Monte Carlo Algorithms for Hardy–Weinberg Proportions

Huber, Mark; Chen, Yuguo; Dinwoodie, Ian H.; Dobra, Adrian; Nicholas, Mike

doi:10.1111/j.1541-0420.2005.00418.x

Cited by 32 publications

(29 citation statements)

References 15 publications

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“…And even for large samples, as in the presence of multi-allelic markers [2], exact testing procedures are advocated. Exact testing is a tedious job and may be computationally intensive, despite several efforts to speed up the exact testing procedure using improved Monte-Carlo algorithms [5]. The one-sided confidence interval approach [15] offers a statistically sound alternative to investigate HWE.…”

Section: Discussionmentioning

confidence: 99%

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

Ziegler¹,

Steen²,

Wellek³

2010

Breast Cancer Res Treat

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Purpose: Yu et al. [2009 Breast Cancer Res Treat 117:675-677] 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 paper is two-fold. First, 2 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. Methods:We sketch possible reasons behind deviation from HWE and provide guidelines for proper investigation of HWE deviations in different study designs. We argue that the standard HWE χ 2 lack of fit test is logically flawed and provide a logically unflawed approach for measuring deviation from HWE using confidence intervals. Our method is applicable to the meta-analysis of both case-control or cohort association studies. We illustrate our approach using the meta-analysis criticized by Yu et al. Results:In case-control studies, deviation from HWE should only be investigated in controls.In population-based cohort studies, deviation from HWE should be investigated using the entire sample. A simple meta-analytic framework based on confidence intervals is available for investigating deviation from HWE and establishing compatibility with HWE.Heterogeneity between studies can be assessed. Conclusions:We advocate the use of a confidence interval-based approach to assess HWE.The latter should only be investigated in control populations. In multicentre studies or metaanalysis, deviation from HWE should be analyzed using a meta-analytic approach.

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Section: Discussionmentioning

confidence: 99%

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

Ziegler¹,

Steen²,

Wellek³

2010

Breast Cancer Res Treat

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“…Their method, with some key enhancements described above, was used in ExactoHW. An alternative method proposed by Huber et al (2006) is optimal for very large sample sizes (n . 10 5 ).…”

Section: Discussionmentioning

confidence: 99%

Exact Tests for Hardy–Weinberg Proportions

Engels

2009

Genetics

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Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments. This requirement is especially common when the sample includes multiple alleles and sparse data, thus rendering asymptotic methods, such as the common x 2 -test, unreliable. Such an exact test can be performed using the likelihood ratio as its test statistic rather than the more commonly used probability test. Conceptual advantages in using the likelihood ratio are discussed. A substantially improved algorithm is described to permit the performance of a full-enumeration exact test on sample sizes that are too large for previous methods. An improved Monte Carlo algorithm is also proposed for samples that preclude full enumeration. These algorithms are about two orders of magnitude faster than those currently in use. Finally, methods are derived to compute the number of possible samples with a given set of allele counts, a useful quantity for evaluating the feasibility of the full enumeration procedure. Software implementing these methods, ExactoHW, is provided. W HEN studying the genetics of a population, one of the first questions to be asked is whether the genotype frequencies fit Hardy-Weinberg (HW) expectations. They will fit HW if the population is behaving like a single randomly mating unit without intense viability selection acting on the sampled loci. In addition, testing for HW proportions is often used for quality control in genotyping, as the test is sensitive to misclassifications or undetected null alleles. Traditionally, geneticists have relied on test statistics with asymptotic x 2 -distributions to test for goodness-of-fit with respect to HW proportions. However, as pointed out by several authors (Elston and Forthofer 1977;Emigh 1980;Louis and Dempster 1987;Hernandez and Weir 1989;Guo and Thompson 1992;Chakraborty and Zhong 1994;Rousset and Raymond 1995;Aoki 2003;Maiste and Weir 2004;Wigginton et al. 2005;Kang 2008;Rohlfs and Weir 2008), these asymptotic tests quickly become unreliable when samples are small or when rare alleles are involved. The latter situation is increasingly common as techniques for detecting large numbers of alleles become widely used. Moreover, loci with large numbers of alleles are intentionally selected for use in DNA identification techniques (e.g., Weir 1992). The result is often sparse-matrix data for which the asymptotic methods cannot be trusted.A solution to this problem is to use an exact test (Levene 1949;Haldane 1954) analogous to Fisher's exact test for independence in a 2 3 2 contingency table and its generalization to rectangular tables (Freeman and Halton 1951). In this approach, one considers only potential outcomes that have the same allele frequencies as observed, thus greatly reducing the number of outcomes that must be analyzed. One then identifies all such outcomes that deviate from the HW null hypothesis by at least as much the observed sample...

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“…An additional major problem with frequentist tests is how to decide upon a threshold for significance, in particular as a function of the sample size. When the exact test is used, computation is an issue when the number of alleles at the locus is not small (Guo and Thompson, 1992; Huber et al, 2006). Recently, there has been great interest in testing for HWE in genome‐wide association studies (GWAS) in which departure from HWE may indicate problems with quality control for the SNP in question (Wigginton, Cutler, and Abecasis, 2005).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Methods for Examining Hardy–Weinberg Equilibrium

Wakefield

2010

Biometrics

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Summary 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.

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Monte Carlo Algorithms for Hardy–Weinberg Proportions

Cited by 32 publications

References 15 publications

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

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

Exact Tests for Hardy–Weinberg Proportions

Bayesian Methods for Examining Hardy–Weinberg Equilibrium

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