Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient

The Relationship Between Time-Varying Achieved HbA1c and Risk of Coronary Events Depends on Haptoglobin Phenotype Among White and Black ACCORD Participants

OBJECTIVE

Intensive glycemic therapy reduced coronary artery disease (CAD) events among White participants in the Action to Control Cardiovascular Risk in Diabetes (ACCORD) study with the haptoglobin (Hp)2-2 phenotype, while participants without the Hp2-2 phenotype had no CAD benefit. The association between achieved glycated hemoglobin (HbA1c) and CAD for each Hp phenotype remains unknown.

RESEARCH DESIGN AND METHODS

Achieved HbA1c was similar in each phenotype throughout the study. Prospectively collected HbA1c data (categorized as <6.0%, 6.0-6.5%, 6.6-6.9%, or ≥8.0% compared with 7.0-7.9%) from the ACCORD study, updated every 4 months over a median of 4.7 years, were analyzed in relation to CAD in the Hp2-2 (n = 3,322) and non-Hp2-2 (n = 5,949) phenotypes separately overall, and within White (63%, 37% Hp2-2) and Black (19%, 26% Hp2-2) participants using Cox proportional hazards regression with time-varying covariables.

RESULTS

Compared with HbA1c of 7.0-7.9%, having HbA1c ≥8.0% was associated with CAD risk among White (adjusted HR [aHR] 1.43, 95% CI 1.03-1.98) and Black (2.86, 1.09-7.51) participants with the Hp2-2 phenotype, but not when all Hp2-2 participants were combined overall (1.30, 0.99-1.70), and not among participants without the Hp2-2 phenotype. HbA1c <7.0% was not associated with a lower risk of CAD for any Hp phenotype.

CONCLUSIONS

Achieving HbA1c >8.0% compared with 7.0-7.9% was consistently associated with incident CAD risk among White and Black ACCORD participants with the Hp2-2 phenotype, while no association was observed among participants without the Hp2-2 phenotype. We found no evidence that HbA1c concentration <7.0% prevents CAD in either Hp phenotype group.

Rank-invariant estimation of inbreeding coefficients

The two alleles an individual carries at a locus are identical by descent (ibd) if they have descended from a single ancestral allele in a reference population, and the probability of such identity is the inbreeding coefficient of the individual. Inbreeding coefficients can be predicted from pedigrees with founders constituting the reference population, but estimation from genetic data is not possible without data from the reference population. Most inbreeding estimators that make explicit use of sample allele frequencies as estimates of allele probabilities in the reference population are confounded by average kinships with other individuals. This means that the ranking of those estimates depends on the scope of the study sample and we show the variation in rankings for common estimators applied to different subdivisions of 1000 Genomes data. Allele-sharing estimators of within-population inbreeding relative to average kinship in a study sample, however, do have invariant rankings across all studies including those individuals. They are unbiased with a large number of SNPs. We discuss how allele sharing estimates are the relevant quantities for a range of empirical applications.

A test for deviations from expected genotype frequencies on the X chromosome for sex-biased admixed populations

Genome-wide scans for deviations from expected genotype frequencies, as determined by the Hardy-Weinberg equilibrium (HWE), are commonly applied to detect genotyping errors and deviations from random mating. In contrast to the autosomes, genotype frequencies on the X chromosome do not reach HWE within a single generation. Instead, if allele frequencies in males and females initially differ, they oscillate for a few generations toward equilibrium. Allele frequency differences between the sexes are expected in populations that have experienced recent sex-biased admixture, namely, their male and female founders differed in ancestry. Sex-biased admixture does not allow testing for HWE on X, because deviations are naturally expected, even under random mating (post admixture) and error-free genotyping. In this paper, we develop a likelihood ratio test and a χ² test to detect deviations from expected genotype frequencies on X, beyond natural deviations due to sex-biased admixture. We demonstrate by simulations that our tests are powerful for detecting deviations due to non-random mating, while at the same time they do not reject the null under historical sex-biased admixture and random mating thereafter. We also demonstrate that when applied to 1000 Genomes project populations, our likelihood ratio test rejects fewer SNPs than other tests, but we describe limitations in the interpretation of the results.

A Bayesian test for Hardy-Weinberg equilibrium of biallelic X-chromosomal markers

The X chromosome is a relatively large chromosome, harboring a lot of genetic information. Much of the statistical analysis of X-chromosomal information is complicated by the fact that males only have one copy. Recently, frequentist statistical tests for Hardy-Weinberg equilibrium have been proposed specifically for dealing with markers on the X chromosome. Bayesian test procedures for Hardy-Weinberg equilibrium for the autosomes have been described, but Bayesian work on the X chromosome in this context is lacking. This paper gives the first Bayesian approach for testing Hardy-Weinberg equilibrium with biallelic markers at the X chromosome. Marginal and joint posterior distributions for the inbreeding coefficient in females and the male to female allele frequency ratio are computed, and used for statistical inference. The paper gives a detailed account of the proposed Bayesian test, and illustrates it with data from the 1000 Genomes project. In that implementation, a novel approach to tackle multiple testing from a Bayesian perspective through posterior predictive checks is used.

