Testing and estimating gene-environment interactions in family-based association studies

Summary .   We propose robust and efficient tests and estimators for gene–environment/gene–drug interactions in family-based association studies in which haplotypes, dichotomous/quantitative phenotypes, and complex exposure/treatment variables are analyzed. Using causal inference methodology, we show that the tests and estimators are robust against unmeasured confounding due to population admixture and stratification, provided that Mendel's law of segregation holds and that the considered exposure/treatment variable is not affected by the candidate gene under study. We illustrate the practical relevance of our approach by an application to a chronic obstructive pulmonary disease study. The data analysis suggests a gene–environment interaction between a single nucleotide polymorphism in the Serpine2 gene and smoking status/pack-years of smoking. Simulation studies show that the proposed methodology is sufficiently powered for realistic sample sizes and that it provides valid tests and effect size estimators in the presence of admixture and stratification.     

Comparison of statistics for candidate-gene association studies using cases and parents.

Studies of association between candidate genes and disease can be designed to use cases with disease, and in place of nonrelated controls, their parents. The advantage of this design is the elimination of spurious differences due to ethnic differences between cases and nonrelated controls. However, several statistical methods of analysis have been proposed in the literature, and the choice of analysis is not always clear. We review some of the statistical methods currently developed and present two new statistical methods aimed at specific genetic hypotheses of dominance and recessivity of the candidate gene. These new methods can be more powerful than other current methods, as demonstrated by simulations. The basis of these new statistical methods is a likelihood approach. The advantage of the likelihood framework is that regression models can be developed to assess genotype-environment interactions, as well as the relative contribution that alleles at the candidate-gene locus make to the relative risk (RR) of disease. This latter development allows testing of (1) whether interactions between alleles exist, on the scale of log RR, and (2) whether alleles originating from the mother or father of a case impart different risks, i.e., genomic imprinting.     

Genotype relative risks: methods for design and analysis of candidate-gene association studies.

Design and analysis methods are presented for studying the association of a candidate gene with a disease by using parental data in place of nonrelated controls. This alternative design eliminates spurious differences in allele frequencies between cases and nonrelated controls resulting from different ethnic origins and population stratification for these two groups. We present analysis methods which are based on two genetic relative risks: (1) the relative risk of disease for homozygotes with two copies of the candidate gene versus homozygotes without the candidate gene and (2) the relative risk for heterozygotes with one copy of the candidate gene versus homozygotes without the candidate gene. In addition to estimating the magnitude of these relative risks, likelihood methods allow specific hypotheses to be tested, namely, a test for overall association of the candidate gene with disease, as well as specific genetic hypotheses, such as dominant or recessive inheritance. Two likelihood methods are presented: (1) a likelihood method appropriate when Hardy-Weinberg equilibrium holds and (2) a likelihood method in which we condition on parental genotype data when Hardy-Weinberg equilibrium does not hold. The results for the relative efficiency of these two methods suggest that the conditional approach may at times be preferable, even when equilibrium holds. Sample-size and power calculations are presented for a multitiered design. The purpose of tier 1 is to detect the presence of an abnormal sequence for a postulated candidate gene among a small group of cases. The purpose of tier 2 is to test for association of the abnormal variant with disease, such as by the likelihood methods presented. The purpose of tier 3 is to confirm positive results from tier 2. Results indicate that required sample sizes are smaller when expression of disease is recessive, rather than dominant, and that, for recessive disease and large relative risks, necessary sample sizes may be feasible, even if only a small percentage of the disease can be attributed to the candidate gene.     

Evidence of association between methylenetetrahydrofolate reductase gene and susceptibility to breast cancer: a candidate-gene association study in a South-eastern European population

The methylenetetrahydrofolate reductase (MTHFR) gene has been proposed as a candidate gene for breast cancer (BC). However, the specific role of MTHFR polymorphisms and haplotypes has not been fully clarified and replicated. We examined the association of two common MTHFR polymorphisms (C677T and A1298C) and their haplotypes in a candidate-gene association study, involving 300 female patients with BC and 283 healthy women. The single locus analysis for the two polymorphisms revealed an association only for the C677T polymorphism [odds ratio (95% confidence interval), OR=2.05 (1.21-3.48)], but adjustment for age diminished this association [OR=1.76 (0.92-3.42)]. The menopausal status showed no significant effect in the association between the MTHFR polymorphisms and BC. The analysis of haplotypes showed an association for the C677-A1298 haplotypes (p=0.04). The available evidence from our study may support a contributory role of MTHFR polymorphisms in BC development. Future larger studies may help in elucidating the genetics of BC further.     

