Systematic search for susceptibility genes in different populations

We analyzed the first replicate of each of the four simulated population samples from three distinct populations by linkage and association genome scans and could identify three regions with susceptibility loci for the disease: on chromosome 1, marker D1G024, with strong evidence for gene x environment interaction; or chromosome 3, around marker D3G045; and on chromosome 5, markers D5G035-D5G042. Our results were obtained without knowing the true disease model and are compared with this model in the discussion.     

Genetic dissection of a complex trait

A number of genetic and statistical tools were applied to various partitions of the simulated data to identify susceptibility loci, relevant environmental factors, and their interaction(s). The distribution of genotypes at D1G24 among affected children in the first population was found to differ significantly from Hardy-Weinberg expectation. Two transmission/disequilibrium tests identified the preferential transmission of allele 1 as the source of the disequilibrium. Simple contingency table analysis revealed a positive association between exposure to environmental factor E1 and disease phenotype. Multipoint linkage analyses on various subsets of the data identified three "signal" regions (in addition to the aforementioned D1G24) localized at D1G9-10, D3G45, and D5G38. The even numbered chromosomes appeared to be devoid of susceptibility loci. Further analyses of subsamples of affected sib pairs, selected according to their disease phenotype and their exposure to E1, clarified some linkage relationships, particularly for D3G45, thereby suggesting the presence of a specific gene x environment interaction. Logistic analysis designed to clarify the relationship between disease phenotype and two risk factors (E1 exposure and the presence of allele 1 at D1G24) in the first population, revealed a significantly negative interaction which, upon learning the details of the generating model, we now attribute to the presence of heterogeneity.     

Comparison of methods incorporating quantitative covariates into affected sib pair linkage analysis

For complex traits, it may be possible to increase the power to detect linkage if one takes advantage of covariate information. Several statistics have been proposed that incorporate quantitative covariate information into affected sib pair (ASP) linkage analysis. However, it is not clear how these statistics perform under different gene-environment (G x E) interactions. We compare representative statistics to each other on simulated data under three biologically-plausible G x E models. We also compared their performance with a model-free method and with quantitative trait locus (QTL) linkage approaches. The statistics considered here are: (1) mixture model; (2) general conditional-logistic model (LODPAL); (3) multinomial logistic regression models (MLRM); (4) extension of the maximum-likelihood-binomial approach (MLB); (5) ordered-subset analysis (OSA); and (6) logistic regression modeling (COVLINK). In all three G x E models, most of these six statistics perform better when using the covariate C1 associated with a G x E interaction effect than when using the environmental risk factor C2 or the random noise covariate C3. Compared with a model-free method without covariates (S(all)), the mixture model performs the best when using C1, with the high-to-low OSA method also performing quite well. Generally, MLB is the least sensitive to covariate choice. However, most of these statistics do not provide better power than S(all). Thus, while inclusion of the "correct" covariate can lead to increased power, careful selection of appropriate covariates is vital for success.     

A joint test of linkage and gene x environment interaction, with affected sib pairs

In the presence of gene x environment (G x E) interaction, the expected proportion of alleles shared identical by descent at a linked marker locus by a pair of affected sibs depends on the exposure profile of the two sibs, i.e., whether both are exposed to E, only one is exposed, or neither are exposed. In this paper, we propose an extension of the commonly used mean test of linkage to test for differential identical-by-descent (IBD) sharing across sib-exposure profiles. The method can be viewed as a test for linkage in the presence of G x E interaction, or as a test for G x E interaction in the presence of linkage. Applied to the simulated GAW11 data, our method successfully localized disease locus C and its interactive relationship with environmental factor E1. At the 5% significance level, use of our method led to increased power to detect linkage (56%) to this disease locus compared to use of the standard mean test (32%); at the 0.001 significance level, the corresponding power estimates were 20% and 4%, respectively. For a gene that interacts with an environmental factor, we conclude that use of the environmental factor in linkage analysis can improve detection rates while also providing information about underlying mechanisms.     

