposed method performs well under all situations and is more powerful than existing approaches.     

MF‐TOWmuT: Testing an optimally weighted combination of common and rare variants with multiple traits using family data

With rapid advancements of sequencing technologies and accumulations of electronic health records, a large number of genetic variants and multiple correlated human complex traits have become available in many genetic association studies. Thus, it becomes necessary and important to develop new methods that can jointly analyze the association between multiple genetic variants and multiple traits. Compared with methods that only use a single marker or trait, the joint analysis of multiple genetic variants and multiple traits is more powerful since such an analysis can fully incorporate the correlation structure of genetic variants and/or traits and their mutual dependence patterns. However, most of existing methods that simultaneously analyze multiple genetic variants and multiple traits are only applicable to unrelated samples. We develop a new method called MF‐TOWmuT to detect association of multiple phenotypes and multiple genetic variants in a genomic region with family samples. MF‐TOWmuT is based on an optimally weighted combination of variants. Our method can be applied to both rare and common variants and both qualitative and quantitative traits. Our simulation results show that (1) the type I error of MF‐TOWmuT is preserved; (2) MF‐TOWmuT outperforms two existing methods such as Multiple Family‐based Quasi‐Likelihood Score Test and Multivariate Family‐based Rare Variant Association Test in terms of power. We also illustrate the usefulness of MF‐TOWmuT by analyzing genotypic and phenotipic data from the Genetics of Kidneys in Diabetes study. R program is available at https://github.com/gaochengPRC/MF-TOWmuT .     

A general statistic to test an optimally weighted combination of common and/or rare variants

Both genome-wide association study and next-generation sequencing data analyses are widely employed to identify disease susceptible common and/or rare genetic variants. Rare variants generally have large effects though they are hard to detect due to their low frequencies. Currently, many existing statistical methods for rare variants association studies employ a weighted combination scheme, which usually puts subjective weights or suboptimal weights based on some adhoc assumptions (e.g., ignoring dependence between rare variants). In this study, we analytically derived optimal weights for both common and rare variants and proposed a general and novel approach to test association between an optimally weighted combination of variants (G-TOW) in a gene or pathway for a continuous or dichotomous trait while easily adjusting for covariates. Results of the simulation studies show that G-TOW has properly controlled type I error rates and it is the most powerful test among the methods we compared when testing effects of either both rare and common variants or rare variants only. We also illustrate the effectiveness of G-TOW using the Genetic Analysis Workshop 17 (GAW17) data. Additionally, we applied G-TOW and other competitive methods to test disease-associated genes in real data of schizophrenia. The G-TOW has successfully verified genes FYN and VPS39 which are associated with schizophrenia reported in existing publications. Both of these genes are missed by the weighted sum statistic and the sequence kernel association test. Simulation study and real data analysis indicate that G-TOW is a powerful test.     

Estimating the effects of copy-number variants on intelligence using hierarchical Bayesian models

It is challenging to estimate the phenotypic impact of the structural genome changes known as copy-number variations (CNVs), since there are many unique CNVs which are nonrecurrent, and most are too rare to be studied individually. In recent work, we found that CNV-aggregated genomic annotations, that is, specifically the intolerance to mutation as measured by the pLI score (probability of being loss-of-function intolerant), can be strong predictors of intellectual quotient (IQ) loss. However, this aggregation method only estimates the individual CNV effects indirectly. Here, we propose the use of hierarchical Bayesian models to directly estimate individual effects of rare CNVs on measures of intelligence. Annotation information on the impact of major mutations in genomic regions is extracted from genomic databases and used to define prior information for the approach we call HBIQ. We applied HBIQ to the analysis of CNV deletions and duplications from three datasets and identified several genomic regions containing CNVs demonstrating significant deleterious effects on IQ, some of which validate previously known associations. We also show that several CNVs were identified as deleterious by HBIQ even if they have a zero pLI score, and the converse is also true. Furthermore, we show that our new model yields higher out-of-sample concordance (78%) for predicting the consequences of carrying known recurrent CNVs compared with our previous approach.     

