A statistical measure for the skewness of X chromosome inactivation for quantitative traits and its application to the MCTFR data

An Efficient Bayesian Method for Estimating the Degree of the Skewness of X Chromosome Inactivation Based on the Mixture of General Pedigrees and Unrelated Females

Skewed X chromosome inactivation (XCI-S) has been reported to be associated with some X-linked diseases. Several methods have been proposed to estimate the degree of XCI-S (denoted as γ) for quantitative and qualitative traits based on unrelated females. However, there is no method available for estimating γ based on general pedigrees. Therefore, in this paper, we propose a Bayesian method to obtain the point estimate and the credible interval of γ based on the mixture of general pedigrees and unrelated females (called mixed data for brevity), which is also suitable for only general pedigrees. We consider the truncated normal prior and the uniform prior for γ. Further, we apply the eigenvalue decomposition and Cholesky decomposition to our proposed methods to accelerate the computation speed. We conduct extensive simulation studies to compare the performances of our proposed methods and two existing Bayesian methods which are only applicable to unrelated females. The simulation results show that the incorporation of general pedigrees can improve the efficiency of the point estimation and the precision and the accuracy of the interval estimation of γ. Finally, we apply the proposed methods to the Minnesota Center for Twin and Family Research data for their practical use.

Robust association tests for quantitative traits on the X chromosome

The genome-wide association study is an elementary tool to assess the genetic contribution to complex human traits. However, such association tests are mainly proposed for autosomes, and less attention has been given to methods for identifying loci on the X chromosome due to their distinct biological features. In addition, the existing association tests for quantitative traits on the X chromosome either fail to incorporate the information of males or only detect variance heterogeneity. Therefore, we propose four novel methods, which are denoted as QXcat, QZmax, QMVXcat and QMVZmax. When using these methods, it is assumed that the risk alleles for females and males are the same and that the locus being studied satisfies the generalized genetic model for females. The first two methods are based on comparing the means of the trait value across different genotypes, while the latter two methods test for the difference of both means and variances. All four methods effectively incorporate the information of X chromosome inactivation. Simulation studies demonstrate that the proposed methods control the type I error rates well. Under the simulated scenarios, the proposed methods are generally more powerful than the existing methods. We also apply our proposed methods to data from the Minnesota Center for Twin and Family Research and find 10 single nucleotide polymorphisms that are statistically significantly associated with at least two traits at the significance level of 1 × 10-3.

BEXCIS: Bayesian methods for estimating the degree of the skewness of X chromosome inactivation

Background

X chromosome inactivation (XCI) is an epigenetic phenomenon that one of two X chromosomes in females is transcriptionally silenced during early embryonic development. Skewed XCI has been reported to be associated with some X-linked diseases. There have been several methods measuring the degree of the skewness of XCI. However, these methods may still have several limitations.

Results

We propose a Bayesian method to obtain the point estimate and the credible interval of the degree of XCI skewing by incorporating its prior information of being between 0 and 2. We consider a normal prior and a uniform prior for it (respectively denoted by BN and BU). We also propose a penalized point estimate based on the penalized Fieller’s method and derive the corresponding confidence interval. Simulation results demonstrate that the BN and BU methods can solve the problems of extreme point estimates, noninformative intervals, empty sets and discontinuous intervals. The BN method generally outperforms other methods with the lowest mean squared error in the point estimation, and well controls the coverage probability with the smallest median and the least variation of the interval width in the interval estimation. We apply all the methods to the Graves’ disease data and the Minnesota Center for Twin and Family Research data, and find that SNP rs3827440 in the Graves’ disease data may undergo skewed XCI towards the allele C.

Conclusions

We recommend the BN method for measuring the degree of the skewness of XCI in practice. The R package BEXCIS is publicly available at https://github.com/Wen-YiYu/BEXCIS.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04721-y.

Gene-Based Methods for Estimating the Degree of the Skewness of X Chromosome Inactivation

Skewed X chromosome inactivation (XCI-S) has been reported to be associated with some X-linked diseases, and currently several methods have been proposed to estimate the degree of the XCI-S (denoted as γ) for a single locus. However, no method has been available to estimate γ for genes. Therefore, in this paper, we first propose the point estimate and the penalized point estimate of γ for genes, and then derive its confidence intervals based on the Fieller’s and penalized Fieller’s methods, respectively. Further, we consider the constraint condition of γ∈[0, 2] and propose the Bayesian methods to obtain the point estimates and the credible intervals of γ, where a truncated normal prior and a uniform prior are respectively used (denoted as GBN and GBU). The simulation results show that the Bayesian methods can avoid the extreme point estimates (0 or 2), the empty sets, the noninformative intervals ([0, 2]) and the discontinuous intervals to occur. GBN performs best in both the point estimation and the interval estimation. Finally, we apply the proposed methods to the Minnesota Center for Twin and Family Research data for their practical use. In summary, in practical applications, we recommend using GBN to estimate γ of genes.