The use of generalized linear models and generalized estimating equations in bioarchaeological studies

The current article explores whether the application of generalized linear models (GLM) and generalized estimating equations (GEE) can be used in place of conventional statistical analyses in the study of ordinal data that code an underlying continuous variable, like entheseal changes. The analysis of artificial data and ordinal data expressing entheseal changes in archaeological North African populations gave the following results. Parametric and nonparametric tests give convergent results particularly for P values <0.1, irrespective of whether the underlying variable is normally distributed or not under the condition that the samples involved in the tests exhibit approximately equal sizes. If this prerequisite is valid and provided that the samples are of equal variances, analysis of covariance may be adopted. GLM are not subject to constraints and give results that converge to those obtained from all nonparametric tests. Therefore, they can be used instead of traditional tests as they give the same amount of information as them, but with the advantage of allowing the study of the simultaneous impact of multiple predictors and their interactions and the modeling of the experimental data. However, GLM should be replaced by GEE for the study of bilateral asymmetry and in general when paired samples are tested, because GEE are appropriate for correlated data. Am J Phys Anthropol 153:473–483, 2014. © 2013 Wiley Periodicals, Inc.     

Number of individuals and molecular markers to use in genetic differentiation studies

Molecular markers are frequently used to study genetic variation among individuals within or between populations. Differences in marker banding patterns can be used to verify if individuals do, or do not, represent distinct groups or populations. Only in 2005, more than 500 studies used molecular markers to group individuals in clusters. Such studies make use of an arbitrary number of molecular markers from each of an arbitrary number of individuals presumed to represent distinct genotypes. However, the greater the genetic variation, the more likely a larger number of individuals and markers will be needed to capture a population's genetic signature. The numbers of both, markers and individuals included thus affect the way in which individuals are organized through cluster analyses, thereby affecting the conclusions drawn. Here we present a method that provides statistical criteria to verify that individual and marker sample sizes are sufficient to accurately depict genetic differentiation among different populations. Our method uses a resampling technique to assess the reproducibility of obtaining a particular grouping pattern for specific data sets. It thus, allows to estimate the robustness of the results obtained without including additional individuals, or markers.     

The association of genetic markers in two related swine breeds]

The combinations of genetic markers (allotypes, blood-group systems, and polymorphic proteins) were analyzed in pigs of two phylogenetically related Siberian populations: the newly selected Siberian specialized meat breed SM-1 (daughter breed) and the reproductive core of the Kemerovo breed (maternal breed). Statistically significant interlocus associations were found between the genetic markers that are known not to be linked, being assigned to different linkage groups, and the main selected meat-productivity traits. Some of these associations were shared by both breeds; others were found to be specific to either maternal or daughter populations. Possible genetic mechanisms underlying these associations and their significance are discussed.     

Identification of individuals by analysis of biallelic DNA markers, using PCR and solid-phase minisequencing.

We have developed a new method for forensic identification of individuals, in which a panel of biallelic DNA markers are amplified by the PCR, and the variable nucleotides are detected in the amplified DNA fragments by the solid-phase minisequencing method. A panel of 12 common polymorphic nucleotides located on different chromosomes with reported allele frequencies close to .5 were chosen for the test. The allele frequencies for most of the markers were found to be similar in the Finnish and other Caucasian populations. We also introduce a novel approach for rapid determination of the population frequencies of biallelic markers. By this approach we were able to determine the allele frequencies of the markers in the Finnish population, by quantitative analysis of three pooled DNA samples representing 3,000 individuals. The power of discrimination and exclusion of the solid-phase minisequencing typing test with 12 markers was similar to that of three VNTR markers that are routinely used in forensic analyses at our institute. The solid-phase minisequencing method was successfully applied to type paternity and forensic case samples. We also show that the quantitative nature of our method allows typing of mixed samples.     