Hierarchical modeling of melanocortin 1 receptor variants with skin cancer risk

The human MC1R gene is highly polymorphic among lightly pigmented populations, and several variants in the MC1R gene have been associated with increased risk of both melanoma and nonmelanoma skin cancers. The functional consequences of MC1R gene variants have been studied in vitro and in vivo in postulated causal pathways, such as G‐protein‐coupled signaling transduction, pigmentation, immune response, inflammatory response, cell proliferation, and extracellular matrix adhesion. In a case‐control study nested within the Nurses’ Health Study, we utilized hierarchical modeling approaches, incorporating quantitative information from these functional studies, to examine the association between particular MC1R alleles and the risk of skin cancers. Different prior matrices were constructed according to the phenotypic associations in controls, cell surface expression, and enzymatic kinetics. Our results showed the parameter variance estimates of each single nucleotide polymorphism (SNP) were smaller when using a hierarchical modeling approach compared to standard multivariable regression. Estimates of second‐level parameters gave information about the relative importance of MC1R effects on different pathways, and odds ratio estimates changed depending on prior models (e.g., the change ranged from ?21% to 7% for melanoma risk assessment). In addition, the estimates of prior model hyperparameters in the hierarchical modeling approach allow us to determine the relevance of individual pathways on the risk of each of the skin cancer types. In conclusion, hierarchical modeling provides a useful analytic approach in addition to the widely used conventional models in genetic association studies that can incorporate measures of allelic function.     

Computationally simple analysis of matched,outcome‐based studies of ordinal disease states

Outcome‐based sampling is an efficient study design for rare conditions, such as glioblastoma. It is often used in conjunction with matching, for increased efficiency and to potentially avoid bias due to confounding. A study was conducted at the Massachusetts General Hospital that involved retrospective sampling of glioblastoma patients with respect to multiple‐ordered disease states, as defined by three categories of overall survival time. To analyze such studies, we posit an adjacent categories logit model and exploit its allowance for prospective analysis of a retrospectively sampled study and its advantageous removal of set and level specific nuisance parameters through conditioning on sufficient statistics. This framework allows for any sampling design and is not limited to one level of disease within each set, such as in previous publications. We describe how this ordinal conditional model can be fit using standard conditional logistic regression procedures. We consider an alternative pseudo‐likelihood approach that potentially offers robustness under partial model misspecification at the expense of slight loss of efficiency under correct model specification for small sample sizes. We apply our methods to the Massachusetts General Hospital glioblastoma study. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison of statistical tests for disease association with rare variants

In anticipation of the availability of next‐generation sequencing data, there is increasing interest in investigating association between complex traits and rare variants (RVs). In contrast to association studies for common variants (CVs), due to the low frequencies of RVs, common wisdom suggests that existing statistical tests for CVs might not work, motivating the recent development of several new tests for analyzing RVs, most of which are based on the idea of pooling/collapsing RVs. However, there is a lack of evaluations of, and thus guidance on the use of, existing tests. Here we provide a comprehensive comparison of various statistical tests using simulated data. We consider both independent and correlated rare mutations, and representative tests for both CVs and RVs. As expected, if there are no or few non‐causal (i.e. neutral or non‐associated) RVs in a locus of interest while the effects of causal RVs on the trait are all (or mostly) in the same direction (i.e. either protective or deleterious, but not both), then the simple pooled association tests (without selecting RVs and their association directions) and a new test called kernel‐based adaptive clustering (KBAC) perform similarly and are most powerful; KBAC is more robust than simple pooled association tests in the presence of non‐causal RVs; however, as the number of non‐causal CVs increases and/or in the presence of opposite association directions, the winners are two methods originally proposed for CVs and a new test called C‐alpha test proposed for RVs, each of which can be regarded as testing on a variance component in a random‐effects model. Interestingly, several methods based on sequential model selection (i.e. selecting causal RVs and their association directions), including two new methods proposed here, perform robustly and often have statistical power between those of the above two classes. Genet. Epidemiol. 2011. © 2011 Wiley Periodicals, Inc. 35:606‐619, 2011     