Hybrid Origins of Citrus Varieties Inferred from DNA Marker Analysis of Nuclear and Organelle Genomes

Most indigenous citrus varieties are assumed to be natural hybrids, but their parentage has so far been determined in only a few cases because of their wide genetic diversity and the low transferability of DNA markers. Here we infer the parentage of indigenous citrus varieties using simple sequence repeat and indel markers developed from various citrus genome sequence resources. Parentage tests with 122 known hybrids using the selected DNA markers certify their transferability among those hybrids. Identity tests confirm that most variant strains are selected mutants, but we find four types of kunenbo (Citrus nobilis) and three types of tachibana (Citrus tachibana) for which we suggest different origins. Structure analysis with DNA markers that are in Hardy-Weinberg equilibrium deduce three basic taxa coinciding with the current understanding of citrus ancestors. Genotyping analysis of 101 indigenous citrus varieties with 123 selected DNA markers infers the parentages of 22 indigenous citrus varieties including Satsuma, Temple, and iyo, and single parents of 45 indigenous citrus varieties, including kunenbo, C. ichangensis, and Ichang lemon by allele-sharing and parentage tests. Genotyping analysis of chloroplast and mitochondrial genomes using 11 DNA markers classifies their cytoplasmic genotypes into 18 categories and deduces the combination of seed and pollen parents. Likelihood ratio analysis verifies the inferred parentages with significant scores. The reconstructed genealogy identifies 12 types of varieties consisting of Kishu, kunenbo, yuzu, koji, sour orange, dancy, kobeni mikan, sweet orange, tachibana, Cleopatra, willowleaf mandarin, and pummelo, which have played pivotal roles in the occurrence of these indigenous varieties. The inferred parentage of the indigenous varieties confirms their hybrid origins, as found by recent studies.

A composite likelihood approach in testing for Hardy Weinberg Equilibrium using family-based genetic survey data

In population-based household surveys, for example, the National Health and Nutrition Examination Survey, households are often sampled by stratified multistage cluster sampling, and multiple individuals related by blood are often sampled within households. Therefore, genetic data collected from these population-based household surveys, called National Genetic Household Surveys, can be correlated because of two levels of correlation. One level of correlation is caused by the multistage geographical cluster sampling and the other is caused by biological inheritance among participants within the same sampled family. In this paper, we develop an efficient Hardy Weinberg Equilibrium (HWE) test utilizing pairwise composite likelihood methods that incorporate the sample weighting effect induced by the differential selection probabilities in complex sample designs, as well as the two-level clustering (correlation) effects described above. Monte Carlo simulation studies show that the proposed HWE test maintains the nominal levels, and is more powerful than existing methods (Li et al. 2011) under various (non)informative sample designs that depend on genotypes (explicitly or implicitly), family relationships or both, especially when within-household sampling depends on the genotypes. The developed tests are further evaluated using simulated genetic data based on the Hispanic Health and Nutrition Survey. Copyright © 2016 John Wiley & Sons, Ltd.

Testing for Hardy-Weinberg equilibrium at biallelic genetic markers on the X chromosome

Testing genetic markers for Hardy–Weinberg equilibrium (HWE) is an important tool for detecting genotyping errors in large-scale genotyping studies. For markers at the X chromosome, typically the χ² or exact test is applied to the females only, and the hemizygous males are considered to be uninformative. In this paper we show that the males are relevant, because a difference in allele frequency between males and females may indicate HWE not to hold. The testing of markers on the X chromosome has received little attention, and in this paper we lay down the foundation for testing biallelic X-chromosomal markers for HWE. We develop four frequentist statistical test procedures for X-linked markers that take both males and females into account: the χ² test, likelihood ratio test, exact test and permutation test. Exact tests that include males are shown to have a better Type I error rate. Empirical data from the GENEVA project on venous thromboembolism is used to illustrate the proposed tests. Results obtained with the new tests differ substantially from tests that are based on female genotype counts only. The new tests detect differences in allele frequencies and seem able to uncover additional genotyping error that would have gone unnoticed in HWE tests based on females only.

A Bayesian Approach to Inferring Rates of Selfing and Locus-Specific Mutation

We present a Bayesian method for characterizing the mating system of populations reproducing through a mixture of self-fertilization and random outcrossing. Our method uses patterns of genetic variation across the genome as a basis for inference about reproduction under pure hermaphroditism, gynodioecy, and a model developed to describe the self-fertilizing killifish Kryptolebias marmoratus. We extend the standard coalescence model to accommodate these mating systems, accounting explicitly for multilocus identity disequilibrium, inbreeding depression, and variation in fertility among mating types. We incorporate the Ewens sampling formula (ESF) under the infinite-alleles model of mutation to obtain a novel expression for the likelihood of mating system parameters. Our Markov chain Monte Carlo (MCMC) algorithm assigns locus-specific mutation rates, drawn from a common mutation rate distribution that is itself estimated from the data using a Dirichlet process prior model. Our sampler is designed to accommodate additional information, including observations pertaining to the sex ratio, the intensity of inbreeding depression, and other aspects of reproduction. It can provide joint posterior distributions for the population-wide proportion of uniparental individuals, locus-specific mutation rates, and the number of generations since the most recent outcrossing event for each sampled individual. Further, estimation of all basic parameters of a given model permits estimation of functions of those parameters, including the proportion of the gene pool contributed by each sex and relative effective numbers.

Estimation of divergence from Hardy-Weinberg form

The Hardy–Weinberg (HW) principle explains how random mating (RM) can produce and maintain a population in equilibrium, that is, with constant genotypic proportions. When proportions diverge from HW form, it is of interest to estimate the fixation index F, which reflects the degree of divergence. Starting from a sample of genotypic counts, a mixed procedure gives first the orthodox estimate of gene frequency q and then a Bayesian estimate of F, based on a credible prior distribution of F, which is described here.

