Modeling maternal‐offspring gene‐gene interactions: the extended‐MFG test

Maternal‐fetal genotype (MFG) incompatibility is an interaction between the genes of a mother and offspring at a particular locus that adversely affects the developing fetus, thereby increasing susceptibility to disease. Statistical methods for examining MFG incompatibility as a disease risk factor have been developed for nuclear families. Because families collected as part of a study can be large and complex, containing multiple generations and marriage loops, we create the Extended‐MFG (EMFG) Test, a model‐based likelihood approach, to allow for arbitrary family structures. We modify the MFG test by replacing the nuclear‐family based “mating type” approach with Ott's representation of a pedigree likelihood and calculating MFG incompatibility along with the Mendelian transmission probability. In order to allow for extension to arbitrary family structures, we make a slightly more stringent assumption of random mating with respect to the locus of interest. Simulations show that the EMFG test has appropriate type‐I error rate, power, and precise parameter estimation when random mating holds. Our simulations and real data example illustrate that the chief advantages of the EMFG test over the earlier nuclear family version of the MFG test are improved accuracy of parameter estimation and power gains in the presence of missing genotypes. Genet. Epidemiol. 34: 512–521, 2010.© 2010 Wiley‐Liss, Inc.     

A global test for gene‐gene interactions based on random matrix theory

Statistical interactions between markers of genetic variation, or gene‐gene interactions, are believed to play an important role in the etiology of many multifactorial diseases and other complex phenotypes. Unfortunately, detecting gene‐gene interactions is extremely challenging due to the large number of potential interactions and ambiguity regarding marker coding and interaction scale. For many data sets, there is insufficient statistical power to evaluate all candidate gene‐gene interactions. In these cases, a global test for gene‐gene interactions may be the best option. Global tests have much greater power relative to multiple individual interaction tests and can be used on subsets of the markers as an initial filter prior to testing for specific interactions. In this paper, we describe a novel global test for gene‐gene interactions, the global epistasis test (GET), that is based on results from random matrix theory. As we show via simulation studies based on previously proposed models for common diseases including rheumatoid arthritis, type 2 diabetes, and breast cancer, our proposed GET method has superior performance characteristics relative to existing global gene‐gene interaction tests. A glaucoma GWAS data set is used to demonstrate the practical utility of the GET method.     

The importance of a genetic component in longitudinal birth cohorts

The risks of most common health and developmental outcomes are contributed to by a combination of genetic and environmental factors. Understanding of ways in which genes influence such outcomes, and especially of how their interaction with environmental factors affects health and development should lead to the identification of causal pathways and thence appropriate intervention strategies.     

Testing gene‐environment interactions in family‐based association studies using trait‐based ascertained samples

The study of gene‐environment interactions is an increasingly important aspect of genetic epidemiological investigation. Historically, it has been difficult to study gene‐environment interactions using a family‐based design for quantitative traits or when parent‐offspring trios were incomplete. The QBAT‐I provides researchers a tool to estimate and test for a gene‐environment interaction in families of arbitrary structure that are sampled without regard to the phenotype of interest, but is vulnerable to inflated type I error if families are ascertained on the basis of the phenotype. In this study, we verified the potential for type I error of the QBAT‐I when applied to samples ascertained on a trait of interest. The magnitude of the inflation increases as the main genetic effect increases and as the ascertainment becomes more extreme. We propose an ascertainment‐corrected score test that allows the use of the QBAT‐I to test for gene‐environment interactions in ascertained samples. Our results indicate that the score test and an ad hoc method we propose can often restore the nominal type I error rate, and in cases where complete restoration is not possible, dramatically reduce the inflation of the type I error rate in ascertained samples. Copyright © 2013 John Wiley & Sons, Ltd.     

