Rational inferences about departures from Hardy-Weinberg equilibrium

Investigating Hardy-Weinberg equilibrium in case-control or cohort studies or meta-analysis

Yu et al. (Breast Cancer Res Treat 117:675-677, 2009) recently stated that testing for deviation from Hardy-Weinberg equilibrium (HWE) is necessary to identify systematic genotyping errors in case-control studies. They criticized a meta-analytic study for the deviation from HWE in the case group of one study. The aim of this article is twofold. First, we derive recommendations on how to test for deviations from HWE in different study designs. Second, we develop a meta-analytic framework for assessing compatibility with HWE or measuring deviation from HWE. The authors sketch the possible reasons behind deviation from HWE and provide guidelines for proper investigation of HWE deviations in different study designs. The authors argue that the standard HWE χ² lack of fit test is logically flawed and provide a logically unflawed approach for measuring deviation from HWE using confidence intervals. The proposed method is applicable to meta-analyses of both case-control or cohort association studies. The proposed approach is illustrated using the meta-analysis criticized by Yu et al. Heterogeneity between studies can be assessed. The critique of Yu et al. to the article of Frank et al. (Breast Cancer Res Treat 111:139-144, 2008) can be refuted. Even more, validity of HWE can be proven for the pooled control sample. The authors advocate the use of a confidence interval-based approach to assess HWE. The latter should only be investigated in control populations. In multicenter studies or meta-analysis, deviation from HWE should be analyzed using a meta-analytic approach.

Genome-wide association scan of Dupuytren's disease

PURPOSE

Dupuytren's disease (DD) has a strong genetic component that is suggested by population studies and family clustering. Genetic studies have yet to identify the gene(s) involved in DD. The purpose of this study was to identify regions of the entire genome (chromosomes 1-23) associated with the disease by performing a genome-wide association scan on DD patients and controls.

METHODS

We isolated genomic DNA from saliva collected from 40 unrelated DD patients and 40 unaffected controls. We conducted the genotyping using CytoSNP-Infinium HD Ultra genotyping assay on the Illumina platform. Using both log regression and mapping by admixture linkage disequilibrium analysis methods, we analyzed the single nucleotide polymorphism genotyping data.

RESULTS

Single nucleotide polymorphism analysis revealed a significant association in regions for chromosomes 1, 3 through 6, 11, 16, 17, and 23. Mapping by admixture linkage disequilibrium analysis showed ancestry-associated regions in chromosomes 2, 6, 8, 11, 16, and 20, which may harbor DD susceptibility genes. Both analysis methods revealed loci association in chromosomes 6, 11, and 16.

CONCLUSIONS

Our data suggest that chromosomes 6, 11, and 16 may contain the genes for DD and that multiple genes may be involved in DD. Future genetic studies on DD should focus on these areas of the genome.

A genetic association study of maternal and fetal candidate genes that predispose to preterm prelabor rupture of membranes (PROM)

OBJECTIVE

We sought to determine whether maternal/fetal single-nucleotide polymorphisms (SNPs) in candidate genes are associated with preterm prelabor rupture of membranes (pPROM).

STUDY DESIGN

A case-control study was conducted in patients with pPROM (225 mothers and 155 fetuses) and 599 mothers and 628 fetuses with a normal pregnancy; 190 candidate genes and 775 SNPs were studied. Single locus/haplotype association analyses were performed; false discovery rate was used to correct for multiple testing (q* = 0.15).

RESULTS

First, a SNP in tissue inhibitor of metalloproteinase 2 in mothers was significantly associated with pPROM (odds ratio, 2.12; 95% confidence interval, 1.47-3.07; P = .000068), and this association remained significant after correction for multiple comparisons. Second, haplotypes for Alpha 3 type IV collagen isoform precursor in the mother were associated with pPROM (global P = .003). Third, multilocus analysis identified a 3-locus model, which included maternal SNPs in collagen type I alpha 2, defensin alpha 5 gene, and endothelin 1.

CONCLUSION

DNA variants in a maternal gene involved in extracellular matrix metabolism doubled the risk of pPROM.

The association between CBS 844ins68 polymorphism and head and neck squamous cell carcinoma risk - a case-control analysis

INTRODUCTION

Susceptibility to head and neck squamous cell carcinoma may be modified by functional polymorphisms in genes involved in the folate pathway, such as cystathionine beta-synthase (CBS). The CBS 844ins68 polymorphism is associated with DNA methylation changes and cancer development.

MATERIAL AND METHODS

A case-control retrospective study was conducted in 322 patients with head and neck squamous cell carcinoma and in 531 control subjects without cancer. The polymerase chain reaction-restriction fragment length polymorphism technique was used to genotype the polymorphism. For statistical analysis, χ(2) test was conducted to examine whether the genotypic frequency of CBS 844ins68 was in Hardy-Weinberg equilibrium and multiple logistic regression was used for comparisons between groups, and for interactions between the polymorphism and risk factors and clinical histopathological parameters.

RESULTS

No significant difference in CBS 844ins68 genotypic distribution was observed between the groups. Age > 50 years, male gender and tobacco consumption were predictors of the disease with increased risk of 7.89 (95% CI: 5.56-11.21), 2.49 (95% CI: 1.72-3.62), 6.44 (95% CI: 4.63-8.96) and 2.29 times (95% CI: 1.71-3.06) respectively. There was no association between the distribution of the CBS 844ins68 genotype and risk factors for this disease. According to clinical histopathological parameters, CBS 884ins68 polymorphism presented high frequency in oral cavity (p < 0.05) and patients with the polymorphism presented less survival time (p < 0.05).

CONCLUSIONS

We concluded that the CBS 844ins68 polymorphism is not associated with HNSCC risk and there is increased risk of this disease in male gender individuals smokers aged over 50 years. In adittion, the polymorphism is more frequent in patients with oral cavity as primary site and in patients with less survival time.