Population-genetic influences on genomic estimates of the inbreeding coefficient: a global perspective

BACKGROUND/AIMS

Culturally driven marital practices provide a key instance of an interaction between social and genetic processes in shaping patterns of human genetic variation, producing, for example, increased identity by descent through consanguineous marriage. A commonly used measure to quantify identity by descent in an individual is the inbreeding coefficient, a quantity that reflects not only consanguinity, but also other aspects of kinship in the population to which the individual belongs. Here, in populations worldwide, we examine the relationship between genomic estimates of the inbreeding coefficient and population patterns in genetic variation.

METHODS

Using genotypes at 645 microsatellites, we compare inbreeding coefficients from 5,043 individuals representing 237 populations worldwide to demographic consanguinity frequency estimates available for 26 populations as well as to other quantities that can illuminate population-genetic influences on inbreeding coefficients.

RESULTS

We observe higher inbreeding coefficient estimates in populations and geographic regions with known high levels of consanguinity or genetic isolation and in populations with an increased effect of genetic drift and decreased genetic diversity with increasing distance from Africa. For the small number of populations with specific consanguinity estimates, we find a correlation between inbreeding coefficients and consanguinity frequency (r = 0.349, p = 0.040).

CONCLUSIONS

The results emphasize the importance of both consanguinity and population-genetic factors in influencing variation in inbreeding coefficients, and they provide insight into factors useful for assessing the effect of consanguinity on genomic patterns in different populations.

Testing Hardy-Weinberg equilibrium with a simple root-mean-square statistic

We provide evidence that, in certain circumstances, a root-mean-square test of goodness of fit can be significantly more powerful than state-of-the-art tests in detecting deviations from Hardy-Weinberg equilibrium. Unlike Pearson's $\chi ^2$ test, the log-likelihood-ratio test, and Fisher's exact test, which are sensitive to relative discrepancies between genotypic frequencies, the root-mean-square test is sensitive to absolute discrepancies. This can increase statistical power, as we demonstrate using benchmark data sets and simulations, and through asymptotic analysis.

A comparison of tests for Hardy-Weinberg Equilibrium in national genetic household surveys

Background

This study is motivated by National Household Surveys that collect genetic data, in which complex samples (e.g. stratified multistage cluster sample), partially from the same family, are selected. In addition to the differential selection probabilities of selecting households and persons within the sampled households, there are two levels of correlations of the collected genetic data in National Genetic Household Surveys (NGHS). The first level of correlation is induced by the hierarchical geographic clustered sampling of households and the second level of correlation is induced by biological inheritances from individuals sampled in the same household.

Results

To test for Hardy-Weinberg Equilibrium (HWE) in NGHS, two test statistics, the CCS method [1] and the QS method [2], appear to be the only existing methods that take account of both correlations. In this paper, I evaluate both methods in terms of the test size and power under a variety of complex designs with different weighting schemes and varying magnitudes of the two correlation effects. Both methods are applied to a real data example from the Hispanic Health and Nutrition Examination Survey with simulated genotype data.

Conclusions

The QS method maintains the nominal size well and consistently achieves higher power than the CCS method in testing HWE under a variety of sample designs, and therefore is recommended for testing HWE of genetic survey data with complex designs.

Testing Hardy–Weinberg disequilibrium using the generalized linear model

Current methods for detecting Hardy–Weinberg disequilibrium (HWD) only deal with one locus at a time. We developed a method that can jointly detect HWD for multiple loci. The method was developed under the generalized linear model (GLM) using the probit link function. When applied to a single locus, the new method is more powerful than the exact test. When applied to two or more loci, the method can reduce false positives caused by linkage disequilibrium (LD). We applied the method to 24 single nucleotide polymorphism (SNP) markers of a single human gene and eliminated several false positive HWDs due to LD. We developed an R package ‘hwdglm’ for joint HWD detection, which can be downloaded from our personal website (www.statgen.ucr.edu).

Testing for Hardy Weinberg Equilibrium in national household surveys that collect family-based genetic data

In population-based household surveys, for example, the National Health and Nutrition Examination Survey (NHANES), blood-related individuals are often sampled from the same household. Therefore, genetic data collected from national household surveys are often correlated due to two levels of clustering (correlation) with one induced by the multistage geographical cluster sampling, and the other induced by biological inheritance among multiple participants within the same sampled household. In this paper, we develop efficient statistical methods that consider the weighting effect induced by the differential selection probabilities in complex sample designs, as well as the clustering (correlation) effects described above. We examine and compare the magnitude of each level of clustering effects under different scenarios and identify the scenario under which the clustering effect induced by one level dominates the other. The proposed method is evaluated via Monte Carlo simulation studies and illustrated using the Hispanic Health and Nutrition Survey (HHANES) with simulated genotype data.