IndOR: a new statistical procedure to test for SNP-SNP epistasis in genome-wide association studies

Epistasis is often cited as the biological mechanism carrying the missing heritability in genome‐wide association studies. However, there is a very few number of studies reported in the literature. The low power of existing statistical methods is a potential explanation. Statistical procedures are also mainly based on the statistical definition of epistasis that prevents from detecting SNP–SNP interactions that rely on some classes of epistatic models. In this paper, we propose a new statistic, called IndOR for independence‐based odds ratio, based on the biological definition of epistasis. We assume that epistasis modifies the dependency between the two causal SNPs, and we develop a Wald procedure to test such hypothesis. Our new statistic is compared with three statistical procedures in a large power study on simulated data sets. We use extensive simulations, based on 45 scenarios, to investigate the effect of three factors: the underlying disease model, the linkage disequilibrium, and the control‐to‐case ratio. We demonstrate that our new test has the ability to detect a wider range of epistatic models. Furthermore, our new statistical procedure is remarkably powerful when the two loci are linked and when the control‐to‐case ratio is higher than 1. The application of our new statistic on the Wellcome Trust Case Control Consortium data set on Crohn's disease enhances our results on simulated data. Our new test, IndOR, catches previously reported interaction with more power. Furthermore, a new combination of variant has been detected by our new test as significantly associated with Crohn's disease. Copyright © 2012 John Wiley & Sons, Ltd.     

Contrasting linkage disequilibrium as a multilocus family‐based association test

Linkage disequilibrium (LD) of genetic loci is routinely estimated and graphically illustrated in genetic association studies. It has been suggested that the information in LD is also useful for association mapping and genetic association can be detected by comparing LD patterns between cases and controls. Here, we extend this idea to analyze case‐parents data by comparing LD patterns between transmitted and nontransmitted genotypes. We provide the condition when contrasting LD is valid for testing gene‐gene interactions. A permutation procedure is given to assess statistical significance. One advantage of our proposed methods is that haplotype information is not required. Thus, the implementation of our methods is straightforward and the resulted tests are free from potential bias caused by assumptions made to estimate haplotypes in silico. Since our test statistics use pairwise LD measurements, they are less affected by missing data than many other multilocus methods. With simulated data, we demonstrate that examining LD patterns of case‐parents data is a useful multilocus association mapping strategy and it complements existing association mapping methods. The application of our methods to a Crohn's disease data set shows that our methods can detect multilocus association that might be missed by other association methods. Our permutation procedure can also be modified to allow multiple offspring from a family to be analyzed. Genet. Epidemiol. 2011. © 2011 Wiley‐Liss, Inc. 35: 487‐498, 2011     

A combination test for detection of gene‐environment interaction in cohort studies

Identifying gene‐environment (G‐E) interactions can contribute to a better understanding of disease etiology, which may help researchers develop disease prevention strategies and interventions. One big criticism of studying G‐E interaction is the lack of power due to sample size. Studies often restrict the interaction search to the top few hundred hits from a genome‐wide association study or focus on potential candidate genes. In this paper, we test interactions between a candidate gene and an environmental factor to improve power by analyzing multiple variants within a gene. We extend recently developed score statistic based genetic association testing approaches to the G‐E interaction testing problem. We also propose tests for interaction using gene‐based summary measures that pool variants together. Although it has recently been shown that these summary measures can be biased and may lead to inflated type I error, we show that under several realistic scenarios, we can still provide valid tests of interaction. These tests use significantly less degrees of freedom and thus can have much higher power to detect interaction. Additionally, we demonstrate that the iSeq‐aSum‐min test, which combines a gene‐based summary measure test, iSeq‐aSum‐G, and an interaction‐based summary measure test, iSeq‐aSum‐I, provides a powerful alternative to test G‐E interaction. We demonstrate the performance of these approaches using simulation studies and illustrate their performance to study interaction between the SNPs in several candidate genes and family climate environment on alcohol consumption using the Minnesota Center for Twin and Family Research dataset.     

Screen and clean: a tool for identifying interactions in genome‐wide association studies

Epistasis could be an important source of risk for disease. How interacting loci might be discovered is an open question for genome‐wide association studies (GWAS). Most researchers limit their statistical analyses to testing individual pairwise interactions (i.e., marginal tests for association). A more effective means of identifying important predictors is to fit models that include many predictors simultaneously (i.e., higher‐dimensional models). We explore a procedure called screen and clean (SC) for identifying liability loci, including interactions, by using the lasso procedure, which is a model selection tool for high‐dimensional regression. We approach the problem by using a varying dictionary consisting of terms to include in the model. In the first step the lasso dictionary includes only main effects. The most promising single‐nucleotide polymorphisms (SNPs) are identified using a screening procedure. Next the lasso dictionary is adjusted to include these main effects and the corresponding interaction terms. Again, promising terms are identified using lasso screening. Then significant terms are identified through the cleaning process. Implementation of SC for GWAS requires algorithms to explore the complex model space induced by the many SNPs genotyped and their interactions. We propose and explore a set of algorithms and find that SC successfully controls Type I error while yielding good power to identify risk loci and their interactions. When the method is applied to data obtained from the Wellcome Trust Case Control Consortium study of Type 1 Diabetes it uncovers evidence supporting interaction within the HLA class II region as well as within Chromosome 12q24. Genet. Epidemiol. 34: 275–285, 2010. © 2010 Wiley‐Liss, Inc.     