Genetic diversity at endoplasmic reticulum aminopeptidases is maintained by balancing selection and is associated with natural resistance to HIV-1 infection

Human ERAP1 and ERAP2 encode two endoplasmic reticulum aminopeptidases. These enzymes trim peptides to optimal size for loading onto major histocompatibility complex class I molecules and shape the antigenic repertoire presented to CD8(+) T cells. Therefore, ERAP1 and ERAP2 may be considered potential selection targets and modulators of infection susceptibility. We resequenced two genic regions in ERAP1 and ERAP2 in three HapMap populations. In both cases, we observed high levels of nucleotide variation, an excess of intermediate-frequency alleles, and reduced population genetic differentiation. The genealogy of ERAP1 and ERAP2 haplotypes was split into two major branches with deep coalescence times. These features suggest that long-standing balancing selection has acted on these genes. Analysis of the Lys528Arg (rs30187 in ERAP1) and Asn392Lys (rs2549782 in ERAP2) variants in an Italian population of HIV-1-exposed seronegative (ESN) individuals and a larger number of Italian controls indicated that rs2549782 significantly deviates from Hardy-Weinberg equilibrium (HWE) in ESN but not in controls. Technical errors were excluded and a goodness-of-fit test indicated that a recessive model with only genetic effects adequately explains HWE deviation. The genotype distribution of rs2549782 is significantly different in the two cohorts (P = 0.004), mainly as the result of an over-representation of Lys/Lys genotypes in the ESN sample (P-value for a recessive model: 0.00097). Our data suggest that genetic diversity in ERAP1 and ERAP2 has been maintained by balancing selection and that variants in ERAP2 confer resistance to HIV-1 infection possibly via the presentation of a distinctive peptide repertoire to CD8(+) T cells.

A confidence-limit-based approach to the assessment of Hardy-Weinberg equilibrium

The classical chi(2)-procedure for the assessment of Hardy-Weinberg equilibrium (HWE) is tailored for detecting violations of HWE. However, many applications in genetic epidemiology require approximate compatibility with HWE. In a previous contribution to the field (Wellek, S. (2004). Biometrics, 60, 694-703), the methodology of statistical equivalence testing was exploited for the construction of tests for problems in which the assumption of approximate compatibility of a given genotype distribution with HWE plays the role of the alternative hypothesis one aims to establish. In this article, we propose a procedure serving the same purpose but relying on confidence limits rather than critical bounds of a significance test. Interval estimation relates to essentially the same parametric function that was previously chosen as the target parameter for constructing an exact conditional UMPU test for equivalence with a HWE conforming genotype distribution. This population parameter is shown to have a direct genetic interpretation as a measure of relative excess heterozygosity. Confidence limits are constructed using both asymptotic and exact methods. The new approach is illustrated by reanalyzing genotype distributions obtained from published genetic association studies, and detailed guidance for choosing the equivalence margin is provided. The methods have been implemented in freely available SAS macros.

Fucosyltransferase 2 (FUT2) non-secretor status is associated with Crohn's disease

Genetic variation in both innate and adaptive immune systems is associated with Crohn's disease (CD) susceptibility, but much of the heritability to CD remains unknown. We performed a genome-wide association study (GWAS) in 896 CD cases and 3204 healthy controls all of Caucasian origin as defined by multidimensional scaling. We found supportive evidence for 21 out of 40 CD loci identified in a recent CD GWAS meta-analysis, including two loci which had only nominally achieved replication (rs4807569, 19p13; rs991804, CCL2/CCL7). In addition, we identified associations with genes involved in tight junctions/epithelial integrity (ASHL, ARPC1A), innate immunity (EXOC2), dendritic cell biology [CADM1 (IGSF4)], macrophage development (MMD2), TGF-beta signaling (MAP3K7IP1) and FUT2 (a physiological trait that regulates gastrointestinal mucosal expression of blood group A and B antigens) (rs602662, P=3.4x10(-5)). Twenty percent of Caucasians are 'non-secretors' who do not express ABO antigens in saliva as a result of the FUT2 W134X allele. We demonstrated replication in an independent cohort of 1174 CD cases and 357 controls between the four primary FUT2 single nucleotide polymorphisms (SNPs) and CD (rs602662, combined P-value 4.90x10(-8)) and also association with FUT2 W143X (P=2.6x10(-5)). Further evidence of the relevance of this locus to CD pathogenesis was demonstrated by the association of the original four SNPs and CD in the recently published CD GWAS meta-analysis (rs602662, P=0.001). These findings strongly implicate this locus in CD susceptibility and highlight the role of the mucus layer in the development of CD.

Data quality control in genetic case-control association studies

This protocol details the steps for data quality assessment and control that are typically carried out during case-control association studies. The steps described involve the identification and removal of DNA samples and markers that introduce bias. These critical steps are paramount to the success of a case-control study and are necessary before statistically testing for association. We describe how to use PLINK, a tool for handling SNP data, to perform assessments of failure rate per individual and per SNP and to assess the degree of relatedness between individuals. We also detail other quality-control procedures, including the use of SMARTPCA software for the identification of ancestral outliers. These platforms were selected because they are user-friendly, widely used and computationally efficient. Steps needed to detect and establish a disease association using case-control data are not discussed here. Issues concerning study design and marker selection in case-control studies have been discussed in our earlier protocols. This protocol, which is routinely used in our labs, should take approximately 8 h to complete.

Genetic association of the GDNF alpha-receptor genes with schizophrenia and clozapine response

GDNF (glial-cell-line derived neurotrophic factor) is a potent neurotrophic factor for dopaminergic neurons. Neuropsychiatric diseases and their treatments are associated with alterations in the levels of both GDNF and its receptor family (GDNF family receptor alpha or GFRA). GFRA1, GFRA2 and GFRA3 are located in chromosomal regions with suggestive linkage to schizophrenia. In this study we analyzed polymorphisms located in all four known GFRA genes and examined association with schizophrenia and clozapine response. We examined SNPs across the genes GFRA1-4 in 219 matched case-control subjects, 85 small nuclear families and 140 schizophrenia patients taking clozapine for 6months. We observed that GFRA3 rs11242417 and GFRA1 rs11197557 variants were significantly associated with schizophrenia after combining results from both schizophrenia samples. Furthermore, we found an overtransmission of the G-C GFRA1 rs7920934-rs730357 haplotype to subjects with schizophrenia and association of A-T-G-G GFRA3 rs10036665-rs10952-rs11242417-rs7726580 with schizophrenia in the case-control sample. On the other hand, GFRA2 variants were not associated with schizophrenia diagnosis but subjects carrying T-G-G rs1128397-rs13250096-rs4567028 haplotype were more likely to respond to clozapine treatment. The statistical significance of results survived permutation testing but not Bonferroni correction. We also found nominally-significant evidence for interactions between GFRA1, 2 and 3 associated with schizophrenia and clozapine response, consistent with the locations of these three genes within linkage regions for schizophrenia.