A new likelihood estimator and its comparison with moment estimators of individual genome-wide diversity

The inbreeding coefficient of an individual, F, is one of the central parameters in population genetics theory. It has found important applications in evolutionary biology, conservation and ecology, such as the study of inbreeding depression. In the absence of detailed and reliable pedigree records, researchers have developed quite a few estimators to estimate F or the genome-wide homozygosity from genetic marker data. The statistical properties and comparative performances of these metrics are rarely known, however, which impedes an informed choice of the most appropriate one in practical applications. In this investigation, I propose a new likelihood F estimator that makes efficient use of marker information and takes into account of allelic dropouts, null alleles and prior knowledge of inbreeding. I compare the likelihood estimator with three moment estimators of F and three metrics of genomic homozygosity (or heterozygosity) by analysing both simulated and empirical datasets. It is shown that the likelihood estimator invariably outperforms the other estimators and metrics across all datasets analysed. For a typical dataset in heterozygosity-fitness correlation studies involving 10-20 microsatellites and 50 individuals, the correlation between the likelihood estimator and F (the simulated true inbreeding coefficient) is about 8 ∼ 35% higher than that between the moment estimators and F. A frequently applied metric, multilocus heterozygosity (MLH), and an F estimator based on the consideration of the proportion of alleles in homozygous conditions, [F R'), are shown to have particularly poor performances. The low correlation between MLH and fitness traits, which is widely observed in numerous empirical studies, might be partially caused by the adoption of this inefficient estimator of genomic inbreeding.

Increased inbreeding and strong kinship structure in Taxus baccata estimated from both AFLP and SSR data

Habitat fragmentation can have severe genetic consequences for trees, such as increased inbreeding and decreased effective population size. In effect, local populations suffer from reduction of genetic variation, and thus loss of adaptive capacity, which consequently increases their risk of extinction. In Europe, Taxus baccata is among a number of tree species experiencing strong habitat fragmentation. However, there is little empirical data on the population genetic consequences of fragmentation for this species. This study aimed to characterize local genetic structure in two natural remnants of English yew in Poland based on both amplified fragment length polymorphism (AFLP) and microsatellite (SSR) markers. We introduced a Bayesian approach that estimates the average inbreeding coefficient using AFLP (dominant) markers. Results showed that, in spite of high dispersal potential (bird-mediated seed dispersal and wind-mediated pollen dispersal), English yew populations show strong kinship structure, with a spatial extent of 50-100 m, depending on the population. The estimated inbreeding levels ranged from 0.016 to 0.063, depending on the population and marker used. Several patterns were evident: (1) AFLP markers showed stronger kinship structure than SSRs; (2) AFLP markers provided higher inbreeding estimates than SSRs; and (3) kinship structure and inbreeding were more pronounced in denser populations regardless of the marker used. Our results suggest that, because both kinship structure and (bi-parental) inbreeding exist in populations of English yew, gene dispersal can be fairly limited in this species. Furthermore, at a local scale, gene dispersal intensity can be more limited in a dense population.

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.

A Hardy-Weinberg equilibrium test for analyzing population genetic surveys with complex sample designs

Testing for deviations from Hardy-Weinberg equilibrium is a widely recommended practice for population-based genetic association studies. However, current methods for this test assume a simple random sample and may not be appropriate for sample surveys with complex survey designs. In this paper, the authors present a test for Hardy-Weinberg equilibrium that adjusts for the sample weights and correlation of data collected in complex surveys. The authors perform this test by using a simple adjustment to procedures developed to analyze data from complex survey designs available within the SAS statistical software package (SAS Institute, Inc., Cary, North Carolina). Using 90 genetic markers from the Third National Health and Nutrition Examination Survey, the authors found that survey-adjusted and -unadjusted estimates of the disequilibrium coefficient were generally similar within self-reported races/ethnicities. However, estimates of the variance of the disequilibrium coefficient were significantly different between the 2 methods. Because the results of the survey-adjusted tests account for correlation among participants sampled within the same cluster, and the possibility of having related individuals sampled from the same household, the authors recommend use of this test when analyzing genetic data originating from sample surveys with complex survey designs to assess deviations from Hardy-Weinberg equilibrium.

STrengthening the REporting of Genetic Association Studies (STREGA)--an extension of the STROBE statement

Making sense of rapidly evolving evidence on genetic associations is crucial to making genuine advances in human genomics and the eventual integration of this information in the practice of medicine and public health. Assessment of the strengths and weaknesses of this evidence, and hence the ability to synthesize it, has been limited by inadequate reporting of results. The STrengthening the REporting of Genetic Association studies (STREGA) initiative builds on the STrengthening the Reporting of OBservational Studies in Epidemiology (STROBE) Statement and provides additions to 12 of the 22 items on the STROBE checklist. The additions concern population stratification, genotyping errors, modelling haplotype variation, Hardy-Weinberg equilibrium, replication, selection of participants, rationale for choice of genes and variants, treatment effects in studying quantitative traits, statistical methods, relatedness, reporting of descriptive and outcome data, and the volume of data issues that are important to consider in genetic association studies. The STREGA recommendations do not prescribe or dictate how a genetic association study should be designed but seek to enhance the transparency of its reporting, regardless of choices made during design, conduct, or analysis.

Bayesian statistical methods for genetic association studies

Bayesian statistical methods have recently made great inroads into many areas of science, and this advance is now extending to the assessment of association between genetic variants and disease or other phenotypes. We review these methods, focusing on single-SNP tests in genome-wide association studies. We discuss the advantages of the Bayesian approach over classical (frequentist) approaches in this setting and provide a tutorial on basic analysis steps, including practical guidelines for appropriate prior specification. We demonstrate the use of Bayesian methods for fine mapping in candidate regions, discuss meta-analyses and provide guidance for refereeing manuscripts that contain Bayesian analyses.

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.