Effects of genotype x sex interaction on linkage analysis of visual event-related evoked potentials

Autosomal genes contributing to variation in many complex traits are influenced by male or female physiological "environments." Accounting for such genotype-by-sex (G x S) interactions has been shown to be important in quantitative genetic, segregation, and linkage analyses of a number of sexually dimorphic traits. In analyses of data simulated for GAW10, we showed that incorporating sex-specific variance components into a variance components-based linkage method increased the power to detect linkage in a trait that exhibited G x S interaction. The goals of this study of data from the Collaborative Study on the Genetics of Alcoholism (COGA) were to screen the event-related brain potential (ERP) data from COGA participants for G x S interaction, and then to conduct variance components linkage analysis of ERP phenotypes showing evidence of G x S interaction using models incorporating sex-specific variance components. Significant G x S interaction was found in four ERP phenotypes: N100 measured at occipital leads 1 and 2, and P300 measured at occipital leads 1 and 2. In linkage analyses of these traits, the most significant lod score found was that between N100 occipital lead 1 amplitude and marker D7S490. The peak lod score at the D7S490 locus was 2.45 without sex-specific variance components, and 3.25 with sex-specific marker and residual polygenic components.     

A generalized estimating equations approach to linkage analysis in sibships in relation to multiple markers and exposure factors

We describe a multiple regression approach to nonparametric linkage analysis in sibships incorporating multiple genetic loci, environmental covariates, and interactions. The covariance in trait residuals between sib pairs is treated as the dependent variable, regressed upon identical-by-descent sharing probabilities and interaction effects, using generalized estimating equations to allow for the correlations among multiple sib pairs within a sibship. Individual covariates can also be introduced in the model for the trait means. An application to the GAW11 simulated data revealed linkage with each of the four simulated loci, as well as gene x environment interactions of E1 with loci C and D and gene x gene interactions among the cluster of loci A, B, and D.     

Candidate gene association analysis for a quantitative trait, using parent-offspring trios

With the increasing availability of genetic data, many studies of quantitative traits focus on hypotheses related to candidate genes, and also gene-environment (G x E) and gene-gene (G x G) interactions. In a population-based sample, estimates and tests of candidate gene effects can be biased by ethnic confounding, also known as population stratification bias. This paper demonstrates that even a modest degree of ethnic confounding can lead to unacceptably high type I error rates for tests of genetic effects. The parent-offspring trio design is reviewed, and several forms of the quantitative transmission disequilibrium test (QTDT) are summarized. A variation of the QTDT (QTDTM) is described that is based on a linear regression model with multiple intercepts, one per parental mating type. This and other models are expanded to allow testing of G x E and G x G interactions. A method for computing required sample sizes using direct computations is described. Sample size requirements for tests of genetic main effects and G x E and G x G interactions are compared across various QTDT approaches to infer their efficiencies relative to one another. The QTDTM is found to meet or exceed the efficiency of other QTDT approaches. For example, the QTDTM is approximately 3% more efficient than the QTDT of Rabinowitz ([1997] Hum. Hered. 47:342-350) for testing a genetic main effect, but can be as much as twice as efficient for testing G x E interaction, and three times more efficient for testing G x G interaction.     

Search for a gene x environment interaction: G x E hunt

We developed a method to identify gene x environment interactions (G x Es). To test this method in the simulated data (Problem 2, GAW11), we first identified an environmental factor (E1) that was associated with the simulated disorder. We stratified affected sibling pairs (ASPs) into two groups, those concordant for the presence of E1 and those concordant for the absence of E1. We then localized genes on chromosomes 3 and 5 using identity-by-descent (IBD) sharing rates among ASPs. Because the stratified IBD sharing rates are independent of the environmental factor if there is no G x E, we inferred the existence of a G x E near loci 3G44 and 3G45 by testing whether the proportion of ASPs sharing no alleles IBD differed among the two groups.     

Complete genomic screen for disease susceptibility loci in nuclear families

We performed genome-wide model dependent and independent analyses on a simulated data set of 400 families segregating for a rare disorder. Regions on chromosomes 1, 3, and 5 were consistently indicated across the various analyses performed. Follow-up analyses included stratification for locus heterogeneity and clinical phenotype and studies of gene x gene and gene x environment interaction. The region around D1G024 was most notable, showing strong association and linkage with the trait. We also identified regions D3G043-46 and D5G037-39 by strong linkage and association findings and region D1G001-09 by linkage analysis. A complex statistical interaction was suggested between D1G024, D3G046 and environmental factor 1. This report suggests that traditional methods of analysis can be implemented to analyze and describe the mechanisms that may underlie the more complex genetic disorders.     