Power of genetic association studies with fixed and random genotype frequencies

When estimating the power of genetic association studies, the allele and genotype frequencies are often assumed to be known, and the numbers of individuals with each genotype are set equal to their expectations under Hardy-Weinberg equilibrium. In fact, both allele and genotype frequencies are unknown and thus random. It has previously been suggested that ignoring uncertainty in these parameters could lead to inflated power expectations. To overcome the problem, one can average power estimates over the distributions of unknown frequencies. We investigate the power-averaging method and find that, despite the intuitive appeal, it may not improve accuracy in practice, while significantly increasing computational time. For a fixed allele frequency, we show that the amount of overestimation diminishes rapidly with sample size and is completely negligible for N > 200. For an unknown frequency, the result of averaging depends on the genetic model, and may not always provide a more conservative estimate of power. We explore the effect of uncertainty in the factors that determine statistical power of association studies and propose a more economical approach to the power analysis.

Common variants in the regulative regions of GRIA1 and GRIA3 receptor genes are associated with migraine susceptibility

Background

Glutamate is the principal excitatory neurotransmitter in the central nervous system which acts by the activation of either ionotropic (AMPA, NMDA and kainate receptors) or G-protein coupled metabotropic receptors. Glutamate is widely accepted to play a major role in the path physiology of migraine as implicated by data from animal and human studies. Genes involved in synthesis, metabolism and regulation of both glutamate and its receptors could be, therefore, considered as potential candidates for causing/predisposing to migraine when mutated.

Methods

The association of polymorphic variants of GRIA1-GRIA4 genes which encode for the four subunits (GluR1-GluR4) of the alpha-amino-3- hydroxy-5-methyl-4-isoxazole-propionic acid (AMPA) receptor for glutamate was tested in migraineurs with and without aura (MA and MO) and healthy controls.

Results

Two variants in the regulative regions of GRIA1 (rs2195450) and GRIA3 (rs3761555) genes resulted strongly associated with MA (P = 0.00002 and P = 0.0001, respectively), but not associated with MO, suggesting their role in cortical spreading depression. Whereas the rs548294 variant in GRIA1 gene showed association primarily with MO phenotype, supporting the hypothesis that MA and MO phenotypes could be genetically related. These variants modify binding sites for transcription factors altering the expression of GRIA1 and GRIA3 genes in different conditions.

Conclusions

This study represents the first genetic evidence of a link between glutamate receptors and migraine.

Impact of Hardy-Weinberg equilibrium deviation on allele-based risk effect of genetic association studies and meta-analysis

Deviations from Hardy-Weinberg equilibrium (HWE) in control subjects may bias the estimates of genetic effects in genetic association studies (GAS) and meta-analysis. A large empirical evaluation was carried out to evaluate the impact of HWE deviation and explore the effect of variance adjustment for the allele-based odds ratio in 833 individual GAS and 72 meta-analyses. In individual GAS, the variance adjustment for any deviation from HWE resulted in stronger associations, and 10 GAS (1%) became significant (P < 0.05). One hundred sixteen GAS (14%) showed significant deviation from HWE (P (HWE) < 0.05); however, only 37 GAS (4%) had more than 90% power to detect significant deviation from HWE at the 5% level. In meta-analyses, adjustment for any deviation from HWE improved the significance in 53 meta-analyses (74%). Then, a formal statistical significance (P < 0.05) was revealed for one previously negative meta-analyses whereas one meta-analysis lost its significance. Between-study heterogeneity was enhanced in 50 meta-analyses (69%). None of the meta-analyses lost the significance of heterogeneity (P ( Q ) < 0.10) whereas in one meta-analysis, the non significant heterogeneity became significant. Sensitivity analysis for studies not conforming to HWE (P (HWE) < 0.05) was applied to 45 meta-analyses (69%). Then, the significance of association was increased in 26 the meta-analyses (58%) and one meta-analysis became significant (P < 0.05) whereas seven meta-analyses (16%) were no longer significant. Adjustment for HWE deviation could be an effective strategy for dealing with HWE violations in GAS and meta-analyses.

β-Arrestin2 influences the response to methadone in opioid-dependent patients

β-Arrestin2 (ARRB2) is a component of the G-protein-coupled receptor complex and is involved in μ-opioid and dopamine D(2) receptor signaling, two central processes in methadone signal transduction. We analyzed 238 patients in methadone maintenance treatment (MMT) and identified a haplotype block (rs34230287, rs3786047, rs1045280 and rs2036657) spanning almost the entire ARRB2 locus. Although none of these single nucleotide polymorphisms (SNPs) leads to a change in amino-acid sequence, we found that for all the SNPs analyzed, with exception of rs34230287, homozygosity for the variant allele confers a nonresponding phenotype (n=73; rs1045280C and rs2036657G: OR=3.1, 95% CI=1.5-6.3, P=0.004; rs3786047A: OR=2.5, 95% CI=1.2-5.1, P=0.02) also illustrated by a 12-fold shorter period of negative urine screening (P=0.01). The ARRB2 genotype may thus contribute to the interindividual variability in the response to MMT and help to predict response to treatment.

Quality control for genome-wide association studies

This chapter is a comprehensive review of quality control (QC) methods for SNP-based genotyping panels used in genome-wide association studies. These include QC on individuals for missingness, gender checks, duplicates and cryptic relatedness, population outliers, heterozygosity and inbreeding, and QC on SNPs for missingness, minor allele frequency and Hardy-Weinberg equilibrium. The emphasis is on the reasons behind each QC step and on the use of intelligent approaches rather than arbitrary QC thresholds. Scripts and code for performing these QC steps are available at www.kcl.ac.uk/mmg/gwascode/ .

RAD51 135G>C does not modify breast cancer risk in non-BRCA1/2 mutation carriers: evidence from a meta-analysis of 12 studies

A single-nucleotide polymorphism (SNP) in the 5'-untranslated region (UTR) of RAD51, 135G>C (rs1801320), was reported to be associated with an increased risk of breast cancer among BRCA2 as well as BRCA1 carriers. A few studies have also investigated the genetic contribution of RAD51 135G>C to the risk of sporadic breast cancers or breast cancer in non-BRCA1/2 carriers, though the results are yet controversial and inconclusive. We, in this study, performed a more precise estimation of the relationship between 135G>C and breast cancer among non-BRCA1/2 mutation carriers by meta-analyzing the currently available evidence from the literature. A total of 12 studies involving 7,065 cases and 6,981 controls were identified. Crude odds ratios (ORs) with 95% confidence intervals (CIs) were used to assess the strength of association. When all the studies were pooled into the meta-analysis, there was no evidence for a significant association between 135G>C and breast cancer risk in non-BRCA1/2 mutation carriers (for CC vs. GG: OR = 0.995, 95%CI: 0.741-1.336; for GC vs. GG: OR = 0.959, 95%CI: 0.869-1.057; for dominant model: OR = 0.988, 95%CI: 0.902-1.082; and for recessive model: OR = 1.037, 95%CI: 0.782-1.376). We also performed subgroup analysis by ethnicity (Caucasian) as well as did analysis using the studies fulfilling Hardy-Weinberg equilibrium, and the results did not change. In summary, the present meta-analysis suggests that the RAD51 135G>C does not modify breast cancer risk in non-BRCA1/2 mutation carriers.