Testing association of statistically inferred haplotypes with discrete and continuous traits in samples of unrelated individuals

There have been increasing efforts to relate drug efficacy and disease predisposition with genetic polymorphisms. We present statistical tests for association of haplotype frequencies with discrete and continuous traits in samples of unrelated individuals. Haplotype frequencies are estimated through the expectation-maximization algorithm, and each individual in the sample is expanded into all possible haplotype configurations with corresponding probabilities, conditional on their genotype. A regression-based approach is then used to relate inferred haplotype probabilities to the response. The relationship of this technique to commonly used approaches developed for case-control data is discussed. We confirm the proper size of the test under H(0) and find an increase in power under the alternative by comparing test results using inferred haplotypes with single-marker tests using simulated data. More importantly, analysis of real data comprised of a dense map of single nucleotide polymorphisms spaced along a 12-cM chromosomal region allows us to confirm the utility of the haplotype approach as well as the validity and usefulness of the proposed statistical technique. The method appears to be successful in relating data from multiple, correlated markers to response.     

The relative efficiency of the Hardy-Weinberg equilibrium-likelihood and the conditional on parental genotype-likelihood methods for candidate-gene association studies.

Selecting a control group that is perfectly matched for ethnic ancestry with a group of affected individuals is a major problem in studying the association of a candidate gene with a disease. This problem can be avoided by a design that uses parental data in place of nonrelated controls. Schaid and Sommer presented two new methods for the statistical analysis using this approach: (1) a likelihood method (Hardy-Weinberg equilibrium [HWE] method), which rests on the assumption that HWE holds, and (2) a conditional likelihood method (conditional on parental genotype [CPG] method) appropriate when HWE is absent. Schaid and Sommer claimed that the CPG method can be more efficient than the HWE method, even when equilibrium holds. It can be shown, however that in the equilibrium situation the HWE method is always more efficient than the CPG method. For a dominant disease, the differences are slim. But for a recessive disease, the CPG method requires a much larger sample size to achieve a prescribed power than the HWE method. Additionally, we show how the relative risks for the various candidate-gene genotypes can be estimated without relying on iterative methods. For the CPG method, we represent an asymptotic power approximation that is sufficiently precise for planning the sample size of an association study.     

Conversion of AFLP markers to sequence-specific markers for closely related lines in rice by use of the rice genome sequence

DNA polymorphism between two major japonica rice cultivars, Nipponbare and Koshihikari, was identified by AFLP. Eighty-four polymorphic AFLP markers were obtained by analysis with 360 combinations of primer pairs. Nucleotide sequences of 73 markers, 29 from Nipponbare and 44 from Koshihikari, were determined, and 46 AFLP markers could be assigned to rice chromosomes based on sequence homology to the rice genome sequence. Specific primers were designed for amplification of the regions covering the AFLP markers and the flanking sequences. Out of the 46 primer pairs, 44 amplified single DNA fragments, six of which showed different sizes between Nipponbare and Koshihikari, yielding codominant SCAR markers. Eight primer pairs amplified only Nipponbare sequences, providing dominant SCAR markers. DNA fragments amplified by 13 primer pairs showed polymorphism by CAPS, and polymorphism of those amplified by 13 other primer pairs were detected by PCR-RF-SSCP (PRS). Nucleotide sequences of the other four DNA fragments were determined in Koshihikari, but no difference was found between Koshihikari and Nipponbare. In total, 40 sequence-specific markers for the combination of Nipponbare and Koshihikari were produced. All the SNPs identified by AFLP were detectable by CAPS and PRS. The same method was applicable to a combination of Kokoromachi and Tohoku 168, and 23 polymorphic markers were identified using these two rice cultivars. The procedure of conversion of AFLP-markers to the sequence-specific markers used in this study enables efficient sequence-specific marker production for closely related cultivars.     

