Assumption Of Hardy-Weinberg Equilibrium Research Articles

Statistical methods for haplotype‐based matched case‐control association studies

Kraft et al. [2005] proposed a method for matched haplotype-based association studies and compared the performances of six analytic strategies for estimating the odds ratio parameters using a conditional likelihood function. Zhang et al. [2006] modified the conditional likelihood and proposed a new method for matched haplotype-based association studies. The main assumptions of Zhang et al. were that the disease was rare, the population was in Hardy-Weinberg equilibrium (HWE), and the haplotypes were independent of the covariates and matching variable(s). In this article, we modify the estimation procedure proposed by Zhang et al. and introduce a fixation index so that the assumption of HWE is relaxed. Using the Wald test, we compare the current modified method with the procedure developed by Kraft et al. through simulations. The results show that the modified method is uniformly more powerful than that described in Kraft et al. Furthermore, the results indicate that the modified method is quite robust to the rare disease assumption.

X-APL: An Improved Family-Based Test of Association in the Presence of Linkage for the X Chromosome

Family-based association methods have been developed primarily for autosomal markers. The X-linked sibling transmission/disequilibrium test (XS-TDT) and the reconstruction-combined TDT for X-chromosome markers (XRC-TDT) are the first association-based methods for testing markers on the X chromosome in family data sets. These are valid tests of association in family triads or discordant sib pairs but are not theoretically valid in multiplex families when linkage is present. Recently, XPDT and XMCPDT, modified versions of the pedigree disequilibrium test (PDT), were proposed. Like the PDT, XPDT compares genotype transmissions from parents to affected offspring or genotypes of discordant siblings; however, the XPDT can have low power if there are many missing parental genotypes. XMCPDT uses a Monte Carlo sampling approach to infer missing parental genotypes on the basis of true or estimated population allele frequencies. Although the XMCPDT was shown to be more powerful than the XPDT, variability in the statistic due to the use of an estimate of allele frequency is not properly accounted for. Here, we present a novel family-based test of association, X-APL, a modification of the test for association in the presence of linkage (APL) test. Like the APL, X-APL can use singleton or multiplex families and properly infers missing parental genotypes in linkage regions by considering identity-by-descent parameters for affected siblings. Sampling variability of parameter estimates is accounted for through a bootstrap procedure. X-APL can test individual marker loci or X-chromosome haplotypes. To allow for different penetrances in males and females, separate sex-specific tests are provided. Using simulated data, we demonstrated validity and showed that the X-APL is more powerful than alternative tests. To show its utility and to discuss interpretation in real-data analysis, we also applied the X-APL to candidate-gene data in a sample of families with Parkinson disease.

Exploiting Hardy-Weinberg Equilibrium for Efficient Screening of Single SNP Associations from Case-Control Studies

In case-control studies, the assessment of the association between a binary disease outcome and a single nucleotide polymorphism (SNP) is often based on comparing the observed genotype distribution for the cases against that for the controls. In this article, we investigate an alternative analytic strategy in which the observed genotype frequencies of cases are compared against the expected genotype frequencies of controls assuming Hardy-Weinberg Equilibrium (HWE). Assuming HWE for controls, we derive closed-form expressions for maximum likelihood estimates of the genotype-specific disease odds ratio (OR) parameters and related variance-covariances. Based on these estimates and their variance-covariance structure, we then propose a two-degree-of-freedom test for disease-SNP association. We show that the proposed test can have substantially higher power than a variety of existing methods, especially when the true effect of the SNP is recessive. We also obtain analytic expressions for the bias of the OR estimates when the underlying HWE assumption is violated. We conclude that the novel test would be particularly useful for analyzing data from the initial ‘screening’ stages of contemporary multi-stage association studies.

Contrasting Linkage-Disequilibrium Patterns between Cases and Controls as a Novel Association-Mapping Method

Identification and description of genetic variation underlying disease susceptibility, efficacy, and adverse reactions to drugs remains a difficult problem. One of the important steps in the analysis of variation in a candidate region is the characterization of linkage disequilibrium (LD). In a region of genetic association, the extent of LD varies between the case and the control groups. Separate plots of pairwise standardized measures of LD (e.g., D') for cases and controls are often presented for a candidate region, to graphically convey case-control differences in LD. However, the observed graphic differences lack statistical support. Therefore, we suggest the "LD contrast" test to compare whole matrices of disequilibrium between two samples. A common technique of assessing LD when the haplotype phase is unobserved is the expectation-maximization algorithm, with the likelihood incorporating the assumption of Hardy-Weinberg equilibrium (HWE). This approach presents a potential problem in that, in the region of genetic association, the HWE assumption may not hold when samples are selected on the basis of phenotypes. Here, we present a computationally feasible approach that does not assume HWE, along with graphic displays and a statistical comparison of pairwise matrices of LD between case and control samples. LD-contrast tests provide a useful addition to existing tools of finding and characterizing genetic associations. Although haplotype association tests are expected to provide superior power when susceptibilities are primarily determined by haplotypes, the LD-contrast tests demonstrate substantially higher power under certain haplotype-driven disease models.