Identification of fetal and maternal single nucleotide polymorphisms in candidate genes that predispose to spontaneous preterm labor with intact membranes

OBJECTIVE

The purpose of this study was to determine whether maternal/fetal single nucleotide polymorphisms (SNPs) in candidate genes are associated with spontaneous preterm labor/delivery.

STUDY DESIGN

A genetic association study was conducted in 223 mothers and 179 fetuses (preterm labor with intact membranes who delivered <37 weeks of gestation [preterm birth (PTB)]), and 599 mothers and 628 fetuses (normal pregnancy); 190 candidate genes and 775 SNPs were studied. Single locus/haplotype association analyses were performed; the false discovery rate was used to correct for multiple testing.

RESULTS

The strongest single locus associations with PTB were interleukin-6 receptor 1 (fetus; P=.000148) and tissue inhibitor of metalloproteinase 2 (mother; P=.000197), which remained significant after correction for multiple comparisons. Global haplotype analysis indicated an association between a fetal DNA variant in insulin-like growth factor F2 and maternal alpha 3 type IV collagen isoform 1 (global, P=.004 and .007, respectively).

CONCLUSION

An SNP involved in controlling fetal inflammation (interleukin-6 receptor 1) and DNA variants in maternal genes encoding for proteins involved in extracellular matrix metabolism approximately doubled the risk of PTB.

Fine mapping of AHI1 as a schizophrenia susceptibility gene: from association to evolutionary evidence

In previous studies, we identified a locus for schizophrenia on 6q23.3 and proposed the Abelson helper integration site 1 (AHI1) as the candidate gene. AHI1 is expressed in the brain and plays a key role in neurodevelopment, is involved in Joubert syndrome, and has been recently associated with autism. The neurodevelopmental role of AHI1 fits with etiological hypotheses of schizophrenia. To definitively confirm our hypothesis, we searched for associations using a dense map of the region. Our strongest findings lay within the AHI1 gene: single-nucleotide polymorphisms rs11154801 and rs7759971 showed significant associations (P=6.23E-06; P=0.84E-06) and haplotypes gave P values in the 10E-8 to 10E-10 range. The second highest significant region maps close to AHI1 and includes the intergenic region between BC040979 and PDE7B (rs2038549 at P=9.70E-06 and rs1475069 at P=6.97E-06), and PDE7B and MAP7. Using a sample of Palestinian Arab families to confirm these findings, we found isolated signals. While these results did not retain their significance after correction for multiple testing, the joint analysis across the 2 samples supports the role of AHI1, despite the presence of heterogeneity. Given the hypothesis of positive selection of schizophrenia genes, we resequenced a 11 kb region within AHI1 in ethnically defined populations and found evidence for a selective sweep. Network analysis indicates 2 haplotype clades, with schizophrenia-susceptibility haplotypes clustering within the major clade. In conclusion, our data support the role of AHI1 as a susceptibility gene for schizophrenia and confirm it has been subjected to positive selection, also shedding light on new possible candidate genes, MAP7 and PDE7B.

Dietary glucosinolate intake, polymorphisms in selected biotransformation enzymes, and risk of prostate cancer

A protective role of glucosinolates in prostate cancer development might be mediated by the induction of biotransformation enzymes. These enzymes, enhancing the elimination of carcinogens from the body, are known to be polymorphic. Therefore, we evaluated whether a possible association between glucosinolate intake and prostate cancer risk is modified by polymorphisms in GSTT1, GSTM1, GSTA1, GSTP1, or NOQ1 genes. A case-control study including 248 prostate cancer cases and 492 matched controls was nested in the prospective European Prospective Investigation into Cancer and Nutrition-Heidelberg cohort. At baseline, participants provided dietary and lifestyle data and blood samples, which were used for genotyping and measurement of serum glutathione S-transferase-alpha concentration. Odds ratios and 95% confidence intervals were calculated by conditional logistic regression. We found an inverse association of glucosinolate intake with prostate cancer risk (adjusted odds ratio, 0.72 per 10 mg/d increment; 95% confidence interval, 0.53-0.96). Stratification by genotype showed significantly reduced risks for subjects with wild-type of NQO1 (C609T) compared with CT or TT carriers (P(interaction) = 0.04). Those with deletions in both GSTM1 and GSTT1 genes combined had a significantly reduced risk with increasing glucosinolate intake (P(interaction) = 0.01). There was no effect modification of glucosinolate intake and cancer risk by GSTA1 (G-52A) or GSTP1 (A313G) genotype, but serum glutathione S-transferase-alpha concentrations were inversely associated with prostate cancer. This study showed that the inverse association between glucosinolate intake and prostate cancer risk was modified by NQO1 (C609T) and GSTM1 and GSTT1 deletion polymorphisms. This information will help to further elucidate the mechanism of action of potentially protective substances in vivo.

Using both cases and controls for testing hardy-weinberg proportions in a genetic association study

OBJECTIVES

Assessment of the Hardy-Weinberg proportion (HWP) in controls has been widely used as a quality control measure in case-control association studies. However, when the disease being studied is common, controls might not represent the general population, which could result in inaccurate HWP test results. Such results could lead investigators to discard important single-nucleotide polymorphisms (SNPs) that could potentially be causal. In this paper, we showed the inappropriateness of the HWP test in controls and proposed a mixture HWP (mHWP) exact test using a mixture sample that mimics the general population.

METHODS

The mHWP exact test estimates HWP in a mixture sample that is a combination of both cases and controls proportional to the prevalence of disease. We implemented a re-sampling procedure to construct mixture samples and then obtained the empirical p value of HWP in the general population. Simulation studies were performed to investigate the performance of the proposed mHWP exact test. The method was also applied to a genetic association study of obesity.