An easy‐to‐implement approach for analyzing case–control and case‐only studies assuming gene–environment independence and Hardy–Weinberg equilibrium

The case–control study is a simple and an useful method to characterize the effect of a gene, the effect of an exposure, as well as the interaction between the two. The control‐free case‐only study is yet an even simpler design, if interest is centered on gene–environment interaction only. It requires the sometimes plausible assumption that the gene under study is independent of exposures among the non‐diseased in the study populations. The Hardy–Weinberg equilibrium is also sometimes reasonable to assume. This paper presents an easy‐to‐implement approach for analyzing case–control and case‐only studies under the above dual assumptions. The proposed approach, the ‘conditional logistic regression with counterfactuals’, offers the flexibility for complex modeling yet remains well within the reach to the practicing epidemiologists. When the dual assumptions are met, the conditional logistic regression with counterfactuals is unbiased and has the correct type I error rates. It also results in smaller variances and achieves higher powers as compared with using the conventional analysis (unconditional logistic regression). Copyright © 2010 John Wiley & Sons, Ltd.     

Unveiling Case‐Control Relationships in Designing a Simple and Powerful Method for Detecting Gene‐Gene Interactions

The detection of gene‐gene interactions (i.e., epistasis) in the human genome is becoming decisive for the complete characterization of the genetic factors associated with complex binary traits. Despite the fact that many methods have been developed to address this challenging issue, their performance still remains insufficient. We will show how case and control groups store complementary information regarding interactions, and the use of this fundamental property in the design of a new, rapid, and highly powerful epistasis analysis method. Unlike previous approaches where statistical methods are tested over a very limited range of situations, we have performed an exhaustive evaluation of the power of our new method. To this end, we also propose a more comprehensive interpretation of epistasis in which genotype interactions may be of risk, protective, or neutral. In this extended view of genetic interactions, we demonstrate that our method has superior performance than existing approaches, thus, providing a highly powerful tool for the identification of gene‐gene interactions associated with binary traits.     

A test for gene–environment interaction in the presence of measurement error in the environmental variable

The identification of gene–environment interactions in relation to risk of human diseases has been challenging. One difficulty has been that measurement error in the exposure can lead to massive reductions in the power of the test, as well as in bias toward the null in the interaction effect estimates. Leveraging previous work on linear discriminant analysis, we develop a new test of interaction between genetic variants and a continuous exposure that mitigates these detrimental impacts of exposure measurement error in ExG testing by reversing the role of exposure and the diseases status in the fitted model, thus transforming the analysis to standard linear regression. Through simulation studies, we show that the proposed approach is valid in the presence of classical exposure measurement error as well as when there is correlation between the exposure and the genetic variant. Simulations also demonstrated that the reverse test has greater power compared to logistic regression. Finally, we confirmed that our approach eliminates bias from exposure measurement error in estimation. Computing times are reduced by as much as fivefold in this new approach. For illustrative purposes, we applied the new approach to an ExGWAS study of interactions with alcohol and body mass index among 1,145 cases with invasive breast cancer and 1,142 controls from the Cancer Genetic Markers of Susceptibility study.     

A cross‐validation procedure for general pedigrees and matched odds ratio fitness metric implemented for the multifactor dimensionality reduction pedigree disequilibrium test

As genetic epidemiology looks beyond mapping single disease susceptibility loci, interest in detecting epistatic interactions between genes has grown. The dimensionality and comparisons required to search the epistatic space and the inference for a significant result pose challenges for testing epistatic disease models. The multifactor dimensionality reduction–pedigree disequilibrium test (MDR‐PDT) was developed to test for multilocus models in pedigree data. In the present study we rigorously tested MDR‐PDT with new cross‐validation (CV) (both 5‐ and 10‐fold) and omnibus model selection algorithms by simulating a range of heritabilities, odds ratios, minor allele frequencies, sample sizes, and numbers of interacting loci. Power was evaluated using 100, 500, and 1,000 families, with minor allele frequencies 0.2 and 0.4 and broad‐sense heritabilities of 0.005, 0.01, 0.03, 0.05, and 0.1 for 2‐ and 3‐locus purely epistatic penetrance models. We also compared the prediction error (PE) measure of effect with a predicted matched odds ratio (MOR) for final model selection and testing. We report that the CV procedure is valid with the permutation test, MDR‐PDT performs similarly with 5‐ and 10‐fold CV, and that the MOR is more powerful than PE as the fitness metric for MDR‐PDT. Genet. Epidemiol. 34: 194–199, 2010. © 2009 Wiley‐Liss, Inc.     