Phylogenetic relationships between Leymus and related diploid Triticeae species revealed by ISSR markers

To investigate the genetic diversity and phylogenetic relationships between polyploid Leymus and related diploid species of the Triticeae tribe, inter-simple sequence repeats (ISSR) markers was used to analyze 41 Leymus accessions representing 22 species and 2 subspecies, together with Pseudoroegneria stipifolia (St), Psathyrostachys fragilis (Ns), Australopyrum retrofractum (W), Hordeum bogdanii, H. chilense (H) and Lophopyrum elongatum (E^e). A total of 376 clear and reproducible DNA fragments were amplified by 29 ISSR primers, among which 368 (97.87%) fragments were found to be polymorphic. 8–18 polymorphic bands were amplified by each polymorphic primer, with an average of 12.69 bands. The data of 376 ISSR bands were used to generate Nei’s similarity coefficients and to construct a dendrogram by means of UPGMA. The similarity coefficients data suggested great genetic diversity in genus Leymus and related diploid Triticeae species, the genetic diversity among the different species more abundant than that of the different accessions. The dendrogram and principal coordinate analysis showed explicit interspecific relationships and demonstrated close phylogenetic relationships between Leymus species and Psathyrostachys.     

Assessing familial aggregation of age at onset, by using estimating equations, with application to breast cancer.

In genetic research of chronic diseases, age-at-onset outcomes within families are often correlated. The nature of correlation of age-at-onset outcomes is indicative of common genetic and/or shared environmental risk factors among family members. Understanding patterns of such correlation may shed light on the disease etiology and, hence, is an important step to take prior to further searching for the responsible genes via segregation and linkage studies. Age-at-onset outcomes are different from those familiar quantitative or qualitative traits for which many statistical methods have been developed. In comparison with the quantitative traits, age-at-onset outcomes are often censored, i.e., instead of actual age-at-onset outcomes, only the current ages or ages at death are observed. They are also different from qualitative traits because of their continuity. Because of the complexity of correlated censored outcomes, few methods have yet been developed. A traditional approach is to impose a parametric joint distribution for the correlated age-at-onset outcomes, which has been criticized for requiring a stringent assumption about the entire distribution of age at onset. The purpose of this paper is to describe a method for assessing familial aggregation of correlated age-at-onset outcomes semiparametrically, by use of estimating equations. This method does not require any parametric assumption for modeling the age at onset. The estimates of parameters, including those quantifying the correlation within families, are consistent and have an asymptotic normal distribution that can be used to make inferences. To illustrate this new method, we analyzed two age-at-onset data sets that were obtained from studies conducted in the States of Washington and Hawaii, with the objective of quantifying the familial aggregations of age at onset of breast cancer.     

Ethnic-affiliation estimation by use of population-specific DNA markers.

During the past 10 years, DNA analysis has revolutionized the determination of identity in a forensic context. Statements about the biological identity of two human DNA samples now can be made with complete confidence. Although DNA markers are very powerful for distinguishing among individuals, most offer little power to distinguish ethnicity or to support any statement about the physical characteristics of an individual. Through a search of the literature and of unpublished data on allele frequencies we have identified a panel of population-specific genetic markers that enable robust ethnic-affiliation estimation for major U.S. resident populations. In this report, we identify these loci and present their levels of allele-frequency differential between ethnically defined samples, and we demonstrate, using log-likelihood analysis, that this panel of markers provides significant statistical power for ethnic-affiliation estimation. In addition to their use in forensic ethnic-affiliation estimation, population-specific genetic markers are very useful in both population- and individual-level admixture estimation and in mapping genes by use of the linkage disequilibrium created when populations hybridize.     

Testing for association between disease and linked marker loci: a log-linear-model analysis.

One approach frequently used for identifying genetic factors involved in the process of a complex disease is the comparison of patients and controls for a number of genetic markers near a candidate gene. The analysis of such association studies raises some specific problems because of the fact that genotypic and not gametic data are generally available. We present a log-linear-model analysis providing a valid method for analyzing such studies. When studying the association of disease with one marker locus, the log-linear model allows one to test for the difference between allelic frequencies among affected and unaffected individuals, Hardy-Weinberg (H-W) equilibrium in both groups, and interaction between the association of alleles at the marker locus and disease. This interaction provides information about the dominance of the disease susceptibility locus, with dominance defined using the epidemiological notion of odds ratio. The degree of dominance measured at the marker locus depends on the strength of linkage disequilibrium between the marker locus and the disease locus. When studying the association of disease with several linked markers, the model becomes rapidly complex and uninterpretable unless it is assumed that affected and unaffected populations are in H-W equilibrium at each locus. This hypothesis must be tested before going ahead in the analysis. If it is not rejected, the log-linear model offers a stepwise method of identification of the parameters causing the difference between populations. This model can be extended to any number of loci, alleles, or populations.     

