Testing genetic markers for Hardy-Weinberg equilibrium is an important issue in genetic association studies. The HardyWeinberg package offers the classical tests for equilibrium, functions for power computation and for the simulation of marker data under equilibrium and disequilibrium. Functions for testing equilibrium in the presence of missing data by using multiple imputation are provided. The package also supplies various graphical tools such as ternary plots with acceptance regions, log-ratio plots and Q-Q plots for exploring the equilibrium status of a large set of diallelic markers. Classical tests for equilibrium and graphical representations for diallelic marker data are reviewed. Several data sets illustrate the use of the package.

Statistical tests for Hardy–Weinberg equilibrium have been an important tool for detecting genotyping errors in the past, and remain important in the quality control of next generation sequence data. In this paper, we analyze complete chromosomes of the 1000 genomes project by using exact test procedures for autosomal and X-chromosomal variants. We find that the rate of disequilibrium largely exceeds what might be expected by chance alone for all chromosomes. Observed disequilibrium is, in about 60% of the cases, due to heterozygote excess. We suggest that most excess disequilibrium can be explained by sequencing problems, and hypothesize mechanisms that can explain exceptional heterozygosities. We report higher rates of disequilibrium for the MHC region on chromosome 6, regions flanking centromeres and p-arms of acrocentric chromosomes. We also detected long-range haplotypes and areas with incidental high disequilibrium. We report disequilibrium to be related to read depth, with variants having extreme read depths being more likely to be out of equilibrium. Disequilibrium rates were found to be 11 times higher in segmental duplications and simple tandem repeat regions. The variants with significant disequilibrium are seen to be concentrated in these areas. For next generation sequence data, Hardy–Weinberg disequilibrium seems to be a major indicator for copy number variation.Electronic supplementary materialThe online version of this article (doi:10.1007/s00439-017-1786-7) contains supplementary material, which is available to authorized users.

The standard exact p-value is overly conservative, in particular for small minor allele frequencies. The mid p-value ameliorates this problem by bringing the rejection rate closer to the nominal level, at the price of occasionally exceeding the nominal level.

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 χ 2 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 χ 2 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.

Objective: We design a graphical test for Hardy-Weinberg equilibrium. This can circumvent the calculation of p values and the statistical (non)significance of a large number of bi-allelic markers can be inferred from their position in a graph. Method: By rewriting expressions for the χ² statistic (with and without continuity correction) in terms of the heterozygote frequency an acceptance region for Hardy-Weinberg equilibrium is obtained that can be depicted in a ternary plot. Results: We obtain equations for curves in the ternary plot that separate markers that are out of Hardy-Weinberg equilibrium from those that are in equilibrium. The curves depend on the chosen significance level, the sample size and on a continuity correction parameter. Some examples of graphical tests using a set of 106 SNPs on the long arm of human chromosome 22 are described. Significant markers and poor markers with a lot of missing values are easily identified in the proposed plots. R software for making the diagrams is provided. Conclusion: The proposed graphs can be used as control charts for spotting problematic markers in large scale genotyping studies, and constitute an excellent tool for the graphical exploration of bi-allelic marker data.