Exploiting gene-environment interaction to detect genetic associations

Complex disease by definition results from the interplay of genetic and environmental factors. However, it is currently unclear how gene-environment interaction can best be used to locate complex disease susceptibility loci, particularly in the context of studies where between 1,000 and 1,000,000 markers are scanned for association with disease. We present a joint test of marginal association and gene-environment interaction for case-control data. We compare the power and sample size requirements of this joint test to other analyses: the marginal test of genetic association, the standard test for gene-environment interaction based on logistic regression, and the case-only test for interaction that exploits gene-environment independence. Although for many penetrance models the joint test of genetic marginal effect and interaction is not the most powerful, it is nearly optimal across all penetrance models we considered. In particular, it generally has better power than the marginal test when the genetic effect is restricted to exposed subjects and much better power than the tests of gene-environment interaction when the genetic effect is not restricted to a particular exposure level. This makes the joint test an attractive tool for large-scale association scans where the true gene-environment interaction model is unknown.     

Mutual Information for Testing Gene-Environment Interaction

Despite current enthusiasm for investigation of gene-gene interactions and gene-environment interactions, the essential issue of how to define and detect gene-environment interactions remains unresolved. In this report, we define gene-environment interactions as a stochastic dependence in the context of the effects of the genetic and environmental risk factors on the cause of phenotypic variation among individuals. We use mutual information that is widely used in communication and complex system analysis to measure gene-environment interactions. We investigate how gene-environment interactions generate the large difference in the information measure of gene-environment interactions between the general population and a diseased population, which motives us to develop mutual information-based statistics for testing gene-environment interactions. We validated the null distribution and calculated the type 1 error rates for the mutual information-based statistics to test gene-environment interactions using extensive simulation studies. We found that the new test statistics were more powerful than the traditional logistic regression under several disease models. Finally, in order to further evaluate the performance of our new method, we applied the mutual information-based statistics to three real examples. Our results showed that P-values for the mutual information-based statistics were much smaller than that obtained by other approaches including logistic regression models.     

SEM: Structural Equation Modeling in Molecular Biology

Structural equation modeling (SEM) is a second-generation multivariate method to estimate the causal interactions in a set of variables and includes, as special cases, several statistical methods (regression analysis, path analysis, and confirmatory factor analysis). This review focuses on all of the main SEM models and various methods used to optimize the model parameters. Representative examples are discussed to illustrate SEM application in molecular biology, including modeling of biochemical processes, relationships between genetic markers and diseases, and interactions within gene networks.     

Gene variation in resistant hypertension: multilocus analysis of the angiotensin 1-converting enzyme, angiotensinogen, and endothelial nitric oxide synthase genes

Resistant hypertension, a complex multifactorial hypertensive disease, is triggered by genetic and environmental factors and involves multiple physiological pathways. Single genetic variants may not reveal significant associations with resistant hypertension because their effects may be dependent on gene-gene or gene-environment interactions. We examined the interaction of angiotensin I-converting enzyme (ACE), angiotensinogen (AGT), and endothelial nitric oxide synthase (NOS3) polymorphisms with environmental factors (gender, age, body mass index, glycemia, total cholesterol, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triglycerides, estimated glomerular filtration rate, and urinary sodium excretion) in 70 resistant, 80 well-controlled hypertensive patients, and 70 normotensive controls. All subjects were genotyped for ACE insertion/deletion (rs1799752); AGT M235T (rs699), and NOS3 Glu298Asp (rs 1799983). Multifactorial associations were tested using two statistical methods: the traditional parametric method (adjusted logistic regression analysis) and gene-gene and gene-environment interactions evaluated by multifactor dimensionality reduction analyses. While adjusted logistic regression found no significant association between the studied polymorphisms and controlled or resistant hypertension, the multifactor dimensionality reduction analyses showed that carriers of the AGT 235T allele were at increased risk for resistant hypertension, especially if they were older than 50 years. The AGT 235T allele constituted an independent risk factor for resistant hypertension.     