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.

Which strategy is better for linkage analysis: single-nucleotide polymorphisms or microsatellites? Evaluation by identity-by-state – identity-by-descent transformation affected sib-pair method on GAW14 data

The central issue for Genetic Analysis Workshop 14 (GAW14) is the question, which is the better strategy for linkage analysis, the use of single-nucleotide polymorphisms (SNPs) or microsatellite markers? To answer this question we analyzed the simulated data using Duffy's SIB-PAIR program, which can incorporate parental genotypes, and our identity-by-state – identity-by-descent (IBS-IBD) transformation method of affected sib-pair linkage analysis which uses the matrix transformation between IBS and IBD. The advantages of our method are as follows: the assumption of Hardy-Weinberg equilibrium is not necessary; the parental genotype information maybe all unknown; both IBS and its related IBD transformation can be used in the linkage analysis; the determinant of the IBS-IBD transformation matrix provides a quantitative measure of the quality of the marker in linkage analysis. With the originally distributed simulated data, we found that 1) for microsatellite markers there are virtually no differences in types I and II error rates when parental genotypes were or were not used; 2) on average, a microsatellite marker has more power than a SNP marker does in linkage detection; 3) if parental genotype information is used, SNP markers show lower type I error rates than microsatellite markers; and 4) if parental genotypes are not available, SNP markers show considerable variation in type I error rates for different methods.

Population Data on 9 STR loci in Crete (Greece)

Crete is one of the 13 regions of Greece and at the same time the southernmost district of the European Community, covering an area of 8.336 km2. The island is divided into four prefectures: Chania (134 000), Rethymno (70 000), Heraklion (265 000), Lasithi (71 000), with a total of population 540 000. The capital of the island is the city of Heraklion. Being an island, it is considered to be fairly isolated and, once geographically well separated, gene frequency differences were expected. There is a lack of population genetic data from most of these STRs despite the fact that the commercially available amplification kits are being used increasingly in forensic casework. Therefore we aimed to evaluate the data for the polymorphic loci for effective use in Crete and check for the suitability of the systems for forensic applications. 310 samples from unrelated individuals were tested for the systems as for their gene and phenotype frequencies. The sampling was done considering the population distribution in the four main residential areas of the island. Following the DNA extraction and quantitation, the PCR amplification of the nine STR loci (CSFPO1, D7S820, D13S317, D16S539, F13A01, FES/FPS, THO1, TPOX, and vWA) was performed using the commercially available triplex amplification kits provided by Promega, and the applicationwas done according to the manufacturer’s instructions. Allele frequencies were estimated by gene counting. The expected genotype frequencies were calculated on the basis of estimated allele frequencies under the assumption of Hardy-Weinberg equilibrium. Accordancewith Hardy-Weinberg

A Method for Evaluating the Impact of Individual Haplotypes on Disease Incidence in Molecular Epidemiology Studies

Estimation of the association between haplotypes and disease from a case-control study is considered. Assuming a single "disease haplotype'' leads to the increased risk, attention focusses on the relative risks associated with a single copy, or two copies of the disease haplotype, relative to individuals with no copies. In this setting, case frequencies of the haplotype pairs are in Hardy-Weinberg Equilibrium (HWE) only if the combined influence of the two copies of the disease haplotype on risk is multiplicative. Thus, imputation cannot rely on the assumption of HWE for cases. A method is presented for obtaining estimates of the relative risks, making use of the EM algorithm and the assumption of HWE only for controls. The method accounts for the additional variation in the estimates due to the imputation of expected frequencies of haplotype pairs from ambiguous genotypes. A simulation study shows that the resulting confidence intervals have nominal coverage, and that the methods based on the assumption of HWE for both cases and controls can lead to bias.

Exact test of Hardy-Weinberg equilibrium by Markov chain Monte Carlo.