RESULTS

The results showed that the mHWP exact test is more likely than either the traditional HWP method in controls or the likelihood-based approach to keep causal SNPs for further analysis when the disease is more common.

CONCLUSION

The mHWP exact test using a mixture sample is a better HWP test for case-control genetic association studies than the traditional HWP in controls or the likelihood-based approach, and it will improve our ability to keep causal SNPs in the case-control genetic association studies.

A robust test for two-stage design in genome-wide association studies

A two-stage design is cost-effective for genome-wide association studies (GWAS) testing hundreds of thousands of single nucleotide polymorphisms (SNPs). In this design, each SNP is genotyped in stage 1 using a fraction of case-control samples. Top-ranked SNPs are selected and genotyped in stage 2 using additional samples. A joint analysis, combining statistics from both stages, is applied in the second stage. Follow-up studies can be regarded as a two-stage design. Once some potential SNPs are identified, independent samples are further genotyped and analyzed separately or jointly with previous data to confirm the findings. When the underlying genetic model is known, an asymptotically optimal trend test (TT) can be used at each analysis. In practice, however, genetic models for SNPs with true associations are usually unknown. In this case, the existing methods for analysis of the two-stage design and follow-up studies are not robust across different genetic models. We propose a simple robust procedure with genetic model selection to the two-stage GWAS. Our results show that, if the optimal TT has about 80% power when the genetic model is known, then the existing methods for analysis of the two-stage design have minimum powers about 20% across the four common genetic models (when the true model is unknown), while our robust procedure has minimum powers about 70% across the same genetic models. The results can be also applied to follow-up and replication studies with a joint analysis.

Genome-wide association studies: a powerful tool for neurogenomics

As their power and utility increase, genome-wide association (GWA) studies are poised to become an important element of the neurosurgeon's toolkit for diagnosing and treating disease. In this paper, the authors review recent findings and discuss issues associated with gathering and analyzing GWA data for the study of neurological diseases and disorders, including those of neurosurgical importance. Their goal is to provide neurosurgeons and other clinicians with a better understanding of the practical and theoretical issues associated with this line of research. A modern GWA study involves testing hundreds of thousands of genetic markers across an entire genome, often in thousands of individuals, for any significant association with a particular disease. The number of markers assayed in a study presents several practical and theoretical issues that must be considered when planning the study. Genome-wide association studies show great promise in our understanding of the genes underlying common neurological diseases and disorders, as well as in leading to a new generation of genetic tests for clinicians.

Association study of DTNBP1 with schizophrenia in a US sample

BACKGROUND

Straub et al. (2002b) located a susceptibility region for schizophrenia at the DTNBP1 locus. At least 40 studies (including one study in US populations) attempted to replicate this original finding, but the reported findings are highly diverse and at least five pathways by which dysbindin protein might be involved in schizophrenia have been proposed. This study aimed to test the association in two common US populations by using powerful analytic methods.

METHODS

Six markers at DTNBP1 were genotyped by mass spectroscopy ('MassARRAY' technique) in a sample of 663 individuals, including 346 healthy individuals European-Americans (EAs) and 48 African-Americans (AAs), and 317 individuals with schizophrenia (235 EAs and 82 AAs). Thirty-eight ancestry-informative markers were genotyped in this sample to infer the ancestry proportions. Diplotype, haplotype, genotype, and allele frequency distributions were compared between the cases and controls, controlling for possible population stratification, admixture, and sex-specific effects, and taking interaction effects into account, using a logistic regression analysis (an extended structured association method).

RESULTS

Conventional case-control comparisons showed that genotypes of the markers P1578 (rs1018381) and P1583 (rs909706) were nominally associated with schizophrenia in EAs and in AAs, respectively. These associations became less or nonsignificant after controlling for population stratification and admixture effects (using structured association or regression analysis), and became nonsignificant after correction for multiple testing. However, regression analysis showed that the common diplotypes (ACCCTT/GCCGCC or GCCGCC/GCCGCC) and the interaction effects of haplotypes GCCGCC/GCCGCC significantly affected risk for schizophrenia in EAs, effects that were modified by sex. Fine-mapping using d or J statistics located the specific markers (d: P1328; J: P1333) closest to the putative risk sites in EAs.

CONCLUSION

This study shows that DTNBP1 is a risk gene for schizophrenia in EAs. Variation at DTNBP1 may modify risk for schizophrenia in this population.

Adapting the logical basis of tests for Hardy-Weinberg Equilibrium to the real needs of association studies in human and medical genetics

The standard procedure to assess genetic equilibrium is a chi(2) test of goodness-of-fit. As is the case with any statistical procedure of that type, the null hypothesis is that the distribution underlying the data is in agreement with the model. Thus, a significant result indicates incompatibility of the observed data with the model, which is clearly at variance with the aim in the majority of applications: to exclude the existence of gross violations of the equilibrium condition. In current practice, we try to avoid this basic logical difficulty by increasing the significance bound to the P-value (e.g. from 5 to 10%) and inferring compatibility of the data with Hardy Weinberg Equilibrium (HWE) from an insignificant result. Unfortunately, such direct inversion of a statistical testing procedure fails to produce a valid test of the hypothesis of interest, namely, that the data are in sufficiently good agreement with the model under which the P-value is calculated. We present a logically unflawed solution to the problem of establishing (approximate) compatibility of an observed genotype distribution with HWE. The test is available in one- and two-sided versions. For both versions, we provide tools for exact power calculation. We demonstrate the merits of the new approach through comparison with the traditional chi(2) goodness-of-fit test in 2x60 genotype distributions from 43 published genetic studies of complex diseases where departure from HWE was noted in either the case or control sample. In addition, we show that the new test is useful for the analysis of genome-wide association studies.

SNP-PHAGE: high-throughput SNP discovery pipeline

High-throughput genotyping technologies have become popular in studies that aim to reveal the genetics behind polygenic traits such as complex disease and the diverse response to some drug treatments. These technologies utilize bioinformatics tools to define strategies, analyze data, and estimate the final associations between certain genetic markers and traits. The strategy followed for an association study depends on its efficiency and cost. The efficiency is based on the assumed characteristics of the polymorphisms' allele frequencies and linkage disequilibrium for putative casual alleles. Statistically significant markers (single mutations or haplotypes) that cause a human disorder should be validated and their biological function elucidated. The aim of this chapter is to present a subset of bioinformatics tools for haplotype inference, tag SNP selection, and genome-wide association studies using a high-throughput generated SNP data set.