Linkage analysis with gene-environment interaction: model illustration and performance of ordered subset analysis

The ordered subset analysis (OSA) method allows for the incorporation of covariates into the linkage analysis of a dichotomous disease phenotype in order to reduce genetic heterogeneity. Complex human diseases may involve gene-environment (G x E) interactions, which represent a special form of heterogeneity. Here, we present results of a simulation study to evaluate the performance of OSA when the disease-generating mechanism includes G x E interaction, in the absence of main effects of gene and environment. First, the complex simulation models are illustrated graphically. Second, we show that OSA is underpowered to detect small to moderate interaction effects, consistent with previous evaluations of other linkage analysis methods. When interaction effects are large enough to produce substantial marginal effects, standard linkage methods have sufficient power to detect significant baseline linkage evidence in the entire dataset. The power of OSA to improve upon a high baseline lod score is then strongly dependent on the underlying genetic model, especially the susceptibility allele frequency. If significant, OSA identifies family subsets that are more efficient for follow-up analysis than the entire dataset, in terms of the proportion of susceptible genotypes among generated marker genotypes. For example, when strong G x E interaction with RR(G x E) = 10 is operating in at least 70% of families in the dataset, OSA has at least 70% power to detect a subset of families with significantly greater linkage evidence, the majority of linked families are captured in the OSA subset, and the per-genotype efficiency in the subset is 20-30% greater than in the entire dataset.     

Path analysis under generalized marital resemblance: evaluation of the assumptions underlying the mixed homogamy model by the Monte Carlo method

Path analysis of nuclear family data has been widely applied to resolve genetic and environmental sources of familial resemblance. Here we report the results of a systematic evaluation of the effects of departures from five modeling assumptions often made when analyzing nuclear family data; i) the observed environmental index is unaffected by the genotype, ii) the basis of marital resemblance is correctly specified in the model, iii) there are no intergenerational differences in either the genetic or cultural heritability, iv) there is no genetic dominance, and v) there is no genotype by family environment interaction. "Deterministic simulations" identified various situations where model misspecification could lead to substantial bias in the estimation of the heritabilities. For these situations, "stochastic simulations" were performed to determine whether the "goodness-of-fit" test used in path analysis would correctly reject the misspecified model. In samples of 500 nuclear families, each comprising two parents and two children, the goodness-of-fit test was found to be sensitive to misspecifications of the source of marital resemblance and the existence of intergenerational differences in heritabilities, although reduced power would make the test less sensitive in smaller samples. The test was largely insensitive to misspecifications of possible genetic effects on the environmental index, and to the existence of multiplicative interaction between the genotype and familial environment. When genetic effects on the index are ignored, the genetic heritability (h2) is underestimated, the cultural heritability (c2) is overestimated, but h2+c2 remains unchanged. Neglecting the interaction was found to result in an overestimate of h2.     

Gene–environment interaction analysis via deep learning

Gene–environment (G–E) interaction analysis plays an important role in studying complex diseases. Extensive methodological research has been conducted on G–E interaction analysis, and the existing methods are mostly based on regression techniques. In many fields including biomedicine and omics, it has been increasingly recognized that deep learning may outperform regression with its unique flexibility (e.g., in accommodating unspecified nonlinear effects) and superior prediction performance. However, there has been a lack of development in deep learning for G–E interaction analysis. In this article, we fill this important knowledge gap and develop a new analysis approach based on deep neural network in conjunction with penalization. The proposed approach can simultaneously conduct model estimation and selection (of important main G effects and G–E interactions), while uniquely respecting the “main effects, interactions” variable selection hierarchy. Simulation shows that it has superior prediction and feature selection performance. The analysis of data on lung adenocarcinoma and skin cutaneous melanoma overall survival further establishes its practical utility. Overall, this study can advance G–E interaction analysis by delivering a powerful new analysis approach based on modern deep learning.     

Identification of gene–environment interactions with marginal penalization

Gene–environment (G–E) interaction analysis has been extensively conducted for complex diseases. In marginal analysis, the common practice is to conduct likelihood-based (and other “standard”) estimation with each marginal model, and then select significant G–E interactions and main effects based on p values and multiple comparisons adjustment. One limitation of this approach is that the identification results often do not respect the “main effects, interactions” hierarchy, which has been stressed in recent G–E interaction analyses. There is some recent effort tackling this problem, however, with very complex formulations. Another limitation of the common practice is that it may not perform well when regularization is needed, for example, because of “non-normal” distributions. In this article, we propose a marginal penalization approach which adopts a novel penalty to directly tackle the aforementioned problems. The proposed approach has a framework more coherent with that of the recently developed joint analysis methods and an intuitive formulation, and can be effectively realized. In simulation, it outperforms the popular significance-based analysis and simple penalization-based alternatives. Promising findings are made in the analysis of a single-nucleotide polymorphism and a gene expression data.     