The assumption of Hardy-Weinberg equilibrium (HWE) among alleles is of fundamental importance in genetic studies. There are numerous testing methods for it using genotype counts data. The exact test is used when the sample size is not large enough for asymptotic approximations. There are several numerical methods to carry out this test, such as complete enumeration, Monte Carlo and Markov chain Monte Carlo simulations. Complete enumeration is impractical in many applications, especially when the table counts are large. The Monte Carlo method is simple to use but still difficult when the table counts become large. The Markov chain Monte Carlo method, by sampling a sub-table each time, is suitable for this latter situation. Based on switches among a few (no more than four) cells, the existing Markov chain samplers are highly dependent and inefficient for large tables. Here we consider a new Markov chain sampling, in which a sub-table of user-specified size is updated at each iteration. The resulting chain is less dependent, and the sampling is flexible and efficient. The conventional test for HWE is based on a few test statistics, such as the likelihood and the chi-squared statistic. To expand the family of test statistics, we consider a class of divergence measures for the departure of HWE. Examples are given as illustrations.

Variations of human killer cell lectin-like receptors: common occurrence of NKG2-C deletion in the general population

CD94 and NKG2 are members of the NK cell receptor families, and are encoded in the natural killer gene complex (NKC) on human chromosome 12p12-13, one of the candidate chromosomal regions for rheumatic diseases. To examine a possible association between variations in CD94 and NKG2 genes and genetic susceptibility to rheumatoid arthritis (RA) and systemic lupus erythematosus (SLE), we carried out a systematic polymorphism screening of NKG2-A (KLRC1), NKG2-C (KLRC2) and CD94 (KLRD1) genes on a population basis. In NKG2-A, previously considered to be highly conserved, 10 polymorphisms in the noncoding region and introns, as well as one rare variation leading to an amino acid substitution within the transmembrane region, c.238T>A (Cys80Ser), were detected. In NKG2-C, in addition to the previously described two nonsynonymous substitutions, c.5G>A (Ser2Asn) and c.305C>T (Ser102Phe), two polymorphisms were newly detected in the noncoding region. In CD94, only one single nucleotide substitution was identified in the 5' untranslated region. When the patients and healthy individuals were genotyped for these variations, no significant association was observed. However, although statistically not significant, NKG2-A c.238T>A (Cys80Ser) was observed in three patients with RA, but in none of the healthy individuals and the patients with SLE. Unexpectedly, in the process of polymorphism screening, we identified homozygous deletion of NKG2-C in approximately 4.3% of healthy donors; under the assumption of Hardy-Weinberg equilibrium, the allele frequency of NKG2-C deletion was estimated to be 20.7%. These results demonstrated that, although human NKG2-A, -C and CD94 are generally conserved with respect to amino acid sequences, NKG2-A is polymorphic in the noncoding region, and that the number of genes encoded in the human NKC is variable among individuals, as previously shown for the leukocyte receptor complex (LRC), HLA and Fcgamma receptor (FCGR) regions.

Global genetic variation at nine short tandem repeat loci and implications on forensic genetics

We have studied genetic variation at nine autosomal short tandem repeat loci in 20 globally distributed human populations defined by geographic and ethnic origins, viz., African, Caucasian, Asian, Native American and Oceanic. The purpose of this study is to evaluate the utility and applicability of these nine loci in forensic analysis in worldwide populations. The levels of genetic variation measured by number of alleles, allele size variance and heterozygosity are high in all populations irrespective of their effective sizes. Single- as well as multi-locus genotype frequencies are in conformity with the assumptions of Hardy-Weinberg equilibrium. Further, alleles across the entire set of nine loci are mutually independent in all populations. Gene diversity analysis shows that pooling of population data by major geographic groupings does not introduce substructure effects beyond the levels recommended by the National Research Council, validating the establishment of population databases based on major geographic and ethnic groupings. A network tree based on genetic distances further supports this assertion, in which populations of common ancestry cluster together. With respect to the power of discrimination and exclusion probabilities, even the relatively reduced levels of genetic variation at these nine STR loci in smaller and isolated populations provide an exclusionary power over 99%. However, in paternity testing with unknown genotype of the mother, the power of exclusion could fall below 80% in some isolated populations, and in such cases use of additional loci supplementing the battery of the nine loci is recommended.