Lack of an association between a functional polymorphism in the interleukin-6 gene promoter and breast cancer risk: a meta-analysis involving 25,703 subjects

The association between a single-nucleotide polymorphism (SNP) -174G > C (rs1800795) located in the IL-6 gene promoter and breast cancer risk is still controversial and ambiguous. We performed in this study a more precise estimation of the relationship by meta-analyzing the currently available evidence from literature. A total of 11 publications containing 12 studies including 10,137 cases and 15,566 controls were identified. Crude odds ratios (ORs) with 95% confidence intervals (CIs) were used to assess the strength of association in the codominant model, dominant model, and recessive model. When all the studies were pooled into the meta-analysis, there was no evidence showing a significant association between -174G > C and breast cancer risk (for CC vs. GG: OR = 1.024, 95% CI: 0.935-1.121; for GC vs. GG: OR = 1.008, 95% CI: 0.946-1.073; for dominant model: OR = 0.980, 95% CI: 0.857-1.121; and for recessive model: OR = 1.027, 95% CI: 0.944-1.117). In the subgroup analyses by ethnicity, no significant associations were observed in any genetic models. In summary, the present meta-analysis suggests that the functional polymorphism -174G > C within the IL-6 gene promoter is not associated with breast cancer risk. Identifying a unique SNP as a breast cancer risk predictor remains a very challenging task.

Genetic ancestry is associated with subclinical cardiovascular disease in African-Americans and Hispanics from the multi-ethnic study of atherosclerosis

BACKGROUND

Differences in cardiovascular disease (CVD) burden exist among racial/ethnic groups in the United States, with African-Americans having the highest prevalence. Subclinical CVD measures have also been shown to differ by race or ethnicity. In the United States, there has been a significant intermixing among racial/ethnic groups creating admixed populations. Very little research exists on the relationship of genetic ancestry and subclinical CVD measures.

METHODS AND RESULTS

These associations were investigated in 712 black and 705 Hispanic participants from the Multi-Ethnic Study of Atherosclerosis candidate gene substudy. Individual ancestry was estimated from 199 genetic markers using STRUCTURE. Associations of ancestry and coronary artery calcium (CAC) and common and internal carotid intima media thickness were evaluated using log-binomial and linear regression models. Splines indicated linear associations of ancestry with subclinical CVD measures in African-Americans but presence of threshold effects in Hispanics. Among African-Americans, each SD increase in European ancestry was associated with an 8% (95% CI, 1.02 to 1.15; P=0.01) higher CAC prevalence. Each SD increase in European ancestry was also associated with a 2% (95% CI -3.4% to -0.5%, P=0.008) lower common carotid intima media thickness in African-Americans. Among Hispanics, the highest tertile of European ancestry was associated with a 34% higher CAC prevalence (P=0.02) when compared with the lowest tertile.

CONCLUSIONS

The linear association of ancestry and subclinical CVD suggests that genetic effects may be important in determining CAC and carotid intima media thickness among African-Americans. Our results also suggest that CAC and common carotid intima media thickness may be important phenotypes for further study with admixture mapping.

A heterozygote-homozygote test of Hardy-Weinberg equilibrium

The century-old Hardy-Weinberg law remains fundamental to population genetics. Typically Hardy-Weinberg equilibrium is tested in unrelated individuals using a chi(2) goodness-of-fit test that compares expected and observed numbers of heterozygotes and homozygotes. In this report, we propose a likelihood ratio test for Hardy-Weinberg equilibrium that accommodates a mixture of pedigree and random sample data. The underlying statistical model depends on a parameter gamma determining the ratio of heterozygous genotypes to homozygous genotypes among pedigree founders. As our heterozygous-homozygous test accommodates markers with dominant and recessive alleles, it can handle the phase ambiguities encountered in combining several linked single nucleotide polymorphisms into a single supermarker. No prior haplotyping is necessary. Our experience on real and simulated data suggests that the heterozygous-homozygous test has good type-one error and power.

Testing Hardy-Weinberg equilibrium using mother-child case-control samples

Genetic association studies of obstetric complications may genotype case and control mothers, or their respective newborns, or both case-control mothers and their children. The relatively high prevalence of many obstetric complications and the availability of both maternal and offspring's genotype data have provided motivation to study new methods for testing for deviations from Hardy-Weinberg equilibrium (HWE). We propose four novel test statistics, each of which uses a different type of data as follows: (1) a test using maternal case-control genotype data, (2) a test using offspring genotype data, (3) a combination of the first and second tests, and (4) a test based on the joint classification of case-control maternal-child genotype data. The selection of case and control mothers (and thus their children) is accounted for by weighting both maternal and child contributions to the test statistics with sampling probabilities. Our tests thus do not require that the phenotype be rare as is the case for HWE tests using only controls, and are particularly suitable for genetic association studies of relatively common complications such as premature birth. The third and fourth tests described above utilize both maternal and child genotype data and appropriately account for the correlation between maternal and child genotypes. On the basis of extensive simulation studies to compare the type-I error and power for proposed tests, we recommend the third combined test statistic for routine use in the analysis of case-control studies of mother-child pairs.

Interaction of serotonin-related genes affects short-term antidepressant response in major depressive disorder

BACKGROUND

Four serotonin-related genes including guanine nucleotide binding protein beta polypeptide 3 (GNB3), 5-hydroxytryptamine receptor 1A (HTR1A; serotonin receptor 1A), 5-hydroxytryptamine receptor 2A (HTR2A; serotonin receptor 2A), and solute carrier family 6 member 4 (SLC6A4; serotonin neurotransmitter transporter) have been suggested to be candidate genes for influencing antidepressant treatment outcome. The aim of this study was to explore whether interaction among these genes could contribute to the pharmacogenomics of short-term antidepressant response in a Taiwanese population with major depressive disorder (MDD).

METHODS

Included in this study were 101 MDD patients who were treated with antidepressants, 35 of whom were rapid responders and 66 non-responders after 2weeks of treatment. We genotyped four single nucleotide polymorphisms (SNPs), including GNB3 rs5443 (C825T), HTR1A rs6295 (C-1019G), HTR2A rs6311 (T102C), and SLC6A4 rs25533, and employed the generalized multifactor dimensionality reduction (GMDR) method to investigate gene-gene interactions.

