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

Bayesian tests for random mating in polyploids

Hardy-Weinberg proportions (HWP) are often explored to evaluate the assumption of random mating. However, in autopolyploids, organisms with more than two sets of homologous chromosomes, HWP and random mating are different hypotheses that require different statistical testing approaches. Currently, the only available methods to test for random mating in autopolyploids (i) heavily rely on asymptotic approximations and (ii) assume genotypes are known, ignoring genotype uncertainty. Furthermore, these approaches are all frequentist, and so do not carry the benefits of Bayesian analysis, including ease of interpretability, incorporation of prior information, and consistency under the null. Here, we present Bayesian approaches to test for random mating, bringing the benefits of Bayesian analysis to this problem. Our Bayesian methods also (i) do not rely on asymptotic approximations, being appropriate for small sample sizes, and (ii) optionally account for genotype uncertainty via genotype likelihoods. We validate our methods in simulations and demonstrate on two real datasets how testing for random mating is more useful for detecting genotyping errors than testing for HWP (in a natural population) and testing for Mendelian segregation (in an experimental S1 population). Our methods are implemented in Version 2.0.2 of the hwep R package on the Comprehensive R Archive Network https://cran.r-project.org/package=hwep.

Quality control and analytic best practices for testing genetic models of sex differences in large populations

Phenotypic sex-based differences exist for many complex traits. In other cases, phenotypes may be similar, but underlying biology may vary. Thus, sex-aware genetic analyses are becoming increasingly important for understanding the mechanisms driving these differences. To this end, we provide a guide outlining the current best practices for testing various models of sex-dependent genetic effects in complex traits and disease conditions, noting that this is an evolving field. Insights from sex-aware analyses will not only teach us about the biology of complex traits but also aid in achieving the goals of precision medicine and health equity for all.

GPR174 and ITM2A Gene Polymorphisms rs3827440 and rs5912838 on the X chromosome in Korean Children with Autoimmune Thyroid Disease

(1) Background: Autoimmune thyroid diseases (AITDs) are female predominant and much attention has been focused on G protein-coupled receptor 174 (GPR174) and integral membrane protein 2A (ITM2A) on the X chromosome as Grave's disease (GD) susceptible locus. (2) Methods: We genotyped four single nucleotide polymorphisms (SNPs), rs3810712, rs3810711, rs3827440, and rs5912838, of GPR174 and ITM2A in 115 Korean children with AITD (M = 25 and F = 90; GD = 74 (14.7 ± 3.6 years), HD = 41 (13.4 ± 3.2 years); GD-thyroid-associated ophthalmopathy (TAO) = 40, GD-non-TAO=34) and 204 healthy Korean individuals (M = 104 and F = 100). The data were analyzed by sex-stratified or combined. (3) Results: Three SNPs, rs3810712, rs3810711 and rs3827440, were found to be in perfect linkage disequilibrium (D' = 1, r² = 1). In AITD, HD, GD, GD-TAO, and GD-non-TAO patients, rs3827440 TT/T and rs5912838 AA/A were susceptible and rs3827440 CC/C and rs5912838 CC/C were protective genotypes. When analyzed by sex, rs3827440 TT and rs5912838 AA were susceptible and rs3827440 CC and rs5912838 CC were protective genotypes in female AITD, GD, GD-TAO, and GD-non-TAO subjects. In male AITD patients, rs3827440 T and rs5912838 A were susceptible and rs3827440 C and rs5912838 C were protective genotypes. (4) Conclusions: Polymorphisms in GPR174 and ITM2A genes on the X chromosome might be associated with AITD in Korean children.

A robust test for X-chromosome genetic association accounting for X-chromosome inactivation and imprinting

The X chromosome is known to play an important role in many sex-specific diseases. However, only a few single-nucleotide polymorphisms on the X chromosome have been found to be associated with diseases. Compared to the autosomes, conducting association tests on the X chromosome is more intractable due to the difference in the number of X chromosomes between females and males. On the other hand, X-chromosome inactivation takes place in female mammals, which is a phenomenon in which the expression of one copy of two X chromosomes in females is silenced in order to achieve the same gene expression level as that in males. In addition, imprinting effects may be related to certain diseases. Currently, there are some existing approaches taking X-chromosome inactivation into account when testing for associations on the X chromosome. However, none of them allows for imprinting effects. Therefore, in this paper, we propose a robust test, ZXCII, which accounts for both X-chromosome inactivation and imprinting effects without requiring specifying the genetic models in advance. Simulation studies are conducted in order to investigate the validity and performance of ZXCII under various scenarios of different parameter values. The simulation results show that ZXCII controls the type I error rate well when there is no association. Furthermore, with regards to power, ZXCII is robust in all of the situations considered and generally outperforms most of the existing methods in the presence of imprinting effects, especially under complete imprinting effects.

Bayesian model selection for the study of Hardy-Weinberg proportions and homogeneity of gender allele frequencies

Standard statistical tests for Hardy-Weinberg equilibrium assume the equality of allele frequencies in the sexes, whereas tests for the equality of allele frequencies in the sexes assume Hardy-Weinberg equilibrium. This produces a circularity in the testing of genetic variants, which has recently been resolved with new frequentist likelihood and exact procedures. In this paper, we tackle the same problem by posing it as a Bayesian model comparison problem. We formulate an exhaustive set of ten alternative scenarios for biallelic genetic variants. Using Dirichlet and Beta priors for genotype and allele frequencies, we derive marginal likelihoods for all scenarios, and select the most likely scenario using the posterior probabilities that each of these scenarios is the one in place. Different from the usual frequentist testing approach, the Bayesian approach allows one to compare any number of models, and not just two at a time, and the models compared do not have to be nested. We illustrate our Bayesian approach with genetic data from the 1,000 genomes project and through a simulation study.

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.

Testing for goodness rather than lack of fit of an X-chromosomal SNP to the Hardy-Weinberg model

The problem of checking the genotype distribution obtained for some diallelic marker for compatibility with the Hardy-Weinberg equilibrium (HWE) condition arises also for loci on the X chromosome. The possible genotypes depend on the sex of the individual in this case: for females, the genotype distribution is trinomial, as in the case of an autosomal locus, whereas a binomial proportion is observed for males. Like in genetic association studies with autosomal SNPs, interest is typically in establishing approximate compatibility of the observed genotype frequencies with HWE. This requires to replace traditional methods tailored for detecting lack of fit to the model with an equivalence testing procedure to be derived by treating approximate compatibility with the model as the alternative hypothesis. The test constructed here is based on an upper confidence bound and a simple to interpret combined measure of distance between true and HWE conforming genotype distributions in female and male subjects. A particular focus of the paper is on the derivation of the asymptotic distribution of the test statistic under null alternatives which is not of the usual Gaussian form. A closed sample size formula is also provided and shown to behave satisfactorily in terms of the approximation error.