A probabilistic neural network approach for modeling and classification of bacterial growth/no-growth data

In this paper, we propose to use probabilistic neural networks (PNNs) for classification of bacterial growth/no-growth data and modeling the probability of growth. The PNN approach combines both Bayes theorem of conditional probability and Parzen's method for estimating the probability density functions of the random variables. Unlike other neural network training paradigms, PNNs are characterized by high training speed and their ability to produce confidence levels for their classification decision. As a practical application of the proposed approach, PNNs were investigated for their ability in classification of growth/no-growth state of a pathogenic Escherichia coli R31 in response to temperature and water activity. A comparison with the most frequently used traditional statistical method based on logistic regression and multilayer feedforward artificial neural network (MFANN) trained by error backpropagation was also carried out. The PNN-based models were found to outperform linear and nonlinear logistic regression and MFANN in both the classification accuracy and ease by which PNN-based models are developed.     

Gene-environment interactions in psychiatry: joining forces with neuroscience

Gene-environment interaction research in psychiatry is new, and is a natural ally of neuroscience. Mental disorders have known environmental causes, but there is heterogeneity in the response to each causal factor, which gene-environment findings attribute to genetic differences at the DNA sequence level. Such findings come from epidemiology, an ideal branch of science for showing that a gene-environment interactions exist in nature and affect a significant fraction of disease cases. The complementary discipline of epidemiology, experimental neuroscience, fuels gene-environment hypotheses and investigates underlying neural mechanisms. This article discusses opportunities and challenges in the collaboration between psychiatry, epidemiology and neuroscience in studying gene-environment interactions.     

Nomograms Aid Interpretation of Complex Regression Models

ABSTRACT Ecologists often develop complex regression models that include multiple categorical and continuous variables, interactions among predictors, and nonlinear relationships between the response and predictor variables. Nomograms, which are graphical devices for presenting mathematical functions and calculating output values, can aid biologists in interpreting and presenting these complex models. To illustrate benefits of nomograms, we developed a logistic regression model of elk (Cervus elaphus) resource selection. With this model, we demonstrated how a nomogram helps scientists and managers interpret interactions among variables, compare the relative biological importance of variables, and examine predicted shapes of relationships (e.g., linear vs. nonlinear) between response and predictor variables. Although our example focused on logistic regression, nomograms are equally useful for other linear and nonlinear models. Regardless of the approach used for model development, nomograms and other graphical summaries can help scientists and managers develop, interpret, and apply statistical models.     

Cigarette smoking strongly modifies the association of LOC387715 and age-related macular degeneration

We used iterative association mapping to identify a susceptibility gene for age-related macular degeneration (AMD) on chromosome 10q26, which is one of the most consistently implicated linkage regions for this disorder. We employed linkage analysis methods, followed by family-based and case-control association analyses, using two independent data sets. To identify statistically the most likely AMD-susceptibility allele, we used the Genotype-IBD Sharing Test (GIST) and conditional haplotype analysis. To incorporate the two most important known AMD risk factors--smoking and the Y402H variant of the complement factor H gene (CFH)--we used logistic regression modeling to test for gene-gene and gene-environment interactions in the case-control data set and used the ordered-subset analysis to account for genetic linkage heterogeneity in the family-based data set. Our results strongly implicate a coding change (Ala69Ser) in the LOC387715 gene as the second major identified AMD-susceptibility allele, confirming earlier suggestions. This variant's effect on AMD is statistically independent of CFH and is of similar magnitude to the effect of Y402H. The overall effect is driven primarily by a strong association in smokers, since we observed significant evidence for a statistical interaction between the LOC387715 variant and a history of cigarette smoking. This gene-environment interaction is supported by statistically independent family-based and case-control analysis methods. We estimate that CFH, LOC387715, and cigarette smoking together explain 61% of the population-attributable risk (PAR) of AMD. The adjusted PAR percentage estimates are 20% for smoking, 36% for LOC387715, and 43% for CFH. We demonstrate, for the first time, that a genetic susceptibility coupled with a modifiable lifestyle factor such as cigarette smoking confers a significantly higher risk of AMD than either factor alone.     