Bayesian hierarchical modeling of longitudinal glaucomatous visual fields using a two‐stage approach

The Bayesian approach has become increasingly popular because it allows to fit quite complex models to data via Markov chain Monte Carlo sampling. However, it is also recognized nowadays that Markov chain Monte Carlo sampling can become computationally prohibitive when applied to a large data set. We encountered serious computational difficulties when fitting an hierarchical model to longitudinal glaucoma data of patients who participate in an ongoing Dutch study. To overcome this problem, we applied and extended a recently proposed two‐stage approach to model these data. Glaucoma is one of the leading causes of blindness in the world. In order to detect deterioration at an early stage, a model for predicting visual fields (VFs) in time is needed. Hence, the true underlying VF progression can be determined, and treatment strategies can then be optimized to prevent further VF loss. Because we were unable to fit these data with the classical one‐stage approach upon which the current popular Bayesian software is based, we made use of the two‐stage Bayesian approach. The considered hierarchical longitudinal model involves estimating a large number of random effects and deals with censoring and high measurement variability. In addition, we extended the approach with tools for model evaluation. Copyright © 2017 John Wiley & Sons, Ltd.     

A comparison of bayesian and frequentist approaches to incorporating external information for the prediction of prostate cancer risk

We present the most comprehensive comparison to date of the predictive benefit of genetics in addition to currently used clinical variables, using genotype data for 33 single‐nucleotide polymorphisms (SNPs) in 1,547 Caucasian men from the placebo arm of the REduction by DUtasteride of prostate Cancer Events (REDUCE®) trial. Moreover, we conducted a detailed comparison of three techniques for incorporating genetics into clinical risk prediction. The first method was a standard logistic regression model, which included separate terms for the clinical covariates and for each of the genetic markers. This approach ignores a substantial amount of external information concerning effect sizes for these Genome Wide Association Study (GWAS)‐replicated SNPs. The second and third methods investigated two possible approaches to incorporating meta‐analysed external SNP effect estimates – one via a weighted PCa 'risk' score based solely on the meta analysis estimates, and the other incorporating both the current and prior data via informative priors in a Bayesian logistic regression model. All methods demonstrated a slight improvement in predictive performance upon incorporation of genetics. The two methods that incorporated external information showed the greatest receiver‐operating‐characteristic AUCs increase from 0.61 to 0.64. The value of our methods comparison is likely to lie in observations of performance similarities, rather than difference, between three approaches of very different resource requirements. The two methods that included external information performed best, but only marginally despite substantial differences in complexity.     

A maximum likelihood method for studying gene-environment interactions under conditional independence of genotype and exposure

Given the biomedical interest in gene-environment interactions along with the difficulties inherent in gathering genetic data from controls, epidemiologists need methodologies that can increase precision of estimating interactions while minimizing the genotyping of controls. To achieve this purpose, many epidemiologists suggested that one can use case-only design. In this paper, we present a maximum likelihood method for making inference about gene-environment interactions using case-only data. The probability of disease development is described by a logistic risk model. Thus the interactions are model parameters measuring the departure of joint effects of exposure and genotype from multiplicative odds ratios. We extend the typical inference method derived under the assumption of independence between genotype and exposure to that under a more general assumption of conditional independence. Our maximum likelihood method can be applied to analyse both categorical and continuous environmental factors, and generalized to make inference about gene-gene-environment interactions. Moreover, the application of this method can be reduced to simply fitting a multinomial logistic model when we have case-only data. As a consequence, the maximum likelihood estimates of interactions and likelihood ratio tests for hypotheses concerning interactions can be easily computed. The methodology is illustrated through an example based on a study about the joint effects of XRCC1 polymorphisms and smoking on bladder cancer. We also give two simulation studies to show that the proposed method is reliable in finite sample situation.     