RESULTS

Single-locus analyses showed the GNB3 rs5443 polymorphism to be associated with short-term antidepressant treatment outcome (P-value=0.029). We did not correct for multiple testing in these multiple exploratory analyses. Finally, the GMDR approach identified a significant gene-gene interaction (P-value=0.025) involving GNB3 and HTR2A, as well as a significant 3-locus model (P-value=0.015) among GNB3, HTR2A, and SLC6A4.

CONCLUSIONS

These results support the hypothesis that GNB3, HTR2A, and SLC6A4 may play a role in the outcome of short-term antidepressant treatment for MDD in an interactive manner. Future research with independent replication using large sample sizes is needed to confirm the functions of the candidate genes identified in this study as being involved in short-term antidepressant treatment response.

Translin-associated factor X gene (TSNAX) may be associated with female major depressive disorder in the Japanese population

Several investigations have reported that the translin-associated factor X gene (TSNAX)/disrupted-in-schizophrenia-1 gene (DISC1) was associated with major psychiatric disorders including schizophrenia, bipolar disorder (BP), and major depressive disorder (MDD). TSNAX is located immediately upstream of DISC1, and has been shown to undergo intergenic splicing with DISC1. It thus may also be influenced by translocation. To our knowledge, there are no reported gene-based association analyses between TSNAX and mood disorders in the Japanese population. We conducted a case-control study of Japanese samples (158 bipolar patients, 314 major depressive disorder patients, and 811 controls) with three tagging SNPs in TSNAX, selected using HapMap database. In addition, we performed an association analysis between TSNAX and the efficacy of fluvoxamine treatment in 120 Japanese patients with MDD. The MDD patients in this study had scores of 12 or higher on the 17 items of the Structured Interview Guide for Hamilton Rating Scale for Depression (SIGH-D). We defined a clinical response as a decrease of more than 50% in baseline SIGH-D within 8 weeks, and clinical remission as an SIGH-D score of less than 7 at 8 weeks. We found an association between rs766288 in TSNAX and female MDD in the allele/genotype analysis. However, we did not find any association between TSNAX and BP or the fluvoxamine therapeutic response in MDD in the allele/genotype analysis or haplotype analysis. Our results suggest that rs766288 in TSNAX may play a role in the pathophysiology of female MDD in the Japanese population. A replication study using larger samples may be required for conclusive results, since our sample size was small.

Phase uncertainty in case-control association studies

The possible evidence for association comprises three types of information: differences between cases and controls in allele frequencies, in parameters for Hardy-Weinberg disequilibrium (HWD), and in parameters for linkage disequilibrium (LD). LD between marker and disease alleles results in a difference in at least one of the three types of parameters [Won and Elston, 2008]. However, the parameters for LD require knowledge about phase, which is usually unknown, making the LD contrast test without modification infeasible in practice. Methods for handling phase uncertainty are: (1) the most probable haplotype pair for each individual can be considered as the true phase; (2) a weighted average of haplotypes can be used; (3) we can consider the composite LD, which does not require any information about phase. We compare these methods to handle phase uncertainty in terms of validity and efficiency, and the effect on them of HWD in the population, at the same time confirming results for the three types of information. When the LD between markers is high, the LD contrast test that uses a weighted average of haplotypes or the most probable haplotypes to calculate the LD is recommended, but otherwise the LD contrast test that uses the composite LD is recommended. We conclude that, even though the difference in allele frequencies is usually the most informative test except in the case of a recessive disease, the LD contrast test can be more powerful if the markers are dense enough.

A functional polymorphism in estrogen receptor alpha gene is associated with Japanese methamphetamine induced psychosis

BACKGROUND

A recent study reported an association between rs2234693, which influences enhancer activity levels in estrogen receptor alpha gene (ESR1), and schizophrenia. This study reported that schizophrenic patients with the CC genotype have significantly lower ESR1 mRNA levels in the prefrontal cortex than patients with other genotypes. The symptoms of methamphetamine induced psychosis are similar to those of paranoid type schizophrenia. Therefore, we conducted an association analysis of rs2234693 with Japanese methamphetamine induced psychosis patients.

METHOD

Using rs2234693, we conducted a genetic association analysis of case-control samples (197 methamphetamine induced psychosis patients and 197 healthy controls). The age and sex of the control subjects did not differ from those of the methamphetamine induced psychosis patients.

RESULTS

We detected a significant association between ESR1 and methamphetamine induced psychosis patients in allele/genotype-wise analysis. For further interpretation of these associations, we performed single marker analysis of subjects divided by sex. Rs2234693 was associated with male methamphetamine induced psychosis.

DISCUSSION

Our results suggest that rs2234693 in ESR1 may play a role in the pathophysiology of Japanese methamphetamine induced psychosis patients.

Family-Based Association Testing of OCD-associated SNPs of SLC1A1 in an autism sample

Reports identified the neuronal glutamate transporter gene, SLC1A1 (OMIM 133550, chromosome 9p24), as a positional and functional candidate gene for obsessive-compulsive disorder (OCD). The presence of obsessions and compulsions similar to OCD in autism, the identification of this region in a genome-wide linkage analysis of individuals with autism spectrum disorders (ASDs), and the hypothesized role of glutamate in ASDs make SLC1A1 a candidate gene for ASD as well. To test for association between SLC1A1 and autism, we typed three single nucleotide polymorphisms (SNPs, rs301430, rs301979, rs301434) previously associated with OCD in 86 strictly defined trios with autism. Family-Based Association Tests (FBAT) with additive and recessive models were used to check for association. Additionally, an rs301430-rs301979 haplotype identified for OCD was investigated. FBAT revealed nominally significant association between autism and one SNP under a recessive model. The G allele of rs301979 was undertransmitted (equivalent to overtransmission of the C allele under a dominant model) to individuals with autism (Z=-2.47, P=0.01). The G allele was also undertransmitted in the T-G haplotype under the recessive model (Z=-2.41, P=0.02). Both findings were also observed in the male-only sample. However, they did not withstand correction for multiple comparisons.

A likelihood ratio test of population Hardy-Weinberg equilibrium for case-control studies

Testing Hardy-Weinberg equilibrium (HWE) in the control group is commonly used to detect genotyping errors in genetic association studies. We propose a likelihood ratio test for testing HWE in the study population using both case and control samples. This test incorporates underlying association models. Another feature is that, when we infer the disease-genotype association, we explicitly incorporate HWE or a possible departure from Hardy-Weinberg equilibrium (DHWE) into the model. Our unified framework enables us to infer the disease-genotype association when a detected DHWE needs to be part of the model after causes for the DHWE are explored. Real data sets are used to illustrate the application of the methodology and its implication in genetic association studies. Our analysis and interpretation touch on issues such as genotyping errors, population selection, population stratification, or the study sampling plan, that all could be the cause of DHWE.