Detection of gene–environment interactions in a family‐based population using SCAD

Gene–environment interaction (GxE) is emphasized as one potential source of missing genetic variation on disease traits, and the ultimate goal of GxE research is prediction of individual risk and prevention of complex diseases. However, there are various challenges in statistical analysis of GxE. In this paper, we focus on the three methodological challenges: (i) the high dimensions of genes; (ii) the hierarchical structure between interaction effects and their corresponding main effects; and (iii) the correlation among subjects from family‐based population studies. In this paper, we propose an algorithm that approaches all three challenges simultaneously. This is the first penalized method focusing on an interaction search based on a linear mixed effect model. For verification, we compare the empirical performance of our new method with other existing methods in simulation study. The results demonstrate the superiority of our method under overall simulation setup. In particular, the outperformance obviously becomes greater as the correlation among subjects increases. In addition, the new method provides a robust estimate for the correlation among subjects. We also apply the new method on Genetics of Lipid Lowering Drugs and Diet Network study data. Copyright © 2017 John Wiley & Sons, Ltd.     

Inference on treatment‐covariate interaction based on a nonparametric measure of treatment effects and censored survival data

The investigation of the treatment‐covariate interaction is of considerable interest in the design and analysis of clinical trials. With potentially censored data observed, non‐parametric and semi‐parametric estimates and associated confidence intervals are proposed in this paper to quantify the interactions between the treatment and a binary covariate. In addition, comparison of interactions between the treatment and two covariates are also considered. The proposed approaches are evaluated and compared by Monte Carlo simulations and applied to a real data set from a cancer clinical trial. Copyright © 2016 John Wiley & Sons, Ltd.     

A powerful association test of multiple genetic variants using a random‐effects model

There is an emerging interest in sequencing‐based association studies of multiple rare variants. Most association tests suggested in the literature involve collapsing rare variants with or without weighting. Recently, a variance‐component score test [sequence kernel association test (SKAT)] was proposed to address the limitations of collapsing method. Although SKAT was shown to outperform most of the alternative tests, its applications and power might be restricted and influenced by missing genotypes. In this paper, we suggest a new method based on testing whether the fraction of causal variants in a region is zero. The new association test, T _REM, is derived from a random‐effects model and allows for missing genotypes, and the choice of weighting function is not required when common and rare variants are analyzed simultaneously. We performed simulations to study the type I error rates and power of four competing tests under various conditions on the sample size, genotype missing rate, variant frequency, effect directionality, and the number of non‐causal rare variant and/or causal common variant. The simulation results showed that T _REM was a valid test and less sensitive to the inclusion of non‐causal rare variants and/or low effect common variants or to the presence of missing genotypes. When the effects were more consistent in the same direction, T _REM also had better power performance. Finally, an application to the Shanghai Breast Cancer Study showed that rare causal variants at the FGFR2 gene were detected by T _REM and SKAT, but T _REM produced more consistent results for different sets of rare and common variants. Copyright © 2013 John Wiley & Sons, Ltd.     

EINVis: A Visualization Tool for Analyzing and Exploring Genetic Interactions in Large‐Scale Association Studies

Epistasis (gene‐gene interaction) detection in large‐scale genetic association studies has recently drawn extensive research interests as many complex traits are likely caused by the joint effect of multiple genetic factors. The large number of possible interactions poses both statistical and computational challenges. A variety of approaches have been developed to address the analytical challenges in epistatic interaction detection. These methods usually output the identified genetic interactions and store them in flat file formats. It is highly desirable to develop an effective visualization tool to further investigate the detected interactions and unravel hidden interaction patterns. We have developed EINVis, a novel visualization tool that is specifically designed to analyze and explore genetic interactions. EINVis displays interactions among genetic markers as a network. It utilizes a circular layout (specially, a tree ring view) to simultaneously visualize the hierarchical interactions between single nucleotide polymorphisms (SNPs), genes, and chromosomes, and the network structure formed by these interactions. Using EINVis, the user can distinguish marginal effects from interactions, track interactions involving more than two markers, visualize interactions at different levels, and detect proxy SNPs based on linkage disequilibrium. EINVis is an effective and user‐friendly free visualization tool for analyzing and exploring genetic interactions. It is publicly available with detailed documentation and online tutorial on the web at http://filer.case.edu/yxw407/einvis/ .     