BRCA1和BRCA2在乳腺疾病中的表达和意义

目的通过检测乳腺癌易感基因1(BRCA1)和乳腺癌易感基因2(BRCA2)在乳腺增生病、乳腺癌癌前病变、乳腺癌中的表达,探讨BRCA1和BRCA2在乳腺癌发生、发展中的作用。方法切除的原发病灶共90例,经福尔马林固定、石蜡包埋,常规切片,应用免疫组织化学技术(IHC),检测乳腺增生病、乳腺癌癌前病变、乳腺癌中的BRCA1和BRCA2表达情况。结果(1)BRCA1和BRCA2在乳腺增生病、乳腺癌癌前病变、乳腺癌中阳性表达率依次递减,在三者中的表达有显著性差异(P<0.05)。(2)BRCA1和BRCA2的表达相互之间无显著性差异(P>0.05)。结论乳腺上皮中BRCA1和BRCA2的表达减少对乳腺癌的发生、发展具有重要作用。对BRCA1和BRCA2的检测有利于筛选出乳腺癌高危人群,早期发现乳腺癌。但BRCA1和BRCA2在乳腺癌中的表达无相关性。     

A rare variant association test in family‐based designs and non‐normal quantitative traits

Rare variant studies are now being used to characterize the genetic diversity between individuals and may help to identify substantial amounts of the genetic variation of complex diseases and quantitative phenotypes. Family data have been shown to be powerful to interrogate rare variants. Consequently, several rare variants association tests have been recently developed for family‐based designs, but typically, these assume the normality of the quantitative phenotypes. In this paper, we present a family‐based test for rare‐variants association in the presence of non‐normal quantitative phenotypes. The proposed model relaxes the normality assumption and does not specify any parametric distribution for the marginal distribution of the phenotype. The dependence between relatives is modeled via a Gaussian copula. A score‐type test is derived, and several strategies to approximate its distribution under the null hypothesis are derived and investigated. The performance of the proposed test is assessed and compared with existing methods by simulations. The methodology is illustrated with an association study involving the adiponectin trait from the UK10K project. Copyright © 2015 John Wiley & Sons, Ltd.     

Bioethics and healthcare policies. The benefit of using genetic tests of BRCA 1 and BRCA 2 in elderly patients

This study focuses on the role of bioethics in designing public healthcare policies towards elderly patients with cancer. The general overview of public administration and healthcare approach to treatment. Interpretation of how the EU public administration faces the challenges of an ageing population and extended human longevity. The significant emotional impact a genetic cancer test holds, both in the patients and their families, is to be explained. From the bioethics' perspective, artificial intelligence and transhumanism are dangerous concerning its absence of boundaries. As a result of daily contact with cancer, we acknowledge the immediate and relevant impact science produces in a patient's life. We converge these subjects to the improvement of public policies and governmental efforts in increasing society's positive results.     

A weighted logistic regression model for estimation of recurrence of adenomas

In a colorectal polyp prevention trial, some participants might have their follow-up colonoscopy conducted before the scheduled time (i.e. at the end of the trial). This results in variable follow-up lengths for participants and the data of recurrence status at the end of the trial can be considered as current status data. In this paper, we use a weighted logistic regression model to estimate recurrence rate of adenoma data at the end of the trial. The weights are used to adjust for variable follow-up. We show that logistic regression tends to underestimate recurrence rate. In a simulation study, we show that Kaplan-Meier estimator derived from the right endpoint of the current status data tends to overestimate recurrence rate in contrast to logistic regression and the weighted logistic regression method can produce reasonable estimates of recurrence rate even under a high non-compliance rate compared to conventional logistic regression and Kaplan-Meier estimator. The method described here is illustrated with an example from a colon cancer study.     

A Cost-Effectiveness Evaluation of Germline BRCA1 and BRCA2 Testing in UK Women with Ovarian Cancer

Objectives

To evaluate the long-term cost-effectiveness of germline BRCA1 and BRCA2 (collectively termed “BRCA”) testing in women with epithelial ovarian cancer, and testing for the relevant mutation in first- and second-degree relatives of BRCA mutation–positive individuals, compared with no testing. Female BRCA mutation–positive relatives of patients with ovarian cancer could undergo risk-reducing mastectomy and/or bilateral salpingo-oophorectomy.