Reproductive factors and familial predisposition for breast cancer by age 50 years. A case-control-family study for assessing main effects and possible gene-environment interaction

BACKGROUND: The effect of environmental/lifestyle factors on breast cancer risk may be modified by genetic predisposition. METHODS: In a population-based case-control-family study performed in Germany including 706 cases by age 50 years, 1381 population, and 252 sister controls, we investigated main effects for environmental/lifestyle factors and genetic susceptibility and gene-environment interaction (G x E). Different surrogate measures for genetic predisposition using pedigree information were used: first-degree family history of breast or ovarian cancer; and gene carrier probability using a genetic model based on rare dominant genes. Possible G x E interaction was studied by (1) logistic regression using cases and population controls including an interaction term; (2) comparing results using sister controls and population controls; (3) case-only analysis with logistic regression and (4) a mixture logistic model. RESULTS: Familial predisposition showed the strongest main effect and the estimated gene carrier probability gave the best fit. High parity and longer duration of breastfeeding reduced breast cancer risk significantly, a history of abortions increased risk and age at menarche showed no significant effect. We found significant G x E interaction between parity and genetic susceptibility using different surrogate measures. In women most likely to have a high genetic susceptibility, high parity was less protective. Later age at menarche was protective in women with a positive family history. No evidence for G x E interaction was found for breastfeeding and abortion. CONCLUSIONS: These findings corroborate results from other studies and provide further evidence that the magnitude of protection from parity is reduced in women most likely to have a genetic risk in spite of the limitations of using surrogate genetic measures.     

Using case-control designs for genome-wide screening for associations between genetic markers and disease susceptibility loci

We used a case-control design to scan the genome for any associations between genetic markers and disease susceptibility loci using the first two replicates of the Mycenaean population from the GAW11 (Problem 2) data. Using a case-control approach, we constructed a series of 2-by-3 tables for each allele of every marker on all six chromosomes. Odds ratios (ORs) and 95% confidence intervals (95% CI) were estimated for all alleles of every marker. We selected the one allele for which the estimated OR had the minimum p-value to plot in the graph. Among these selected ORs, we calculated 95% CI for those that had a p-value < or = adjusted alpha level. Significantly high ORs were taken to indicate an association between a marker locus and a suspected disease-susceptibility gene. For the Mycenaean population, the case-control design identified allele number 1 of marker 24 on chromosome 1 to be associated with a disease susceptibility gene, OR = 2.10 (95% CI 1.66-2.62). Our approach failed to show any other significant association between case-control status and genetic markers. Stratified analysis on the environmental risk factor (E1) provided no further evidence of significant association other than allele 1 of marker 24 on chromosome 1. These data indicate the absence of linkage disequilibrium for markers flanking loci A, B, and C. Finally, we examined the effect of gene x environment (G x E) interaction for the identified allele. Our results provided no evidence of G x E interaction, but suggested that the environmental exposure alone was a risk factor for the disease.     

A penalized robust semiparametric approach for gene–environment interactions

In genetic and genomic studies, gene‐environment (G×E) interactions have important implications. Some of the existing G×E interaction methods are limited by analyzing a small number of G factors at a time, by assuming linear effects of E factors, by assuming no data contamination, and by adopting ineffective selection techniques. In this study, we propose a new approach for identifying important G×E interactions. It jointly models the effects of all E and G factors and their interactions. A partially linear varying coefficient model is adopted to accommodate possible nonlinear effects of E factors. A rank‐based loss function is used to accommodate possible data contamination. Penalization, which has been extensively used with high‐dimensional data, is adopted for selection. The proposed penalized estimation approach can automatically determine if a G factor has an interaction with an E factor, main effect but not interaction, or no effect at all. The proposed approach can be effectively realized using a coordinate descent algorithm. Simulation shows that it has satisfactory performance and outperforms several competing alternatives. The proposed approach is used to analyze a lung cancer study with gene expression measurements and clinical variables. Copyright © 2015 John Wiley & Sons, Ltd.     

Elementary methods for the analysis of dichotomous outcomes in unselected samples of twins.