STrengthening the REporting of Genetic Association studies (STREGA)--an extension of the STROBE statement

Making sense of rapidly evolving evidence on genetic associations is crucial to making genuine advances in human genomics and the eventual integration of this information in the practice of medicine and public health. Assessment of the strengths and weaknesses of this evidence, and hence the ability to synthesize it, has been limited by inadequate reporting of results. The STrengthening the REporting of Genetic Association studies (STREGA) initiative builds on the STrengthening the Reporting of OBservational Studies in Epidemiology (STROBE) Statement and provides additions to 12 of the 22 items on the STROBE checklist. The additions concern population stratification, genotyping errors, modelling haplotype variation, Hardy-Weinberg equilibrium, replication, selection of participants, rationale for choice of genes and variants, treatment effects in studying quantitative traits, statistical methods, relatedness, reporting of descriptive and outcome data and the volume of data issues that are important to consider in genetic association studies. The STREGA recommendations do not prescribe or dictate how a genetic association study should be designed, but seek to enhance the transparency of its reporting, regardless of choices made during design, conduct or analysis.

STrengthening the REporting of Genetic Association Studies (STREGA): an extension of the STROBE statement

Making sense of rapidly evolving evidence on genetic associations is crucial to making genuine advances in human genomics and the eventual integration of this information in the practice of medicine and public health. Assessment of the strengths and weaknesses of this evidence, and hence the ability to synthesize it, has been limited by inadequate reporting of results. The STrengthening the REporting of Genetic Association studies (STREGA) initiative builds on the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) Statement and provides additions to 12 of the 22 items on the STROBE checklist. The additions concern population stratification, genotyping errors, modelling haplotype variation, Hardy-Weinberg equilibrium, replication, selection of participants, rationale for choice of genes and variants, treatment effects in studying quantitative traits, statistical methods, relatedness, reporting of descriptive and outcome data, and the volume of data issues that are important to consider in genetic association studies. The STREGA recommendations do not prescribe or dictate how a genetic association study should be designed but seek to enhance the transparency of its reporting, regardless of choices made during design, conduct, or analysis.

Strengthening the reporting of genetic association studies (STREGA): an extension of the STROBE statement

Making sense of rapidly evolving evidence on genetic associations is crucial to making genuine advances in human genomics and the eventual integration of this information in the practice of medicine and public health. Assessment of the strengths and weaknesses of this evidence, and hence the ability to synthesize it, has been limited by inadequate reporting of results. The STrengthening the REporting of Genetic Association studies (STREGA) initiative builds on the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) Statement and provides additions to 12 of the 22 items on the STROBE checklist. The additions concern population stratification, genotyping errors, modeling haplotype variation, Hardy–Weinberg equilibrium, replication, selection of participants, rationale for choice of genes and variants, treatment effects in studying quantitative traits, statistical methods, relatedness, reporting of descriptive and outcome data, and the volume of data issues that are important to consider in genetic association studies. The STREGA recommendations do not prescribe or dictate how a genetic association study should be designed but seek to enhance the transparency of its reporting, regardless of choices made during design, conduct, or analysis.

Quantifying inbreeding in natural populations of hermaphroditic organisms

We review molecular methods for estimating selfing rates and inbreeding in populations. Two main approaches are available: the population structure approach (PSA) and progeny-array approach (PAA). The PSA approach relies on single-generation samples and produces estimates that integrate the inbreeding history over several generations, but is based on strong assumptions (for example, inbreeding equilibrium). The PSA has classically relied on single-locus inbreeding coefficients averaged over loci. Unfortunately PSA estimates are very sensitive to technical problems such as the occurrence of null alleles at one or more of the loci. Consequently inbreeding might be substantially overestimated, especially in outbred populations. However, the robustness of the PSA has recently been greatly improved by the development of multilocus methods free of such bias. The PAA, on the other hand, is based on the comparison between offspring and mother genotypes. As a consequence, PAA estimates do not reflect long-term inbreeding history but only recent mating events of the maternal individuals studied ('here and now' selfing). In addition to selfing rates, the PAA allows estimating other mating system parameters, including biparental inbreeding and the correlation of selfing among sibs. Although PAA estimates could also be biased by technical problems, incompatibilities between the mother's genotype and her offspring allow the identification and correction of such bias. For all methods, we provide guidelines on the required number of loci and sample sizes. We conclude that the PSA and PAA are equally robust, provided multilocus information is used. Although experimental constraints may make the PAA more demanding, especially in animals, the two methods provide complementary information, and can fruitfully be conducted together.

Reliable selfing rate estimates from imperfect population genetic data

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies (FIS) and obtain the selfing rate s from FIS = s/(2 - s), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of FIS and free of technical biases. Their statistical power and precision are comparable to those of FIS, although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not FIS. We analyse four real data sets spanning a range of mating systems. In two examples, we obtain s = 0 despite positive FIS, strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and user-friendly software called rmes (robust multilocus estimate of selfing) available at http://ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progeny-array approaches, to investigate selfing rates.

A Markov chain Monte Carlo approach for joint inference of population structure and inbreeding rates from multilocus genotype data

Nonrandom mating induces correlations in allelic states within and among loci that can be exploited to understand the genetic structure of natural populations (Wright 1965). For many species, it is of considerable interest to quantify the contribution of two forms of nonrandom mating to patterns of standing genetic variation: inbreeding (mating among relatives) and population substructure (limited dispersal of gametes). Here, we extend the popular Bayesian clustering approach STRUCTURE (Pritchard et al. 2000) for simultaneous inference of inbreeding or selfing rates and population-of-origin classification using multilocus genetic markers. This is accomplished by eliminating the assumption of Hardy-Weinberg equilibrium within clusters and, instead, calculating expected genotype frequencies on the basis of inbreeding or selfing rates. We demonstrate the need for such an extension by showing that selfing leads to spurious signals of population substructure using the standard STRUCTURE algorithm with a bias toward spurious signals of admixture. We gauge the performance of our method using extensive coalescent simulations and demonstrate that our approach can correct for this bias. We also apply our approach to understanding the population structure of the wild relative of domesticated rice, Oryza rufipogon, an important partially selfing grass species. Using a sample of n = 16 individuals sequenced at 111 random loci, we find strong evidence for existence of two subpopulations, which correlates well with geographic location of sampling, and estimate selfing rates for both groups that are consistent with estimates from experimental data (s approximately 0.48-0.70).