The v-MFG test: investigating maternal, offspring and maternal-fetal genetic incompatibility effects on disease and viability

The MFG test is a family-based association test that detects genetic effects contributing to disease in offspring, including offspring allelic effects, maternal allelic effects and MFG incompatibility effects. Like many other family-based association tests, it assumes that the offspring survival and the offspring-parent genotypes are conditionally independent provided the offspring is affected. However, when the putative disease-increasing locus can affect another competing phenotype, for example, offspring viability, the conditional independence assumption fails and these tests could lead to incorrect conclusions regarding the role of the gene in disease. We propose the v-MFG test to adjust for the genetic effects on one phenotype, e.g., viability, when testing the effects of that locus on another phenotype, e.g., disease. Using genotype data from nuclear families containing parents and at least one affected offspring, the v-MFG test models the distribution of family genotypes conditional on offspring phenotypes. It simultaneously estimates genetic effects on two phenotypes, viability and disease. Simulations show that the v-MFG test produces accurate genetic effect estimates on disease as well as on viability under several different scenarios. It generates accurate type-I error rates and provides adequate power with moderate sample sizes to detect genetic effects on disease risk when viability is reduced. We demonstrate the v-MFG test with HLA-DRB1 data from study participants with rheumatoid arthritis (RA) and their parents, we show that the v-MFG test successfully detects an MFG incompatibility effect on RA while simultaneously adjusting for a possible viability loss.     

A case‐association cluster detection and visualisation tool with an application to Legionnaires’ disease

Statistical methods used in spatio‐temporal surveillance of disease are able to identify abnormal clusters of cases but typically do not provide a measure of the degree of association between one case and another. Such a measure would facilitate the assignment of cases to common groups and be useful in outbreak investigations of diseases that potentially share the same source. This paper presents a model‐based approach, which on the basis of available location data, provides a measure of the strength of association between cases in space and time and which is used to designate and visualise the most likely groupings of cases. The method was developed as a prospective surveillance tool to signal potential outbreaks, but it may also be used to explore groupings of cases in outbreak investigations. We demonstrate the method by using a historical case series of Legionnaires’ disease amongst residents of England and Wales. Copyright © 2013 John Wiley & Sons, Ltd.     

Power and sample size calculations for the Wilcoxon–Mann–Whitney test in the presence of death‐censored observations

We consider a clinical trial of a potentially lethal disease in which patients are randomly assigned to two treatment groups and are followed for a fixed period of time; a continuous endpoint is measured at the end of follow‐up. For some patients; however, death (or severe disease progression) may preclude measurement of the endpoint. A statistical analysis that includes only patients with endpoint measurements may be biased. An alternative analysis includes all randomized patients, with rank scores assigned to the patients who are available for the endpoint measurement on the basis of the magnitude of their responses and with ‘worst‐rank’ scores assigned to those patients whose death precluded the measurement of the continuous endpoint. The worst‐rank scores are worse than all observed rank scores. The treatment effect is then evaluated using the Wilcoxon–Mann–Whitney test. In this paper, we derive closed‐form formulae for the power and sample size of the Wilcoxon–Mann–Whitney test when missing measurements of the continuous endpoints because of death are replaced by worst‐rank scores. We distinguish two approaches for assigning the worst‐rank scores. In the tied worst‐rank approach, all deaths are weighted equally, and the worst‐rank scores are set to a single value that is worse than all measured responses. In the untied worst‐rank approach, the worst‐rank scores further rank patients according to their time of death, so that an earlier death is considered worse than a later death, which in turn is worse than all measured responses. In addition, we propose four methods for the implementation of the sample size formulae for a trial with expected early death. We conduct Monte Carlo simulation studies to evaluate the accuracy of our power and sample size formulae and to compare the four sample size estimation methods. Copyright © 2014 John Wiley & Sons, Ltd.