This paper presents an elementary statistical method for analyzing dichotomous outcomes in unselected samples of twin pairs using stratified estimators of the odds ratio. The methodology begins by first randomly designating one member of each twin pair as an "index" twin and the other member as the "co-twin." Stratifying on zygosity, odds ratios are used to measure the association between disease in the index twin and disease in the co-twin. From these zygosity-specific tables we calculate the Woolf-Haldane estimator of the common odds ratio (psi F, the weighted average of the zygosity-specific odds ratios), the Mantel-Haenszel test statistic (chi 2M-H) for the common odds ratio, and a test (chi 2G) for the difference in the zygosity-specific odds ratios. In this application, psi F provides an estimate of the familial association for disease and the accompanying chi 2M-H provides a test of the null hypothesis, psi F = 1 (i.e., there is no evidence for a familial influence on disease). The chi 2G is a test of the null hypothesis that psi MZ = psi DZ; a significant value for chi 2G suggests a genetic influence on disease (assuming that the observed odds ratios follow a pattern where psi MZ greater than psi DZ). A new test statistic (chi 2c) is proposed that incorporates the expectation that psi MZ = psi 2DZ under a purely additive genetic model with no common environmental effects. A significant value of chi c2 indicates that the different odds ratios across zygosity are partly due to common environmental influences. Conversely, a nonsignificant value of chi 2c is an indication that the zygosity-specific odds ratios are due solely to additive genetic effects and not to common environment. This basic approach is extended to examine the effects of measured indicators of the specific environment and the assessment of certain forms of gene by environment interaction. All of the methods are easily understood, highly flexible, readily computed using a hand calculator, and incorporate the inherent genetic information contained within twin samples.     

Accommodating missingness in environmental measurements in gene‐environment interaction analysis

For the prognosis of complex diseases, beyond the main effects of genetic (G) and environmental (E) factors, gene‐environment (G‐E) interactions also play an important role. Many approaches have been developed for detecting important G‐E interactions, most of which assume that measurements are complete. In practical data analysis, missingness in E measurements is not uncommon, and failing to properly accommodate such missingness leads to biased estimation and false marker identification. In this study, we conduct G‐E interaction analysis with prognosis data under an accelerated failure time (AFT) model. To accommodate missingness in E measurements, we adopt a nonparametric kernel‐based data augmentation approach. With a well‐designed weighting scheme, a nice “byproduct” is that the proposed approach enjoys a certain robustness property. A penalization approach, which respects the “main effects, interactions” hierarchy, is adopted for selection (of important interactions and main effects) and regularized estimation. The proposed approach has sound interpretations and a solid statistical basis. It outperforms multiple alternatives in simulation. The analysis of TCGA data on lung cancer and melanoma leads to interesting findings and models with superior prediction.     

Detecting interactions between gene, site, and environmental variables using GAP

Regressive models that incorporate measured variables and assumed genetic parameters were used to detect interactions between gene, research site, and environmental variables in GAW11 Problem 2. Replicates 1 to 5 were used in the analyses. Significant three-way gene x environment x site interactions were seen for all models, regardless of what assumptions were made about genetic transmission. Therefore, regressive models within each of the four sites were examined for significant gene x environment interactions. At one site, there was a pattern of gene x environment interaction that was consistent in most of the genetic models assumed. Joint and separate segregation and linkage analyses were compared in this site. No patterns of gene x environment interaction were seen in the other sites. Results from this analysis show that regressive modeling can identify complex interactions in data from heterogeneous populations even when ascertainment assumptions are violated.     

Sample size requirements for indirect association studies of gene-environment interactions (G x E)

Association studies accounting for gene-environment interactions (G x E) may be useful for detecting genetic effects. Although current technology enables very dense marker spacing in genetic association studies, the true disease variants may not be genotyped. Thus, causal genes are searched for by indirect association using genetic markers in linkage disequilibrium (LD) with the true disease variants. Sample sizes needed to detect G x E effects in indirect case-control association studies depend on the true genetic main effects, disease allele frequencies, whether marker and disease allele frequencies match, LD between loci, main effects and prevalence of environmental exposures, and the magnitude of interactions. We explored variables influencing sample sizes needed to detect G x E, compared these sample sizes with those required to detect genetic marginal effects, and provide an algorithm for power and sample size estimations. Required sample sizes may be heavily inflated if LD between marker and disease loci decreases. More than 10,000 case-control pairs may be required to detect G x E. However, given weak true genetic main effects, moderate prevalence of environmental exposures, as well as strong interactions, G x E effects may be detected with smaller sample sizes than those needed for the detection of genetic marginal effects. Moreover, in this scenario, rare disease variants may only be detectable when G x E is included in the analyses. Thus, the analysis of G x E appears to be an attractive option for the detection of weak genetic main effects of rare variants that may not be detectable in the analysis of genetic marginal effects only.