The merits of testing Hardy-Weinberg equilibrium in the analysis of unmatched case-control data: a cautionary note

Testing for departures from the assumption of Hardy-Weinberg equilibrium (HWE) has been widely recommended as a preliminary step in the analysis of genetic case-control studies. Some authors suggest using a two-stage procedure in which gene/disease associations are ultimately evaluated using either the Pearson chi-square procedure or the Cochran-Armitage test for trend. Other authors go further and encourage investigators to discard data that are in violation of HWE, essentially using the test as a tool for identifying genotyping errors. In this paper we show that 1) testing for HWE should not be used as a tool to identify genotyping errors; and 2) it is not necessary, and possibly even harmful, to test the HWE assumption before testing for association between alleles and disease. Instead one should inherently account for deviations from HWE with an adjusted chi-square test statistic, a procedure which in the present context is identical to the trend test. Examples from previous reports are used to illustrate the methodology.

Association between apolipoprotein E polymorphisms and age-related macular degeneration: A HuGE review and meta-analysis

A possible association between apolipoprotein E polymorphisms and age-related macular degeneration has been investigated numerous times, with conflicting results. A previous analysis pooling results from four studies (Schmidt et al., Ophthalmic Genet 2002;23:209-23) suggested an association, but those investigators did not document allele frequencies, the magnitude of the association, or the possible genetic mode of action. Thus, the authors searched MEDLINE from 1966 to December 2005 for any English-language studies reporting genetic associations. Data and study quality were assessed in duplicate. Pooling was performed while checking for heterogeneity and publication bias. Frequencies of the E2 and E4 alleles in Caucasians were approximately 8% and 15%, respectively. Allele- and genotype-based tests of association indicated a risk effect of up to 20% for E2 and a protective effect of up to 40% for E4. E2 appeared to act in a recessive mode and E4 in a dominant mode. There appears to be a differential effect of the E2 and E4 alleles on the risk of age-related macular degeneration, although the possibility of survivor bias needs to be ruled out more definitively.

The appropriate use of subpopulation corrections for differences in endogamous communities

Zhivotovsky et al. [L.A. Zhivotovsky, S. Ahmed, W. Wang, A. Bittles, The forensic DNA implications of genetic differentiation between endogamous communities, Forensic Sci. Int. 119 (2001) 269-272] gave an estimate of 0.13 for the coancestry coefficient, theta in three co-resident Pakistani communities. Wang et al. [W. Wang, S.G. Sullivan, S. Ahmed, D. Chandler, L.A. Zhivotovsky, A.H. Bittles, A genome-based study of consanguinity in three co-resident endogamous Pakistan communities, Ann. Hum. Genet. 94 (2000) 41-49] explain that the sampling is from extended families but conclude that "the present findings show that differentiation resulting from genetic stratification by genetic relatedness can be very pronounced in specific populations and thus be important in the evaluation of forensic DNA evidence." In this paper we present simulation results that show that sampling from families will be expected to produce high values of theta regardless of the population value for theta. A theta value estimated in this way cannot be used in formulae suggested by NRC II [NRC II, National Research Council Committee on DNA Forensic Science, The Evaluation of Forensic DNA Evidence, National Academy Press, Washington, DC, 1996] (Eqs. (1) and (2)) to estimate the match probability for a DNA profile in a subpopulation. Whilst it may have some application to estimating the match probability from the pedigree itself there are superior methods for assigning match probabilities for relatives.

Modeling the effect of inbreeding among founders in linkage analysis

In this paper, we present a unified mathematical model for linkage analysis that allows for inbreeding among founders in all families. The identical by descent (IBD) configuration of each pedigree is modeled as a Markov process containing two parameters; the inverse inbreeding and kinship coefficient and a rate parameter proportional to the inverse expected length of chromosome segments shared IBD by two different founder haplotypes. We use hidden Markov models and define a forward-backward algorithm for computing the conditional IBD-distribution given marker data, thereby extending the multipoint method of Lander and Green [1987. Construction of multilocus genetic maps in humans, Proc. Natl. Acad. Sci. USA 84, 2363-2367] to situations where founders are inbred. Our methodology is valid for arbitrary pedigree structures. Simulation and theoretical approximations for nonparametric linkage (NPL) analysis based on affected sib pairs reveal that NPL scores are inflated and type 1 errors increased when the inbreeding coefficient or rate parameter is underestimated. When the parents are genotyped, we present a general way of modifying the score function to drastically reduce this effect.