Moderation of antidepressant response by the serotonin transporter gene

BACKGROUND

There have been conflicting reports on whether the length polymorphism in the promoter of the serotonin transporter gene (5-HTTLPR) moderates the antidepressant effects of selective serotonin reuptake inhibitors (SSRIs). We hypothesised that the pharmacogenetic effect of 5-HTTLPR is modulated by gender, age and other variants in the serotonin transporter gene.

AIMS

To test the hypothesis that the 5-HTTLPR differently influences response to escitalopram (an SSRI) compared with nortriptyline (a noradrenaline reuptake inhibitor).

METHOD

The 5-HTTLPR and 13 additional markers across the serotonin transporter gene were genotyped in 795 adults with moderate-to-severe depression treated with escitalopram or nortriptyline in the Genome Based Therapeutic Drugs for Depression (GENDEP) project.

RESULTS

The 5-HTTLPR moderated the response to escitalopram, with long-allele carriers improving more than short-allele homozygotes. A significant three-way interaction between 5-HTTLPR, drug and gender indicated that the effect was concentrated in males treated with escitalopram. The single-nucleotide polymorphism rs2020933 also influenced outcome.

CONCLUSIONS

The effect of 5-HTTLPR on antidepressant response is SSRI specific conditional on gender and modulated by another polymorphism at the 5' end of the serotonin transporter gene.

Genetic variants of GSNOR and ADRB2 influence response to albuterol in African-American children with severe asthma

African Americans are disproportionately affected by asthma. Social and economic factors play a role in this disparity, but there is evidence that genetic factors may also influence the development of asthma and response to therapy in African American children. Our hypothesis is that variations in asthma related genes contribute to the observed asthma disparities by influencing the response to asthma-specific therapy. In order to test this hypothesis, we characterized the clinical response to asthma-specific therapy in 107 African American children who presented to the emergency room in status asthmaticus, with a primary outcome indicator of length of time on continuous albuterol. Single locus analysis indicated that genotype variation in glutathione-dependent S-nitrosoglutathione reductase (GSNOR) is associated with a decreased response to asthma treatment in African American children. A post hoc multi-locus analysis revealed that a combination of four single nucleotide polymorphisms (SNPs) within GSNOR, adrenergic receptor beta 2, and carbamoyl phosphate synthetase-1 give a 70% predictive value for lack of response to therapy. This predictive model needs replication in other cohorts of patients with asthma, but suggests gene-gene interactions may have greater significance than that identified with single variants. Our findings also suggest that genetic variants may contribute to the observed population disparities in asthma.

Recovering unused information in genome-wide association studies: the benefit of analyzing SNPs out of Hardy-Weinberg equilibrium

Although the rapid advancements in high throughput genotyping technology have made genome-wide association studies possible, these studies remain an expensive undertaking, especially when considering the large sample sizes necessary to find the small to moderate effect sizes that define complex diseases. It is therefore prudent to utilize all possible information contained in a genome-wide scan. We propose a straightforward analytical approach that tests often unused SNP data without sacrificing statistical validity. We simulate genotype miscalls under a variety of models consistent with observed miscall rates and test for departures from HWE using the standard Pearson's chi(2)-test. We find that true disease susceptibility loci subjected to various patterns of genotype miscalls can be largely out of HWE and, thus, be candidates for removal before association testing. These loci, we demonstrate, can maintain sufficient statistical power even under extreme error models. We additionally show that random miscalls of null SNPs, independent of the phenotype, do not induce bias in case-control or cohort studies, and we suggest that a significant HWE test should not prevent a SNP from being tested when conducting genome-wide association studies in these scenarios. However, association findings for SNPs that are out of HWE must be treated more carefully than 'regular' findings, for example, by re-genotyping the SNP in the same study using a different genotyping technology.

Association study of phosphodiesterase genes in the Sequenced Treatment Alternatives to Relieve Depression sample

A recent study has reported a significant association of variants in phosphodiesterase (PDE) genes with antidepressant treatment outcome in a Mexican American sample. We set out to investigate these findings in a large sample of patients from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study. STAR*D is a longitudinal study of antidepressant outcome in depressed outpatients. We genotyped three single nucleotide polymorphisms (SNPs) in PDE11A (rs1880916), PDE1A (rs1549870), and PDE9A (rs729861) for replication and we also report three additional SNPs in PDE11A (rs3770016, rs4893975, rs6433687) that had been genotyped for a previous study. Single marker analysis of remission within the Hispanic subsamples (n=268) revealed no significant evidence of association with markers in PDE11A, PDE9A, or PDE1A. Additional analyses of remission within the total STAR*D sample (n=1914) were also largely negative, as were analyses utilizing a narrower definition of remission. Haplotype analyses were carried out with the four PDE11A SNPs we genotyped; these also failed to show significant evidence of association in the STAR*D sample. In conclusion, we could not reproduce the reported association between PDE genes and antidepressant outcome in a sample of participants comparable to that reported previously. We conclude that PDE11A, PDE9A, and PDE1A are unlikely to play an important role in antidepressant outcome in this sample.

Bayesian methods for examining Hardy-Weinberg equilibrium

Testing for Hardy-Weinberg equilibrium is ubiquitous and has traditionally been carried out via frequentist approaches. However, the discreteness of the sample space means that uniformity of p-values under the null cannot be assumed, with enumeration of all possible counts, conditional on the minor allele count, offering a computationally expensive way of p-value calibration. In addition, the interpretation of the subsequent p-values, and choice of significance threshold depends critically on sample size, because equilibrium will always be rejected at conventional levels with large sample sizes. We argue for a Bayesian approach using both Bayes factors, and the examination of posterior distributions. We describe simple conjugate approaches, and methods based on importance sampling Monte Carlo. The former are convenient because they yield closed-form expressions for Bayes factors, which allow their application to a large number of single nucleotide polymorphisms (SNPs), in particular in genome-wide contexts. We also describe straightforward direct sampling methods for examining posterior distributions of parameters of interest. For large numbers of alleles at a locus we resort to Markov chain Monte Carlo. We discuss a number of possibilities for prior specification, and apply the suggested methods to a number of real datasets.