Similarity coefficients for molecular markers in studies of genetic relationships between individuals for haploid, diploid, and polyploid species

Determining true genetic dissimilarity between individuals is an important and decisive point for clustering and analysing diversity within and among populations, because different dissimilarity indices may yield conflicting outcomes. We show that there are no acceptable universal approaches to assessing the dissimilarity between individuals with molecular markers. Different measures are relevant to dominant and codominant DNA markers depending on the ploidy of organisms. The Dice coefficient is the suitable measure for haploids with codominant markers and it can be applied directly to (0,1)-vectors representing banding profiles of individuals. None of the common measures, Dice, Jaccard, simple mismatch coefficient (or the squared Euclidean distance), is appropriate for diploids with codominant markers. By transforming multiallelic banding patterns at each locus into the corresponding homozygous or heterozygous states, a new measure of dissimilarity within locus was developed and expanded to assess dissimilarity between multilocus states of two individuals by averaging across all codominant loci tested. There is no rigorous well-founded solution in the case of dominant markers. The simple mismatch coefficient is the most suitable measure of dissimilarity between banding patterns of closely related haploid forms. For distantly related haploid individuals, the Jaccard dissimilarity is recommended. In general, no suitable method for measuring genetic dissimilarity between diploids with dominant markers can be proposed. Banding patterns of diploids with dominant markers and polyploids with codominant markers represent individuals' phenotypes rather than genotypes. All dissimilarity measures proposed and developed herein are metrics.     

No association between mitochondrial DNA haplotypes and a female-limited mimicry phenotype in Papilio glaucus

Abstract Alternative alleles at a locus on the W chromosome of Papilio glaucus (causing dark or yellow wing colors, respectively) underlie a female-limited mimicry polymorphism thought to be maintained by balancing selection. In species with heterogametic females (i.e., the ZZ-male/ZW-female sex chromosome system), the mitochondrial DNA and the W chromosome are genetically linked because they are both maternally transmitted. We investigate the association of COI and COII mitochondrial DNA haplotypes with alternative W-linked phenotypes. Surprisingly, we find no congruence between mitochondrial DNA genealogies and inferred W-linked color alleles in P. glaucus. Using a maximum-likelihood phylogenetic approach, we reject the hypothesis of monophyly for darkmorph mitochondrial DNA lineages, even in the presence of putative low-frequency mimicry suppressor alleles or alternative melanizing factors. The most likely genealogical tree topologies assume more than one exchange event between mitochondrial DNA cytotype and the W-linked color morph. These results suggest that there is either paternal leakage of mitochondrial DNA or that more than two W-linked alleles underlie the alternative color morphs. Using data from an additional mitochondrial DNA locus, ND5, we show that pairwise linkage disequilibrium decays with physical distance between polymorphic sites. This finding suggests that genetic exchanges between maternal and paternal mitochondrial DNAs may have contributed to the lack of association we observe between phenotype and genotype.     

Testing for association based on excess allele sharing in a sample of related cases and controls

Samples consisting of a mix of unrelated cases and controls, small pedigrees, and much larger pedigrees present a unique challenge for association studies. Few methods are available for efficient analysis of such a broad spectrum of data structures. In this paper we introduce a new matching statistic that is well suited to complex data structures and compare it with frequency-based methods available in the literature. To investigate and compare the power of these methods we simulate datasets based on complex pedigrees. We examine the influence of various levels of linkage disequilibrium (LD) of the disease allele with a marker allele (or equivalently a haplotype). For low frequency marker alleles/haplotypes, frequency-based statistics are more powerful in detecting association. In contrast, for high frequency marker alleles, the matching statistic has greater power. The highest power for frequency-based statistics occurs when the disease allele frequency closely matches the frequency of the linked marker allele. In contrast maximum power of the matching statistic always occurs for intermediate marker allele frequency regardless of the disease allele frequency. Moreover, the matching and frequency-based statistics exhibit little correlation. We conclude that these two approaches can be viewed as complementary in finding possible association between a disease and a marker for many different situations.