Algorithms for Selecting Informative Marker Panels for Population Assignment

Given a set of potential source populations, genotypes of an individual of unknown origin at a collection of markers can be used to predict the correct source population of the individual. For improved efficiency, informative markers can be chosen from a larger set of markers to maximize the accuracy of this prediction. However, selecting the loci that are individually most informative does not necessarily produce the optimal panel. Here, using genotypes from eight species--carp, cat, chicken, dog, fly, grayling, human, and maize--this univariate accumulation procedure is compared to new multivariate "greedy" and "maximin" algorithms for choosing marker panels. The procedures generally suggest similar panels, although the greedy method often recommends inclusion of loci that are not chosen by the other algorithms. In seven of the eight species, when applied to five or more markers, all methods achieve at least 94% assignment accuracy on simulated individuals, with one species--dog--producing this level of accuracy with only three markers, and the eighth species--human--requiring approximately 13-16 markers. The new algorithms produce substantial improvements over use of randomly selected markers; where differences among the methods are noticeable, the greedy algorithm leads to slightly higher probabilities of correct assignment. Although none of the approaches necessarily chooses the panel with optimal performance, the algorithms all likely select panels with performance near enough to the maximum that they all are suitable for practical use.

Heterozygosity, inbreeding and neonatal traits in Soay sheep on St Kilda

We investigated whether birth weight and neonatal survival, a period within which 24% of all mortalities occur, were correlated with levels of inbreeding in St Kilda Soay sheep, using pedigree inbreeding coefficients and four marker-based estimators of inbreeding. None of the inbreeding estimators, either of the offspring, or of their mothers, explained significant variation in a lamb's birth weight or probability of surviving the neonatal period, suggesting low inbreeding depression for these traits. We evaluated the correlation between the marker-based measures of inbreeding and inbreeding coefficients obtained from the Soay pedigree, where paternal links were inferred using the same panel of microsatellite markers. Even when using a relatively complete portion of the pedigree, in which all individuals had known maternal and paternal grandparents, the correlation was found to be weak (r = -0.207, where mean f = 0.0168). These results add support to the recent prediction that when the mean and variance in inbreeding are low in a population, heterozygosity-fitness correlations can be very weak or even undetectable. The pursuit of more detailed pedigrees offers the best prospect for identifying inbreeding depression within this study population.

A Non-iterative Confidence Interval Estimating Procedure for the Intraclass Kappa Statistic with Multinomial Outcomes

We obtain the asymptotic sample variance of the intraclass kappa statistic for multinomial outcome data. A modified Wald type procedure based on this theory is then used for confidence interval construction. The results of a simulation study show that the proposed non-iterative approach performs very well in terms of confidence interval coverage and width for samples as small as 50. The procedure is illustrated with two examples from previously published medical studies.

Hardy–Weinberg equilibrium in genetic association studies: an empirical evaluation of reporting, deviations, and power

We evaluated the testing and reporting of Hardy-Weinberg equilibrium (HWE) in recent genetic association studies, detected how frequently HWE was violated and estimated the power for HWE testing in this literature. Genetic association studies published in 2002 in Nature Genetics, American Journal of Human Genetics, and American Journal of Medical Genetics were assessed. Data were analyzed on 239 biallelic associations using 154 distinct genotype distribution data sets where HWE could be tested. Any information on HWE was given only for 150 (62.8%) associations (92 (59.7%) data sets). Reanalysis of the data showed significant deviation from HWE in the disease-free controls of 20 associations (13 data sets), but only four of them (two data sets) were admitted in the published articles. Another four deviations (in two data sets) were observed in the combined sample of cases and controls of studies where both cases and controls were diseased, and none were reported in the papers. In all six tested multiallelic associations (six data sets), there was violation of HWE, but this was not admitted in the published articles. Power calculations showed that most studies conforming to HWE simply were largely underpowered to detect HWE deviation; for example, power to detect an inbreeding of magnitude F=0.10 exceeded 80% in only 11 (7%) of the data sets being tested. This empirical evidence suggests that, even in high profile genetics journals, testing and reporting for HWE is often neglected and deviations are rarely admitted in the published reports. Moreover, power is limited for HWE testing in most current genetic association studies.

Bayesian approaches for the analysis of population genetic structure: an example from Platanthera leucophaea (Orchidaceae)

We describe four extensions to existing Bayesian methods for the analysis of genetic structure in populations: (i) use of beta distributions to approximate the posterior distribution of f and theta(B); (ii) use of an entropy statistic to describe the amount of information about a parameter derived from the data; (iii) use of the Deviance Information Criterion (DIC) as a model choice criterion for determining whether there is evidence for inbreeding within populations or genetic differentiation among populations; and (iv) use of samples from the posterior distributions for f and theta(B) derived from different data sets to determine whether the estimates are consistent with one another. We illustrate each of these extensions by applying them to data derived from previous allozyme and random amplified polymorphic DNA surveys of an endangered orchid, Platanthera leucophaea, and we conclude that differences in theta(B) from the two data sets may represent differences in the underlying mutational processes.

Polymorphism of LDLR, GYPA, HBGG, D7S8, GC, HLA-DQA1, Ig-JH, D17S30, ApoB and D1S80 loci in northwestern Russians

Allele frequencies for polymarker, HLA-DQA1, Ig-JH, D17S30, ApoB and D1S80 loci and population genetic parameters were obtained from a sample of 501 unrelated individuals born in the northwestern Federal Region of Russia.

Bayesian inference of inbreeding depression in controlled crosses

This study shows how a Gibbs sampling approach can be used for Bayesian inference of inbreeding depression. The method presented is mainly concerned with organisms that can be both selfed and outcrossed. Tests performed on simulated data with unequal variances and missing observations show that the method works well. Real data from the plant Scabiosa canescens is also analyzed.