Rapid Testing of SNPs and Gene-Environment Interactions in Case-Parent Trio Data Based on Exact Analytic Parameter Estimation

Summary Case-parent trio studies concerned with children affected by a disease and their parents aim to detect single nucleotide polymorphisms (SNPs) showing a preferential transmission of alleles from the parents to their affected offspring. A popular statistical test for detecting such SNPs associated with disease in this study design is the genotypic transmission/disequilibrium test (gTDT) based on a conditional logistic regression model, which usually needs to be fitted by an iterative procedure. In this article, we derive exact closed-form solutions for the parameter estimates of the conditional logistic regression models when testing for an additive, a dominant, or a recessive effect of a SNP, and show that such analytic parameter estimates also exist when considering gene-environment interactions with binary environmental variables. Because the genetic model underlying the association between a SNP and a disease is typically unknown, it might further be beneficial to use the maximum over the gTDT statistics for the possible effects of a SNP as test statistic. We therefore propose a procedure enabling a fast computation of the test statistic and the permutation-based p-value of this MAX gTDT. All these methods are applied to whole-genome scans of the case-parent trios from the International Cleft Consortium. These applications show our procedures dramatically reduce the required computing time compared to the conventional iterative methods allowing, for example, the analysis of hundreds of thousands of SNPs in a few minutes instead of several hours.     

Gene-gene and gene-environment interactions involving HLA-DRB1, PTPN22, and smoking in two subsets of rheumatoid arthritis

Gene-gene and gene-environment interactions are key features in the development of rheumatoid arthritis (RA) and other complex diseases. The aim of this study was to use and compare three different definitions of interaction between the two major genetic risk factors of RA--the HLA-DRB1 shared epitope (SE) alleles and the PTPN22 R620W allele--in three large case-control studies: the Swedish Epidemiological Investigation of Rheumatoid Arthritis (EIRA) study, the North American RA Consortium (NARAC) study, and the Dutch Leiden Early Arthritis Clinic study (in total, 1,977 cases and 2,405 controls). The EIRA study was also used to analyze interactions between smoking and the two genes. "Interaction" was defined either as a departure from additivity, as interaction in a multiplicative model, or in terms of linkage disequilibrium--for example, deviation from independence of penetrance of two unlinked loci. Consistent interaction, defined as departure from additivity, between HLA-DRB1 SE alleles and the A allele of PTPN22 R620W was seen in all three studies regarding anti-CCP-positive RA. Testing for multiplicative interactions demonstrated an interaction between the two genes only when the three studies were pooled. The linkage disequilibrium approach indicated a gene-gene interaction in EIRA and NARAC, as well as in the pooled analysis. No interaction was seen between smoking and PTPN22 R620W. A new pattern of interactions is described between the two major known genetic risk factors and the major environmental risk factor concerning the risk of developing anti-CCP-positive RA. The data extend the basis for a pathogenetic hypothesis for RA involving genetic and environmental factors. The study also raises and illustrates principal questions concerning ways to define interactions in complex diseases.     

Ozone prediction on the basis of neural networks,support vector regression and methods with uncertainty

The article presents modeling of daily average ozone level prediction by means of neural networks, support vector regression and methods based on uncertainty. Based on data measured by a monitoring station of the Pardubice micro-region, the Czech Republic, and optimization of the number of parameters by a defined objective function and genetic algorithm a model of daily average ozone level prediction in a certain time has been designed. The designed model has been optimized in light of its input parameters. The goal of prediction by various methods was to compare the results of prediction with the aim of various recommendations to micro-regional public administration management. It is modeling by means of feed-forward perceptron type neural networks, time delay neural networks, radial basis function neural networks, ε-support vector regression, fuzzy inference systems and Takagi–Sugeno intuitionistic fuzzy inference systems. Special attention is paid to the adaptation of the Takagi–Sugeno intuitionistic fuzzy inference system and adaptation of fuzzy logic-based systems using evolutionary algorithms. Based on data obtained, the daily average ozone level prediction in a certain time is characterized by a root mean squared error. The best possible results were obtained by means of an ε-support vector regression with polynomial kernel functions and Takagi–Sugeno intuitionistic fuzzy inference systems with adaptation by means of a Kalman filter.     

Variance components models for gene-environment interaction in twin analysis.

Gene-environment interaction is likely to be a common and important source of variation for complex behavioral traits. Often conceptualized as the genetic control of sensitivity to the environment, it can be incorporated in variance components twin analyses by partitioning genetic effects into a mean part, which is independent of the environment, and a part that is a linear function of the environment. The model allows for one or more environmental moderator variables (that possibly interact with each other) that may i). be continuous or binary ii). differ between twins within a pair iii). interact with residual environmental as well as genetic effects iv) have nonlinear moderating properties v). show scalar (different magnitudes) or qualitative (different genes) interactions vi). be correlated with genetic effects acting upon the trait, to allow for a test of gene-environment interaction in the presence of gene-environment correlation. Aspects and applications of a class of models are explored by simulation, in the context of both individual differences twin analysis and, in a companion paper (Purcell & Sham, 2002) sibpair quantitative trait locus linkage analysis. As well as elucidating environmental pathways, consideration of gene-environment interaction in quantitative and molecular studies will potentially direct and enhance gene-mapping efforts.     