HLA-DQA1 and Polymarker Allele Frequencies in Two New York City Jewish Populations

Allele and genotype frequencies were determined for the HLA-DQA1 and Amplitype Polymarker loci (low density lipoprotein receptor (LDLR), glycophorin A (GYPA), hemoglobin G gammaglobin (HBGG), D7S8, and group-specific component (Gc)) in Hasidic and non-Hasidic Ashkenazi New York City Jewish subpopulations. For all loci tested, except HBGG, the 2 subpopulations meet the assumption of Hardy-Weinberg equilibrium. Comparison of various allele and genotype frequencies for the Hasidic and the non-Hasidic groups showed no significant differences. Comparison of the various allele frequencies in the two subpopulations to another Caucasian group revealed significant differences at the HLA-DQA1 and D7S8 loci in the Hasidic group. These frequency data can be used for comparison to other populations and for frequency estimates in DNA profiling.

No Excess of Homozygosity at Loci Used for DNA Fingerprinting

Variable number of tandem repeat (VNTR) loci are extremely valuable for the forensic technique known as DNA fingerprinting because of their hypervariability. Nevertheless, the use of these loci in forensics has been controversial. One criticism of DNA fingerprinting is that the VNTR loci used for the "fingerprints" violate the assumption of Hardy-Weinberg equilibrium (H-W), making it difficult to calculate the probability of observing a genotype in the population. If one can assume H-W, the probability of observing the pair of alleles constituting an individual's genotype can be calculated by taking the product of the alleles' frequencies in the population and multiplying by two if the alleles are different. The evidence cited against assuming H-W is homozygote excess, which is presumed to be caused by an undetected mixture of two or more populations with limited interpopulational mating and distinct allele frequencies. For most VNTR loci, measurement error makes it impossible to test these claims by standard methods. The Lifecodes database of three VNTR loci used for forensics was used to show that the claimed excess of homozygotes is not necessarily real because many heterozygotes with similar allele sizes are misclassified as homozygotes. A simple test of H-W that takes such misclassifications into account was developed to test for an overall excess or dearth of heterozygotes in the sample (the complement of homozygote dearth or excess). The application of this test to the Lifecodes database revealed that there was no consistent evidence of violation of H-W for the Caucasian, black, or Hispanic populations.

日本人経産婦に認められた抗Di<sup>a</sup>の2例

During routine post natal screening, two examples of anti-Dia stimulated by pregnancies were were found. One of the antibodies caused hemolytic disease of the newborn.Case 1. Mrs. H. K., a Dia negative, 28-year-old Japanese woman, had no history of blood transfusion and had a healthy child. The routine antibody tests during her first pregnancy revealed no immunization. When her serum was tested again six months after the birth, anti-Dia with a titre of 1:2-1:4 against Di (a+b+) cells by the anti-globulin technique was detected. A year later the antibody in her serum was not detectable.Case 2. Mrs. K. O., a 35-year-old Japanese woman, was found to contain anti-Dia in her serum when a routine direct anti-globulin screening on the cord cells of her third child was found to be positive. She was Di (a-b+), and had never been transfused. Her first child was Di (a-b+), and her husband and second child were Di (a+b+). Primary antibody response may has been due to stimulation by her second pregnancy. The third child became jaundiced within three days of birth; serum bilirubin level at the fifth days was 16.0mg/100ml decreasing to 13.7mg/100ml at the sixth day. The child was placed under phototherapy and survived. The anti-Dia serum from Mrs. K. O. reacted best by the papain- and ficin-antiglobulin techniques using anti-IgG; the titre of which was 1:64-1:128 against Di (a+b+) cells, it was not denatured by 2-mercaptoethanol. The antibody was also detectable by the papainized or ficinized cells in saline (titre 1:2-1:4), but the antibody dit not combine the complement. In titration studies with five Di (a+b-) and five Di (a+b+) cell samples, the anti-Dia showed dosage effect; the titration scores were 38.2 (on the average) for Di (a+b-) and 28.2 for Di (a+b+), and the difference was significant (F0=23.4, P<0.01).Distribution of the Diego groups. Random 3, 425 blood samples from Japanese in and around Tokyo were tested for Dia and Dib antigens by one of the present authors (H. N.). The phenotypes and gene frequencies obtained are shown in Table 1. The agreement with expectation on the assumption of Hardy-Weinberg equilibrium was satisfactory.The chances of antibody-production by pregnancy and by transfusion are expected to be 0.04-0.08 for anti-Dia and 0.002 for anti-Dib. As far as we know, four examples of anti-Dia, including two examples described in this paper, and three examples of anti-Db- have been found in Japan, suggesting that the potency of Dia antigen is lower than that of Db-.