Likelihood Ratio Test for Excess Homozygosity at Marker Loci on X Chromosome

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.

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.

On the testing of Hardy-Weinberg proportions and equality of allele frequencies in males and females at biallelic genetic markers

Standard statistical tests for equality of allele frequencies in males and females and tests for Hardy‐Weinberg equilibrium are tightly linked by their assumptions. Tests for equality of allele frequencies assume Hardy‐Weinberg equilibrium, whereas the usual chi‐square or exact test for Hardy‐Weinberg equilibrium assume equality of allele frequencies in the sexes. In this paper, we propose ways to break this interdependence in assumptions of the two tests by proposing an omnibus exact test that can test both hypotheses jointly, as well as a likelihood ratio approach that permits these phenomena to be tested both jointly and separately. The tests are illustrated with data from the 1000 Genomes project.

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.

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.