Estimating Risks and Relative Risks in Case-Base Studies under the Assumptions of Gene-Environment Independence and Hardy-Weinberg Equilibrium

Many diseases result from the interactions between genes and the environment. An efficient method has been proposed for a case-control study to estimate the genetic and environmental main effects and their interactions, which exploits the assumptions of gene-environment independence and Hardy-Weinberg equilibrium. To estimate the absolute and relative risks, one needs to resort to an alternative design: the case-base study. In this paper, the authors show how to analyze a case-base study under the above dual assumptions. This approach is based on a conditional logistic regression of case-counterfactual controls matched data. It can be easily fitted with readily available statistical packages. When the dual assumptions are met, the method is approximately unbiased and has adequate coverage probabilities for confidence intervals. It also results in smaller variances and shorter confidence intervals as compared with a previous method for a case-base study which imposes neither assumption.     

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.     

Gene-Environment Dependence Creates Spurious Gene-Environment Interaction

Gene-environment interactions have the potential to shed light on biological processes leading to disease and to improve the accuracy of epidemiological risk models. However, relatively few such interactions have yet been confirmed. In part this is because genetic markers such as tag SNPs are usually studied, rather than the causal variants themselves. Previous work has shown that this leads to substantial loss of power and increased sample size when gene and environment are independent. However, dependence between gene and environment can arise in several ways including mediation, pleiotropy, and confounding, and several examples of gene-environment interaction under gene-environment dependence have recently been published. Here we show that under gene-environment dependence, a statistical interaction can be present between a marker and environment even if there is no interaction between the causal variant and the environment. We give simple conditions under which there is no marker-environment interaction and note that they do not hold in general when there is gene-environment dependence. Furthermore, the gene-environment dependence applies to the causal variant and cannot be assessed from marker data. Gene-gene interactions are susceptible to the same problem if two causal variants are in linkage disequilibrium. In addition to existing concerns about mechanistic interpretations, we suggest further caution in reporting interactions for genetic markers.     

Natural and orthogonal interaction framework for modeling gene-environment interactions with application to lung cancer

Objectives: We aimed at extending the Natural and Orthogonal Interaction (NOIA) framework, developed for modeling gene-gene interactions in the analysis of quantitative traits, to allow for reduced genetic models, dichotomous traits, and gene-environment interactions. We evaluate the performance of the NOIA statistical models using simulated data and lung cancer data. Methods: The NOIA statistical models are developed for additive, dominant, and recessive genetic models as well as for a binary environmental exposure. Using the Kronecker product rule, a NOIA statistical model is built to model gene-environment interactions. By treating the genotypic values as the logarithm of odds, the NOIA statistical models are extended to the analysis of case-control data. Results: Our simulations showed that power for testing associations while allowing for interaction using the NOIA statistical model is much higher than using functional models for most of the scenarios we simulated. When applied to lung cancer data, much smaller p values were obtained using the NOIA statistical model for either the main effects or the SNP-smoking interactions for some of the SNPs tested. Conclusion: The NOIA statistical models are usually more powerful than the functional models in detecting main effects and interaction effects for both quantitative traits and binary traits.     

Predictive modeling of competitive biosorption equilibrium data

This paper compares regression and neural network modeling approaches to predict competitive biosorption equilibrium data. The regression approach is based on the fitting of modified Langmuir-type isotherm models to experimental data. Neural networks, on the other hand, are non-parametric statistical estimators capable of identifying patterns in data and correlations between input and output. Our results show that the neural network approach outperforms traditional regression-based modeling in correlating and predicting the simultaneous uptake of copper and cadmium by a microbial biosorbent. The neural network is capable of accurately predicting unseen data when provided with limited amounts of data for training. Because neural networks are purely data-driven models, they are more suitable for obtaining accurate predictions than for probing the physical nature of the biosorption process.