Bayesian analysis of genetic differentiation between populations

We introduce a Bayesian method for estimating hidden population substructure using multilocus molecular markers and geographical information provided by the sampling design. The joint posterior distribution of the substructure and allele frequencies of the respective populations is available in an analytical form when the number of populations is small, whereas an approximation based on a Markov chain Monte Carlo simulation approach can be obtained for a moderate or large number of populations. Using the joint posterior distribution, posteriors can also be derived for any evolutionary population parameters, such as the traditional fixation indices. A major advantage compared to most earlier methods is that the number of populations is treated here as an unknown parameter. What is traditionally considered as two genetically distinct populations, either recently founded or connected by considerable gene flow, is here considered as one panmictic population with a certain probability based on marker data and prior information. Analyses of previously published data on the Moroccan argan tree (Argania spinosa) and of simulated data sets suggest that our method is capable of estimating a population substructure, while not artificially enforcing a substructure when it does not exist. The software (BAPS) used for the computations is freely available from http://www.rni.helsinki.fi/~mjs.

Hardy-Weinberg equilibrium diagnostics

We propose two diagnostics for the statistical assessment of Hardy-Weinberg equilibrium. One diagnostic is the posterior probability of the complement of the smallest highest posterior density credible region that includes points in the parameter space consistent with the hypothesis of equilibrium. The null hypothesis of equilibrium is to be rejected if this probability is less than a pre-selected critical level. The second diagnostic is the proportion of the parameter space occupied by the highest posterior density credible region associated with the critical level. These Bayesian diagnostics can be interpreted as analogues of the classical types I and II error probabilities. They are broadly applicable: they can be computed for any hypothesis test, using samples of any size generated according to any distribution.

The effect of reproductive compensation on recessive disorders within consanguineous human populations

We investigate the effects of consanguinity and population substructure on genetic health using the UK Asian population as an example. We review and expand upon previous treatments dealing with the deleterious effects of consanguinity on recessive disorders and consider how other factors, such as population substructure, may be of equal importance. For illustration, we quantify the relative risks of recessive lethal disorders by presenting some simple calculations that demonstrate the effect 'reproductive compensation' has on the maintenance of recessive alleles. The results show how reproductive compensation can effectively counteract the purging of deleterious alleles within consanguineous populations. Whereas inbreeding does not elevate the equilibrium frequency of affected individuals, reproductive compensation does. We suggest this effect must be built into interpretations of the incidence of genetic disease within populations such as the UK Asians. Information of this nature will benefit health care workers who inform such communities.

Molecular analysis of the beta-globin gene cluster in the Niokholo Mandenka population reveals a recent origin of the beta(S) Senegal mutation

A large and ethnically well-defined Mandenka sample from eastern Senegal was analyzed for the polymorphism of the beta-globin gene cluster on chromosome 11. Five RFLP sites of the 5' region were investigated in 193 individuals revealing the presence of 10 different haplotypes. The frequency of the sickle-cell anemia causing mutation (beta(S)) in the Mandenka estimated from this sample is 11.7%. This mutation was found strictly associated with the single Senegal haplotype. Approximately 600 bp of the upstream region of the beta-globin gene were sequenced for a subset of 94 chromosomes, showing the presence of four transversions, five transitions, and a composite microsatellite polymorphism. The sequence of 22 beta(S) chromosomes was also identical to the previously defined Senegal haplotype, suggesting that this mutation is very recent. Monte Carlo simulations (allowing for a specific balancing selection model, a logistic growth of the population, and variable initial frequencies of the Senegal haplotype) were used to estimate the age of the beta(S) mutation. Resulting maximum-likelihood estimates are 45-70 generations (1,350-2,100 years) for very different demographic scenarios. Smallest confidence intervals (25-690 generations) are obtained under the hypothesis that the Mandenka population is large (N(e) >5,000) and stationary or that it has undergone a rapid demographic expansion to a current size of >5,000 reproducing individuals, which is quite likely in view of the great diversity found on beta(A) chromosomes.

An unconditional exact test for the Hardy-Weinberg equilibrium law: sample-space ordering using the Bayes factor

Much forensic inference based upon DNA evidence is made assuming that the Hardy-Weinberg equilibrium (HWE) is valid for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, each having advantages and limitations. The limitations become more obvious when testing for deviation within multiallelic DNA loci is attempted. Here we present an exact test for HWE in the biallelic case, based on the ratio of weighted likelihoods under the null and alternative hypotheses, the Bayes factor. This test does not depend on asymptotic results and minimizes a linear combination of type I and type II errors. By ordering the sample space using the Bayes factor, we also define a significance (evidence) index, P value, using the weighted likelihood under the null hypothesis. We compare it to the conditional exact test for the case of sample size n = 10. Using the idea under the method of chi(2) partition, the test is used sequentially to test equilibrium in the multiple allele case and then applied to two short tandem repeat loci, using a real Caucasian data bank, showing its usefulness.

Measuring gametic disequilibrium from multilocus data

We describe a Bayesian approach to analyzing multilocus genotype or haplotype data to assess departures from gametic (linkage) equilibrium. Our approach employs a Markov chain Monte Carlo (MCMC) algorithm to approximate the posterior probability distributions of disequilibrium parameters. The distributions are computed exactly in some simple settings. Among other advantages, posterior distributions can be presented visually, which allows the uncertainties in parameter estimates to be readily assessed. In addition, background knowledge can be incorporated, where available, to improve the precision of inferences. The method is illustrated by application to previously published datasets; implications for multilocus forensic match probabilities and for simple association-based gene mapping are also discussed.